h$})      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMN O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                                                                                                                                                              ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " # $ $ $ $ $ $ $ $ $ % % % % % % % % % % % % % % % % % % % & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) * + + + + + + + + + + + + + + + + + + , , , , , , , , , , , , , , , , , , , , - - - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . / / / / / / / / / / / / / 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 888899999999999999999999999999999999999999999999999:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;<<<========>>>>>>>>>??????????????????????????????????????????????@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBCCCCCCCCCCCCCCCCCCDDDDDDDEEEFFFFFFFFFFFGGGGGGHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHIIIIIIIIJJKLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNNNNNOPPPQQQQQQQQQQQQQRRRRRRRRRRRSTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTUUUVVWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWXXYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYZZZZZZZZZZZZZZZZZZZZZZZZZZZ[[[[[[[[[\\\\\\\\\]]]]]^^^____________```````````````````````````````````````````````aaaabbbbbbbbbccccccccddeeeefffffffghhiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiijjjkkkkkkkkkkkkkkkkkklllllllllllllllllllmmmmmmmmmmmmmmmnnnnnoooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooopqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqrrrrrrstttttttttttttttttttttttttttttttttttttttttuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuvvvvvvvvvvvwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwxyyyz{{{||}}}}}~~~~~~~~~~~                                                                                                                                !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""################################################################################################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))Noneq"futhark&Whether an option accepts an argument.$futharkThe ) becomes part of the help text.&futharkSpecification if a single command line option. The option must have a long name, and may also have a short name.In the action, the option argument (if any) is stored as in the char*-typed variable optarg.,futharkGenerate an option parser as a function of the given name, that accepts the given command line options. The result is a function that should be called with argc and argv'. The function returns the number of argv# elements that have been processed.If option parsing fails for any reason, the entire process will terminate with error code 1. "#$%&'()*+, &'()*+"#$%,Noner%/0123451/50234NonerR6789:6789: Safe-Inferreds;futhark8A heuristic for setting the default value for something.Afuthark&A size that can be assigned a default.GfutharkThe value supplies by a heuristic can be a constant, or inferred from some device information.Jfuthark9The type of OpenCL device that this heuristic applies to.MfutharkAll of our heuristics.;<=>?@ACDBEFGHIJKLM;<=>?@JKLACDBEFGHIM None ~[futharkA mapping from package paths to their chosen revisions. This is the result of the version solver.^futharkA structure corresponding to a  futhark.pkg file, including comments. It is an invariant that duplicate required packages do not occcur (the parser will verify this).`futharkThe name of the package.cfutharkAn entry in the required section of a  futhark.pkg file.efutharkName of the required package.ffutharkThe minimum revision.gfutharkAn optional hash indicating what this revision looked like the last time we saw it. Used for integrity checking.hfutharkWraps a value with an annotation of preceding line comments. This is important to our goal of being able to programmatically modify the  futhark.pkg$ file while keeping comments intact.lfutharkA line comment.mfutharkThe dependencies of a (revision of a) package is a mapping from package paths to minimum versions (and an optional hash pinning).ofutharkA package path is a unique identifier for a package, for example  github.comuserfoo.pfutharkTurn a package path (which always uses forward slashes) into a file path in the local file system (which might use different slashes).qfutharkVersions of the form (0,0,0)-timestamp+hash are treated specially, as a reference to the commit identified uniquely with hash (typically the Git commit ID). This function detects such versions.rfutharkcommitVersion timestamp commit constructs a commit version.sfutharkUnfortunately, Data.Versions has a buggy semver parser that collapses consecutive zeroes in the metadata field. So, we define our own parser here. It's a little simpler too, since we don't need full semver.tfuthark9The name of the file containing the futhark-pkg manifest.ufutharkPossibly given a package path, construct an otherwise-empty manifest file.vfutharkPrettyprint a package manifest such that it can be written to a  futhark.pkg file.wfuthark3The required packages listed in a package manifest.xfutharkWhere in the corresponding repository archive we can expect to find the package files.yfutharkAdd new required package to the package manifest. If the package was already present, return the old version.)futharkCheck if the manifest specifies a required package with the given package path.zfuthark6Remove a required package from the manifest. Returns ) if the package was not found in the manifest, and otherwise the new manifest and the c that was present.}futharkPrettyprint a build list; one package per line and newline-terminated.0NOPQRWVUSTXZY[\]^_`abcdefghijklmnopqrstuvwxyz{|}0opmnOPQRWVUSTXZYrqs^_`abuwxyzvlhijkcdefgt{|N[\]} NoneIfutharkLike  mapAccumL, but monadic.futhark chunk n a splits a into n!-size-chunks. If the length of a is not divisible by n', the last chunk will have fewer than n' elements (but it will never be empty).futhark chunks ns a splits a, into chunks determined by the elements of ns. It must hold that sum ns == length a, or the resulting list may contain too few chunks, or not all elements of a.futhark dropAt i n drops n elements starting at element i.futhark takeLast n l takes the last n elements of l.futhark dropLast n l drops the last n elements of l.futharkA combination of ) and ).futharkReturn the list element at the given index, if the index is valid.futhark3Return the first element of the list, if it exists.futharkLike ), but from the end.futharkLike ), but produces three lists.futharkReturn the list element at the given index, if the index is valid, along with the elements before and after.futhark7The Unix environment when the Futhark compiler started.futharkLike ), but also wraps exceptions when the indicated binary cannot be launched, or some other exception is thrown. Also does shenanigans to handle improperly encoded outputs.futhark7Every non-directory file contained in a directory tree.futhark9Round a single-precision floating point number correctly.futharkRound a single-precision floating point number upwards correctly.futharkRound a single-precision floating point number downwards correctly.futhark9Round a double-precision floating point number correctly.futharkRound a double-precision floating point number upwards correctly.futharkRound a double-precision floating point number downwards correctly.futharkThe system-level lgamma() function.futharkThe system-level  lgammaf() function.futharkThe system-level tgamma() function.futharkThe system-level  tgammaf() function.futhark?|futhark*Typeclass for monads that support logging.futharkAdd one log entry.futharkAppend an entire log.futharkTypeclass for things that can be turned into a single-entry log.futharkTransform a log into text. Every log entry becomes its own line (or possibly more, in case of multi-line entries).None futharkMonads that support a stateful package registry. These are also required to be instances of ) because most package registry operations involve network operations.futharkA package registry is a mapping from package paths to information about the package. It is unlikely that any given registry is global; rather small registries are constructed on-demand based on the package paths referenced by the user, and may also be combined monoidically. In essence, the PkgRegistry is just a cache.futharkInformation about a package. The name of the package is stored separately.futharkLook up information about a specific commit, or HEAD in case of Nothing.futharkInformation about a version of a single package. The version number is stored separately.futhark1The directory inside the zipball containing the lib directory, in which the package files themselves are stored (Based on the package path).futharkThe commit ID can be used for verification ("freezing"), by storing what it was at the time this version was last selected.futhark8Timestamp for when the revision was made (rarely used).futharkThe manifest is stored as a monadic action, because we want to fetch them on-demand. It would be a waste to fetch it information for every version of every package if we only actually need a small subset of them.)futhark!Download URL via shelling out to curl.)futharkCreate memoisation around a  action to ensure that multiple inspections of the same revisions will not result in potentially expensive network round trips.futharkRetrieve information about a package based on its package path. This uses Semantic Import Versioning when interacting with repositories. For example, a package  github.comuserrepo6 will match version 0.* or 1.* tags only, a package  github.comuserrepo/v2$ will match 2.* tags, and so forth..futhark:Look up information about a specific version of a package.futhark%Find the newest version of a package.None ?futharkA mapping of package revisions to the dependencies of that package. Can be considered a  without the option of obtaining more information from the Internet. Probably useful only for testing the solver.)futharkA rough build list is like a build list, but may contain packages that are not reachable from the root. Also contains the dependencies of each package.)futharkGiven a list of immediate dependency minimum version constraints, find dependency versions that fit, including transitive dependencies.futharkRun the solver, producing both a package registry containing a cache of the lookups performed, as well as a build list.futharkPerform package resolution with only pre-known information. This is useful for testing.None futhark.Prettyprint a value, wrapped to 80 characters.futharkPrettyprint a value to a ), wrapped to 80 characters.futhark2Prettyprint a value without any width restriction.futhark Re-export of ).futhark,Prettyprint a list enclosed in curly braces.futhark The document  ds separates ds1 with commas and encloses them with parentheses.futharkMake sure that the given document is printed on just a single line.futharkLike  , but splits the string into words and permits line breaks between all of them.futharkStack and prepend a list of   s to another  ?, separated by a linebreak. If the list is empty, the second  1 will be returned without a preceding linebreak.futharkSurround the given document with enclosers and add linebreaks and indents.futharkPrettyprint on a single line up to at most some appropriate number of characters, with trailing ... if necessary. Used for error messages. ))))  !)  !Noneŵfuthark+Conversion operators try to generalise the from t0 x to t1 instructions from LLVM.futharkZero-extend the former integer type to the latter. If the new type is smaller, the result is a truncation.futharkSign-extend the former integer type to the latter. If the new type is smaller, the result is a truncation.futharkConvert value of the former floating-point type to the latter. If the new type is smaller, the result is a truncation.futharkConvert a floating-point value to the nearest unsigned integer (rounding towards zero).futharkConvert a floating-point value to the nearest signed integer (rounding towards zero).futhark6Convert an unsigned integer to a floating-point value.futhark3Convert a signed integer to a floating-point value.futharkConvert an integer to a boolean value. Zero becomes false; anything else is true.futharkConvert a boolean to an integer. True is converted to 1 and False to 0.futharkComparison operators are like s, but they return s. The somewhat ugly constructor names are straight out of LLVM.futharkAll types equality.futharkUnsigned less than.futharkUnsigned less than or equal.futharkSigned less than.futharkSigned less than or equal.futharkFloating-point less than.futhark"Floating-point less than or equal.futharkBoolean less than.futharkBoolean less than or equal.futharkBinary operators. These correspond closely to the binary operators in LLVM. Most are parametrised by their expected input and output types.futharkInteger addition.futharkFloating-point addition.futharkInteger subtraction.futharkFloating-point subtraction.futharkInteger multiplication.futharkFloating-point multiplication.futharkUnsigned integer division. Rounds towards negativity infinity. Note: this is different from LLVM.futharkSigned integer division. Rounds towards negativity infinity. Note: this is different from LLVM.futharkFloating-point division.futharkFloating-point modulus.futhark,Unsigned integer modulus; the countepart to .futhark*Signed integer modulus; the countepart to .futharkSigned integer division. Rounds towards zero. This corresponds to the sdiv instruction in LLVM.futharkSigned integer division. Rounds towards zero. This corresponds to the srem instruction in LLVM.futhark,Returns the smallest of two signed integers.futhark.Returns the smallest of two unsigned integers.futhark3Returns the smallest of two floating-point numbers.futhark,Returns the greatest of two signed integers.futhark.Returns the greatest of two unsigned integers.futhark3Returns the greatest of two floating-point numbers.futhark Left-shift.futhark#Logical right-shift, zero-extended.futhark&Arithmetic right-shift, sign-extended.futhark Bitwise and.futhark Bitwise or.futharkBitwise exclusive-or.futharkInteger exponentiation.futharkFloating-point exponentiation.futhark#Boolean and - not short-circuiting.futhark"Boolean or - not short-circuiting.futharkVarious unary operators. It is a bit ad-hoc what is a unary operator and what is a built-in function. Perhaps these should all go away eventually.futharkE.g., ! True == False.futharkE.g.,  ~(~1) = 1.futhark abs(-2) = 2.futharkfabs(-2.0) = 2.0.futharkSigned sign function:  ssignum(-2) = -1.futharkUnsigned sign function:  usignum(2) = 1.futharkNon-array values.futharkThe only value of type cert.futharkA floating-point value.futharkAn integer value.futharkLow-level primitive types.futharkA floating point type.futharkAn integer type, ordered by size. Note that signedness is not a property of the type, but a property of the operations performed on values of these types.futharkA list of all integer types.futhark#A list of all floating-point types.futharkA list of all primitive types.futhark Create an  from a type and an ).futhark Convert an  to any ) type.futhark Create a  from a type and a ).futharkThe type of a basic value.futharkA "blank" value of the given primitive type - this is zero, or whatever is close to it. Don't depend on this value, but use it for e.g. creating arrays to be populated by do-loops.futhark,A list of all unary operators for all types.futhark-A list of all binary operators for all types.futhark1A list of all comparison operators for all types.futhark1A list of all conversion operators for all types.futharkE.g.,  ~(~1) = 1.futhark abs(-2) = 2.futharkabs(-2.0) = 2.0.futhark ssignum(-2) = -1.futhark usignum(-2) = -1.futharkInteger addition.)futharkInteger subtraction.futharkInteger multiplication.)futharkUnsigned integer division. Rounds towards negativity infinity. Note: this is different from LLVM.futharkSigned integer division. Rounds towards negativity infinity. Note: this is different from LLVM.)futhark,Unsigned integer modulus; the countepart to .futhark*Signed integer modulus; the countepart to .)futharkSigned integer division. Rounds towards zero. This corresponds to the sdiv instruction in LLVM.)futharkSigned integer division. Rounds towards zero. This corresponds to the srem instruction in LLVM.*futharkMinimum of two signed integers.*futhark!Minimum of two unsigned integers.*futharkMaximum of two signed integers.*futhark!Maximum of two unsigned integers.*futhark Left-shift.*futhark#Logical right-shift, zero-extended.*futhark&Arithmetic right-shift, sign-extended.*futhark Bitwise and.*futhark Bitwise or.*futharkBitwise exclusive-or.futharkSigned integer exponentatation.futharkZero-extend the given integer value to the size of the given type. If the type is smaller than the given value, the result is a truncation.futharkSign-extend the given integer value to the size of the given type. If the type is smaller than the given value, the result is a truncation.futhark5Convert the former floating-point type to the latter.futharkConvert a floating-point value to the nearest unsigned integer (rounding towards zero).futharkConvert a floating-point value to the nearest signed integer (rounding towards zero).futhark6Convert an unsigned integer to a floating-point value.futhark3Convert a signed integer to a floating-point value.futhark3Compare any two primtive values for exact equality.futharkUnsigned less than.futharkUnsigned less than or equal.futharkSigned less than.futharkSigned less than or equal.futharkFloating-point less than.futhark"Floating-point less than or equal.futhark Translate an  to . This is guaranteed to fit.futhark Translate an  to . This is guaranteed to fit.*futhark.Careful - there is no guarantee this will fit.futhark%The result type of a binary operator.futhark+The operand types of a comparison operator.futhark0The operand and result type of a unary operator.futhark4The input and output types of a conversion operator.futharkA mapping from names of primitive functions to their parameter types, their result type, and a function for evaluating them.futhark Is the given value kind of zero?futharkIs the given value kind of one?futhark$Is the given value kind of negative?futhark(Is the given integer value kind of zero?futhark'Is the given integer value kind of one?*futhark,Is the given integer value kind of negative?futhark7The size of a value of a given primitive type in bites.futharkThe size of a value of a given primitive type in eight-bit bytes.futhark?The size of a value of a given integer type in eight-bit bytes.futharkThe size of a value of a given floating-point type in eight-bit bytes.futhark1True if the given binary operator is commutative.futhark;True if signed. Only makes a difference for integer types.None?futharkAn error that is not the users fault, but a bug (or limitation) in the compiler. Compiler passes should only ever report this error - any problems after the type checker are *our* fault, not the users. These are generally thrown as IO exceptions, and caught at the top level.futharkAn error that happened due to something the user did, such as provide incorrect code or options.futharkAn internal compiler error. The second text is extra data for debugging, which can be written to a file.futharkThere are two classes of internal errors: actual bugs, and implementation limitations. The latter are already known and need not be reported.NonenfutharkA table entry. Consists of the content as well a list of SGR commands to color/stylelize the entry.futhark.Makes a table entry with the default SGR mode.futharkBuilds a table from a list of entries and a padding amount that determines padding from the right side of the widest entry in each column.None DfutharkA name tagged with some integer. Only the integer is used in comparisons, no matter the type of vn.futharkThe abstract (not really) type representing names in the Futhark compiler. )4s, being lists of characters, are very slow, while )s are based on byte-arrays.futhark2Whether some operator is commutative or not. The *: instance returns the least commutative of its arguments.futharkThe uniqueness attribute of a type. This essentially indicates whether or not in-place modifications are acceptable. With respect to ordering,  is greater than .futhark-May have references outside current function.futhark'No references outside current function.futhark3The name of the default program entry point (main).futhark7Convert a name to the corresponding list of characters.futhark7Convert a list of characters to the corresponding name.futhark$Convert a name to the corresponding ).futhark Convert a ) to the corresponding name.futhark/A human-readable location string, of the form filename:lineno:columnno?. This follows the GNU coding standards for error messages: 8https://www.gnu.org/prep/standards/html_node/Errors.htmlThis function assumes that both start and end position is in the same file (it is not clear what the alternative would even mean).futharkLike , but locStrRel prev now prints the location now- with the file name left out if the same as prev. This is useful when printing messages that are all in the context of some initially printed location (e.g. the first mention contains the file name; the rest just line and column name).futharkGiven a list of strings representing entries in the stack trace and the index of the frame to highlight, produce a final newline-terminated string for showing to the user. This string should also be preceded by a newline. The most recent stack frame must come first in the list.futhark Return the tag contained in the .futhark!Return the name contained in the .futharkReturn the base  converted to a string.futharkEnclose a string in the prefered quotes used in error messages. These are picked to not collide with characters permitted in identifiers.futharkAs ,, but works on prettyprinted representation.""None>?.futharkA part of an error message.futharkA literal string.futharkA run-time integer value.futharkAn error message is a list of error parts, which are concatenated to form the final message.futharkAn element of a pattern - consisting of a name (essentially a pair of the name and type) and an addditional parametric attribute. This attribute is what is expected to contain the type of the resulting variable.futharkThe name being bound.futharkPattern element attribute.futhark A list of s, indicating how an array should be sliced. Whenever a function accepts a , that slice should be total, i.e, cover all dimensions of the array. Deviators should be indicated by taking a list of  es instead.futhark,How to index a single dimension of an array.futharkFix index in this dimension.futhark&DimSlice start_offset num_elems stride.futharkA function or lambda parameter.futharkName of the parameter.futharkFunction parameter attribute.futharkA subexpression is either a scalar constant or a variable. One important property is that evaluation of a subexpression is guaranteed to complete in constant time.futhark:A list of names used for certificates in some expressions.futharkAn identifier consists of its name and the type of the value bound to the identifier.futharkInformation about which parts of a value/type are consumed. For example, we might say that a function taking three arguments of types ([int], *[int], [int]) has diet [Observe, Consume, Observe].futharkConsumes this value.futharkOnly observes value in this position, does not consume. A result may alias this.futharkAs , but the result will not alias, because the parameter does not carry aliases.futharkAn > with uniqueness information, used for function return types.futharkA type with shape and uniqueness information, used declaring return- and parameters types.futharkA type with existentially quantified shapes - used as part of function (and function-like) return types. Generally only makes sense when used in a list.futharkA type with shape information, used for describing the type of variables.futharkAn Futhark type is either an array or an element type. When comparing types for equality with *, shapes must match.futharkA fancier name for ()% - encodes no uniqueness information.futhark:A string representing a specific non-default memory space.futhark!The memory space of a block. If , this is the "default" space, whatever that is. The exact meaning of the SpaceID depends on the backend used. In GPU kernels, for example, this is used to distinguish between constant, global and shared memory spaces. In GPU-enabled host code, it is used to distinguish between host memory () and GPU space.futharkA special kind of memory that is a statically sized array of some primitive type. Used for private memory on GPUs.futhark>A class encompassing types containing array shape information.futhark0Return the rank of an array with the given size.futharkstripDims n shape strips the outer n dimensions from shape.futhark5Check whether one shape if a subset of another shape.futharkThe size of an array type as merely the number of dimensions, with no further information.futharkLike  but some of its elements may be bound in a local environment instead. These are denoted with integral indices.futharkThe size of this dimension.futhark"Something that may be existential.futharkThe size of an array as a list of subexpressions. If a variable, that variable must be in scope where this array is used.futharkThe size of an array type as a list of its dimension sizes, with the type of sizes being parametric.futharkIf the argument is a , return its component.futharkIf the slice is all s, return the components.futhark3The dimensions of the array produced by this slice.futharkA slice with a stride of one.futharkFix the ?s of a slice. The number of indexes must equal the length of  for the slice.futharkHow many non-constant parts does the error message have, and what is their type?Nonefuthark$If a Haskell type is an instance of , it means that a value of that type can be converted to a Futhark . This is intended to cut down on boilerplate when writing compiler code - for example, you'll quickly grow tired of writing Constant (LogVal True) loc.futhark Create a   containing the given value.futhark1Utility definition for reasons of type ambiguity.futhark1Utility definition for reasons of type ambiguity.None>?0futharkSomething with an existential context that can be (partially) fixed.futharkFix the given existentional variable to the indicated free value.futhark/Typeclass for things whose type can be changed.futhark"Typeclass for things that contain s.futhark"Typeclass for things that contain s.futhark"Typeclass for things that contain s.futhark"Typeclass for things that contain s.futhark%Remove shape information from a type.futharkReturn the dimensionality of a type. For non-arrays, this is zero. For a one-dimensional array it is one, for a two-dimensional it is two, and so forth.futhark:Return the shape of a type - for non-arrays, this is the *.futharkModify the shape of an array - for non-arrays, this does nothing.futharkSet the shape of an array. If the given type is not an array, return the type unchanged.futharkTrue if the given type has a dimension that is existentially sized.futhark Return the uniqueness of a type.futharkunique t is *' if the type of the argument is unique.futharkConvert types with non-existential shapes to types with non-existential shapes. Only the representation is changed, so all the shapes will be .futharkAs , but on a single type.futhark arrayOf t s u constructs an array type. The convenience compared to using the  constructor directly is that t can itself be an array. If t is an n-dimensional array, and s is a list of length n, the resulting type is of an n+m6 dimensions. The uniqueness of the new array will be u, no matter the uniqueness of t. If the shape s has rank 0, then the t will be returned, although if it is an array, with the uniqueness changed to u.futharkConstruct an array whose rows are the given type, and the outer size is the given dimension. This is just a convenient wrapper around .futharkConstruct an array whose rows are the given type, and the outer size is the given -. This is just a convenient wrapper around .futharkSet the dimensions of an array. If the given type is not an array, return the type unchanged.futharkReplace the size of the outermost dimension of an array. If the given type is not an array, it is returned unchanged.futharkReplace the size of the given dimension of an array. If the given type is not an array, it is returned unchanged.futhark2Replace the outermost dimension of an array shape.futhark2Replace the specified dimension of an array shape.futhark peelArray n t4 returns the type resulting from peeling the first n array dimensions from t . Returns Nothing if t has less than n dimensions.futharkstripArray n t removes the n outermost layers of the array. Essentially, it is the type of indexing an array of type t with n indexes.futharkReturn the size of the given dimension. If the dimension does not exist, the zero constant is returned.futharkReturn the dimensions of a type - for non-arrays, this is the empty list.futharkReturn the existential dimensions of a type - for non-arrays, this is the empty list.futharkReturn the size of the given dimension. If the dimension does not exist, the zero constant is returned.futharkReturn the size of the given dimension in the first element of the given type list. If the dimension does not exist, or no types are given, the zero constant is returned.futhark0Return the immediate row-type of an array. For [[int]], this would be [int].futharkA type is a primitive type if it is not an array or memory block.futhark.Returns the bottommost type of an array. For [[int]], this would be int5. If the given type is not an array, it is returned.futhark*Swap the two outer dimensions of the type.futharkRearrange the dimensions of the type. If the length of the permutation does not match the rank of the type, the permutation will be extended with identity.futharkdiet t< returns a description of how a function parameter of type t might consume its argument.futharkx `subtypeOf` y is true if x is a subtype of y (or equal to y ), meaning x is valid whenever y is.futharkxs `subtypesOf` ys is true if xs is the same size as ys, and each element in xs/ is a subtype of the corresponding element in ys..futharkGiven the existential return type of a function, and the shapes of the values returned by the function, return the existential shape context. That is, those sizes that are existential in the return type.futharkThe set of identifiers used for the shape context in the given s.futharkIf all dimensions of the given RetType9 are statically known, return the corresponding list of .futharkGiven two lists of (s of the same length, return a list of s that is a subtype (as per  isSubtypeOf) of the two operands.futharkGiven a list of s and a list of "forbidden" names, modify the dimensions of the s such that they are  where they were previously 0 with a variable in the set of forbidden names.futhark In the call shapeMapping ts1 ts2 , the lists ts1 and ts must be of equal length and their corresponding elements have the same types modulo exact dimensions (but matching array rank is important). The result is a mapping from named dimensions of ts1. to a set of the corresponding dimensions in ts2% (because they may not fit exactly).This function is useful when ts10 are the value parameters of some function and ts2 are the value arguments, and we need to figure out which shape context to pass.*futharkLike  shapeMapping%, but works with explicit dimensions.futharkLike 4, but produces a mapping for the dimensions context.<<None> sfutharkA type representing the return type of a function. In practice, a list of these will be used. It should contain at least the information contained in an 5, but may have more, notably an existential context.futhark-Contruct a return type from a primitive type.futharkGiven a function return type, the parameters of the function, and the arguments for a concrete call, return the instantiated return type for the concrete call, if valid.futharkA type representing the return type of a body. It should contain at least the information contained in a list of 6s, but may have more, notably an existential context.futhark,Construct a body type from a primitive type.futharkGiven shape parameter names and value parameter types, produce the types of arguments accepted.None? _futhark)Annotation for every let-pattern element.futhark Annotation for every expression.futharkAnnotation for every body.futhark5Annotation for every (non-lambda) function parameter.futhark/Annotation for every lambda function parameter.futhark-The return type annotation of function calls.futhark'The return type annotation of branches.futharkExtensible operation. None 2>?#9futharkAn entire Futhark program.futharkTop-level constants that are computed at program startup, and which are in scope inside all functions.futharkThe functions comprising the program. All funtions are also available in scope in the definitions of the constants, so be careful not to introduce circular dependencies (not currently checked).futharkEvery entry point argument and return value has an annotation indicating how it maps to the original source program type.futhark6Is an unsigned integer or array of unsigned integers.futharkA black box type comprising this many core values. The string is a human-readable description with no other semantics.futharkMaps directly.futharkInformation about the parameters and return value of an entry point. The first element is for parameters, the second for return value.futharkFunction Declarationsfuthark5Contains a value if this function is an entry point.futhark#Type alias for namespacing reasons.futhark%Anonymous function for use in a SOAC.futhark#A type alias for namespace control.futharkAn ordinary branch.futharkA branch where the "true" case is what we are actually interested in, and the "false" case is only present as a fallback for when the true case cannot be safely evaluated. the compiler is permitted to optimise away the branch if the true case contains only safe statements.futharkData associated with a branch.futharkFor-loop or while-loop?futharkWhether something is safe or unsafe (mostly function calls, and in the context of whether operations are dynamically checked). When we inline an : function, we remove all safety checks in its body. The * instance picks  as being less than .futhark'The root Futhark expression type. The  constructor contains a lore-specific operation. Do-loops, branches and function calls are special. Everything else is a simple .futhark#A simple (non-recursive) operation.futhark'loop {a} = {v} (for i < n|while b) do b. The merge parameters are divided into context and value part.futharkA primitive operation that returns something of known size and does not itself contain any bindings.futharkA variable or constant.futharkSemantically and operationally just identity, but is invisible/impenetrable to optimisations (hopefully). This is just a hack to avoid optimisation (so, to work around compiler limitations).futharkArray literals, e.g., [ [1+x, 3], [2, 1+4] ]. Second arg is the element type of the rows of the array. Scalar operationsfutharkUnary operation.futharkBinary operation.futhark+Comparison - result type is always boolean.futharkConversion "casting".futharkTurn a boolean into a certificate, halting the program with the given error message if the boolean is false.futhark5The certificates for bounds-checking are part of the .futharkAn in-place update of the given array at the given position. Consumes the array.futharkconcat!0([1],[2, 3, 4]) = [1, 2, 3, 4]@.futhark:Copy the given array. The result will not alias anything.futharkManifest an array with dimensions represented in the given order. The result will not alias anything.futhark$iota(n, x, s) = [x,x+s,..,x+(n-1)*s].The  indicates the type of the array returned and the offset/stride arguments, but not the length argument.futhark +replicate([3][2],1) = [[1,1], [1,1], [1,1]]futharkRepeat each dimension of the input array some number of times, given by the corresponding shape. For an array of rank k, the list must contain k shapes. A shape may be empty (in which case the dimension is not repeated, but it is still present). The last shape indicates the amount of extra innermost dimensions. All other extra dimensions are added *before* the original dimension.futhark>Create array of given type and shape, with undefined elements.futhark71st arg is the new shape, 2nd arg is the input array *)futharkPermute the dimensions of the input array. The list of integers is a list of dimensions (0-indexed), which must be a permutation of [0,n-1], where n1 is the number of dimensions in the input array.futharkRotate the dimensions of the input array. The list of subexpressions specify how much each dimension is rotated. The length of this list must be equal to the rank of the array.futhark A list of -s, indicating the new dimensions of an array.futharkThe new dimension in a -like operation. This allows us to disambiguate "real" reshapes, that change the actual shape of the array, from type coercions that are just present to make the types work out. The two constructors are considered equal for purposes of *.futharkThe new dimension is guaranteed to be numerically equal to the old one.futharkThe new dimension is not necessarily numerically equal to the old one.futhark!Type alias for namespace reasons.futharkA body consists of a number of bindings, terminating in a result (essentially a tuple literal).futhark5The result of a body is a sequence of subexpressions.futharkA sequence of statements.futharkA local variable binding.futhark3Auxilliary Information associated with a statement.futhark#A type alias for namespace control.futhark?A pattern is conceptually just a list of names and their types.futhark-existential context (sizes and memory blocks)futhark "real" valuesfuthark#A type alias for namespace control.None0futharkThe new dimension.futhark6The new dimensions resulting from a reshape operation.futhark Construct a " where all dimension changes are s.1The new shape resulting from a reshape operation.futhark Construct a pair suitable for a .futhark%Modify the shape of an array type as  would dofuthark reshapeOuter newshape n oldshape returns a % expression that replaces the outer n dimensions of oldshape with newshape.futhark reshapeInner newshape n oldshape returns a % expression that replaces the inner m-n dimensions (where m is the rank of oldshape) of src with newshape.futharkIf the shape change is nothing but shape coercions, return the new dimensions. Otherwise, return ).futharkfuseReshape s1 s2 creates a new 2 that is semantically the same as first applying s1 and then s2-. This may take advantage of properties of  versus  to preserve information.futharkGiven concrete information about the shape of the source array, convert some s into s.futhark!reshapeIndex to_dims from_dims is transforms the index list is" (which is into an array of shape  from_dims) into an index list is'", which is into an array of shape to_dims. is must have the same length as  from_dims, and is' will have the same length as to_dims.futharkunflattenIndex dims i: computes a list of indices into an array with dimension dims given the flat index i2. The resulting list will have the same size as dims.futharkflattenIndex dims is computes the flat index of is into an array with dimensions dims. The length of dims and is must be the same.futharkGiven a length n list of dimensions dims, sizeSizes dims will compute a length n+1 list of the size of each possible array slice. The first element of this list will be the product of dims!, and the last element will be 1.None?5futharkThe  of a parameter.futharkThe  of a parameter.futharkAn  corresponding to a parameter.futharkAn $ corresponding to a pattern element.futharkThe type of a name bound by a .futharkSet the lore of a .futharkAll pattern elements in the pattern - context first, then values.futharkReturn a list of the s bound by the .futharkReturn a list of the context s bound by the .futharkReturn a list of the value s bound by the .futharkReturn a list of the s bound by the .futharkReturn a list of the #s bound by the context part of the .futharkReturn a list of the !s bound by the value part of the .futharkReturn a list of the typess bound by the .futharkReturn a list of the Types!s bound by the value part of the .futhark(Return the number of names bound by the .futharkCreate a pattern using  as the attribute.None>?6futhark:The class of lores whose annotations can be prettyprinted.futhark=Class for values that may have some prettyprinted annotation.None-2>?= futhark4A monad transformer that carries around an extended . Its ( method will first look in the extended , and then use the  method of the underlying monad.futharkThe class of things that can provide a scope. There is no overarching rule for what this means. For a +, it is the corresponding pattern. For a *, is is the parameters (including index).futhark,The class of monads that not only provide a 1, but also the ability to locally extend it. A * containing a - is the prototypical example of such a monad.futharkRun a computation with an extended type environment. Note that this is intended to *add* to the current type environment, it does not replace it.futharkThe class of applicative functors (or more common in practice: monads) that permit the lookup of variable types. A default method for  exists, which is sufficient (if not always maximally efficient, and using * to fail) when  is defined.futharkReturn the type of the given variable, or fail if it is not in the type environment.futharkReturn the info of the given variable, or fail if it is not in the type environment.futharkReturn the type environment contained in the applicative functor.futharkReturn the result of applying some function to the type environment.futharkA scope is a mapping from variable names to information about that name.futhark!How some name in scope was bound.futharkIf two scopes are really the same, then you can convert one to the other.futhark3Run a computation in the extended type environment.NoneAfutharkExpress a monad expression on a syntax node. Each element of this structure expresses the action to be performed on a given child.futharkExpress a monad mapping operation on a syntax node. Each element of this structure expresses the operation to be performed on a given child.futharkMost bodies are enclosed in a scope, which is passed along for convenience.futhark/A mapper that simply returns the tree verbatim.futharkMap a monadic action across the immediate children of an expression. Importantly, the mapOnExp action is not invoked for the expression itself, and the mapping does not descend recursively into subexpressions. The mapping is done left-to-right.futharkLike  , but in the * monad.futharkA no-op traversal.futharkAs $, but do not construct a result AST.None >?EfutharkAny operation must define an instance of this class, which describes the type of the operation (at the value level).futharkThe type of a subexpression.futharkmapType f arrts* wraps each element in the return type of f in an array with size equal to the outermost dimension of the first element of arrts.futhark"The type of a primitive operation.futharkThe type of an expression.futhark/The number of values returned by an expression. futharkThe type of a body. Watch out: this only works for the degenerate case where the body does not already return its context.*futhark:Given the context and value merge parameters of a Futhark loop, produce the return type.)  None>?K* futharkEither return precomputed free names stored in the attribute, or the freshly computed names. Relies on lazy evaluation to avoid the work. futharkA class indicating that we can obtain free variable information from values of this type. futhark+A computation to build a free variable set. futharkA set of names. futhark(Does the set of names contain this name? futhark(Construct a name set from a list. Slow. futhark,Turn a name set into a list of names. Slow. futhark(Construct a name set from a single name. futhark"The intersection of two name sets. futharkDo the two name sets intersect? futhark-Subtract the latter name set from the former. futharkMap over the names in a set. futhark-Consider a variable to be bound in the given   computation. futhark"Take note of a variable reference. futhark*Take note of a set of variable references. futharkReturn the set of variable names that are free in the given statements and result. Filters away the names that are bound by the statements. futhark/The free variables of some syntactic construct. futhark1The names bound by the bindings immediately in a . futharkThe names bound by a binding. futhark The names bound by the bindings. futhark?YY futhark:Lores in which all annotations support name substitution. futharkA type that is an instance of this class supports substitution of any names contained within. futharksubstituteNames m e replaces the variable names in e* with new names, based on the mapping in m$. It is assumed that all names in e( are unique, i.e. there is no shadowing. futharkThe substitutions to be made are given by a mapping from names to names.  #NoneY futharkGeneralization (anti-unification) We assume that the two expressions have the same type.  $None;\- futharkA name source is conceptually an infinite sequence of names with no repeating entries. In practice, when asked for a name, the name source will return the name along with a new name source, which should then be used in place of the original.The * instance is based on how many names have been extracted from the name source. futhark9Produce a fresh name, using the given name as a template. futharkA blank name source. futhark=A new name source that starts counting from the given number.  %None>`( futharkA monad that stores a name source. The following is a good instance for a monad in which the only state is a  NameSource vn:  instance MonadFreshNames vn MyMonad where getNameSource = get putNameSource = put futharkRun a computation needing a fresh name source and returning a new one, using   and  # before and after the computation. futhark9Produce a fresh name, using the given name as a template. futharkAs newName, but takes a ) for the name template.*futharkProduce a fresh ID*, using the given base name as a template. futharkProduce a fresh *, using the given base name as a template. futharkProduce a fresh %, using the given name as a template. futharkProduce a fresh , using the given 1 as a template, but possibly modifying the name. futharkProduce a fresh %, using the given name as a template. &None->?h futhark.Lores in which all annotations are renameable. futharkMembers of class   can be uniquely renamed. futharkRename the given value such that it does not contain shadowing, and has incorporated any substitutions present in the   environment. futhark)The monad in which renaming is performed. futharkRename variables such that each is unique. The semantics of the program are unaffected, under the assumption that the program was correct to begin with. In particular, the renaming may make an invalid program valid. futharkRename bound variables such that each is unique. The semantics of the expression is unaffected, under the assumption that the expression was correct to begin with. Any free variables are left untouched. futharkRename bound variables such that each is unique. The semantics of the binding is unaffected, under the assumption that the binding was correct to begin with. Any free variables are left untouched, as are the names in the pattern of the binding. futharkRename bound variables such that each is unique. The semantics of the body is unaffected, under the assumption that the body was correct to begin with. Any free variables are left untouched. futharkRename bound variables such that each is unique. The semantics of the lambda is unaffected, under the assumption that the body was correct to begin with. Any free variables are left untouched. Note in particular that the parameters of the lambda are renamed. futharkProduce an equivalent pattern but with each pattern element given a new name.*futharkProduce a map of the substitutions that should be performed by the renamer. futharkPerform a renaming using the   instance. This only works if the argument does not itself perform any name binding, but it can save on boilerplate for simple types. futharkRename some statements, then execute an action with the name substitutions induced by the statements active. 'None->?o futharkLore-specific attributes; also means the lore supports some basic facilities. futharkGiven a pattern, construct the type of a body that would match it. An implementation for many lores would be  . futharkA type class for operations. futharkLike  , but for arbitrary ops. futhark,Should we try to hoist this out of branches? futharkisBuiltInFunction k is * if k is an element of  . futhark0A map of all built-in functions and their types. futharkIf the expression is a , return that  , otherwise ). futharkAn expression is safe if it is always well-defined (assuming that any required certificates have been checked) in any context. For example, array indexing is not safe, as the index may be out of bounds. On the other hand, adding two numbers cannot fail. futhark"Return the variable names used in * subexpressions. May contain duplicates. futharkIf the  is a  return the variable name. futhark>Return the variable dimension sizes. May contain duplicates. futharkDoes the given lambda represent a known commutative function? Based on pattern matching and checking whether the lambda represents a known arithmetic operator; don't expect anything clever here. futharkHow many value parameters are accepted by this entry point? This is used to determine which of the function parameters correspond to the parameters of the original function (they must all come at the end). futharkA  with empty . futhark-The certificates associated with a statement. futhark Add certificates to a statement. futharkConstruct the type of an expression that would match the pattern.  (None>?r! futhark*Something that contains alias information. futhark"The alias of the argument element.  Noner )Nonext futhark5Expand the usage table based on aliasing information. futharkHas the given name been used directly (i.e. could we rename it or remove it without anyone noticing?)*futharkCheck whether the bits that are set in the first argument are also set in the second.*futharkx - y, but for Usages.  *None?x  +None'(-x  ,None ?yX -None?z futharkA mapping from a variable name v,, to those variables on which the value of v is dependent. The intuition is that we could remove all other variables, and v would still be computable. This also includes names bound in loops or by lambdas. futhark1Compute the data dependencies for an entire body.  .None?~` futharkA function that checks whether a variable name corresponds to a scalar expression. futhark0Representation of a scalar expression, which is:1(i) an algebraic expression, e.g., min(a+b, a*b),&(ii) a relational expression: a+b < 5,/(iii) a logical expression: e1 and (not (a+b>5) futharkRelational operators. futhark)Number of nodes in the scalar expression. futhark-Non-recursively convert a subexpression to a  . The (scalar) type of the subexpression must be given in advance. futharkIf you have a scalar expression that has been created with incomplete symbol table information, you can use this function to grow its   leaves.*futhark"Smart constructor" that checks whether we are subtracting zero, and if so just returns the first argument.  /None>*futharkenvironment recording the position and a list of variable-to-range bindings.*futharkThe number of simplifications to do before bailing out, to avoid spending too much time. futharkRanges are inclusive. futharkPrettyprint a  . Do not rely on the format of this string. Does not include the loop nesting depth information.*futhark1Binds an array name to the set of used-array vars futhark+Applies Simplification at Expression level: futharkGiven a symbol i and a scalar expression e, it decomposes e = a*i + b and returns (a,b) if possible, otherwise Nothing. futhark:Extracts sufficient conditions for a LTH0 relation to hold  0None ->?V futharkSomething that contains range information for several things, most notably  or . futharkThe ranges of the argument. futhark*Something that contains range information. futhark"The range of the argument element. futharkThe lore has embedded range information. Note that it may not be up to date, unless whatever maintains the syntax tree is careful. futhark*The range as a pair of scalar expressions. futhark&Upper and lower bound, both inclusive. futhark&A possibly undefined bound on a value. futharkA known bound on a value. futharkHas the same bounds as this variable. VERY IMPORTANT: this variable may be an array, so it cannot be immediately translated to a ScalExp. futhark+Bounded by the minimum of these two bounds. futhark+Bounded by the maximum of these two bounds. futhark"Bounded by this scalar expression. futharkConvert the bound to a scalar expression if possible. This is possible for all bounds that do not contain  s. futhark Construct a   from two possibly known bounds. The resulting bound will be unknown unless both of the given  s are known. This may seem counterintuitive, but it actually makes sense when you consider the task of combining the lower bounds for two different flows of execution (like an if expression). If we only have knowledge about one of the branches, this means that we have no useful information about the combined lower bound, as the other branch may take any value. futharkLike  , but constructs a  . futhark:A range in which both upper and lower bounds are 'Nothing.*futhark!The range of a scalar expression. futhark,Ranges of the value parts of the expression.  1None >? futhark&The lore for the basic representation. 2None? futharkPerform variable range analysis on the given program, returning a program with embedded range annotations.  3None? futharkA compiler pass transforming a  of a given lore to a  of another lore. futharkName of the pass. Keep this short and simple. It will be used to automatically generate a command-line option name via  . futharkA slightly longer description, which will show up in the command-line help text. futhark"The monad in which passes execute. futhark Execute a   action, yielding logging information and either an error text or a result. futharkTurn an * computation into a   . If the * is *, the result is a . futharkTurn an * monadic computation into a   . If the * is *, the result is an exception. futharkTake the name of the pass, turn spaces into dashes, and make all characters lowercase. futharkApply a   operation in parallel to multiple elements, joining together the name sources and logs, and propagating any error properly. 4None? futharkA monad that supports the creation of bindings from expressions and bodies from bindings, with a specific lore. This is the main typeclass that a monad must implement in order for it to be useful for generating or modifying Futhark code.Very important: the methods should not have any significant side effects! They may be called more often than you think, and the results thrown away. It is acceptable for them to create new bindings, however. futharkThe class of lores that can be constructed solely from an expression, within some monad. Very important: the methods should not have any significant side effects! They may be called more often than you think, and the results thrown away. If used exclusively within a   instance, it is acceptable for them to create new bindings, however. futhark1Add several bindings at the outermost level of a . futhark1Add a single binding at the outermost level of a .&   5None ->?c futharkLike  , but throw away the result and just return the added bindings. futharkAs   , but uses  8 to add the returned bindings to the surrounding monad.;  6None>? futhark'The aliases of what is returned by the %, and what is consumed inside of it. futhark&Everything consumed in the expression. futhark&The aliases of the let-bound variable. futharkA wrapper around  ) to get around the fact that we need an * instance, which   does not have. futhark&The lore for the basic representation. futharkEverything consumed in the given statements and result (even transitively).  7None? futharkPre-existing aliases for variables. Used to add transitive aliases. futhark,Perform alias analysis on a Futhark program.  8None>?|*futharkWisdom about a body. futharkWisdom about an expression. futhark%The wisdom of the let-bound variable.  9None>?futharkInstances of this class can be converted to Futhark expressions within a  .futharkAs  , but an  can be given.futharkNote: unsigned division.futhark Construct an 3 expressions that slices an array with unit stride.futhark.Are these indexes out-of-bounds for the array?futharkWrite to an index of the array, if within bounds. Otherwise, nothing. Produces the updated array.futhark1Construct an unspecified value of the given type.futhark&Sign-extend to the given integer type.futhark&Zero-extend to the given integer type.futharkApply a binary operator to several subexpressions. A left-fold.futharkCreate a two-parameter lambda whose body applies the given binary operation to its arguments. It is assumed that both argument and result types are the same. (This assumption should be fixed at some point.)futharkAs  , but for s.futhark)Slice a full dimension of the given size.futharkfullSlice t slice returns slice , but with ?s of entire dimensions appended to the full dimensionality of t. This function is used to turn incomplete indexing complete, as required by .futhark sliceAt t n slice returns slice but with s of the outer n dimensions prepended, and as many appended as to make it a full slice. This is a generalisation of .futharkLike (, but the dimensions are simply numeric.futharkDoes the slice describe the full size of the array? The most obvious such slice is one that s the full span of every dimension, but also one that fixes all unit dimensions.futhark8Conveniently construct a body that contains no bindings.futharkConveniently construct a body that contains no bindings - but this time, monadically!futharkEvaluate the action, producing a body, then wrap it in all the bindings it created using  .futharkChange that result where evaluation of the body would stop. Also change type annotations at branches.futharkInstantiate all existential parts dimensions of the given type, using a monadic action to create the necessary s. You should call this function within some monad that allows you to collect the actions performed (say, *).futhark!Can be used as the definition of   for a  & instance for simple representations. -:None9>?0futhark,The class of lores that can be type-checked.futhark/Used at top level; can be locally changed with .futhark$The type checker runs in this monad.*futharkThe environment contains a variable table and a function table. Type checking happens with access to this environment. The function table is only initialised at the very beginning, but the variable table will be extended during type-checking when let-expressions are encountered.*futharkThe * data structure is used to keep track of which variables have been consumed, as well as whether a violation has been detected.*futharkA tuple of a return type and a list of parameters, possibly named.futhark A type error.futhark6Information about an error during type checking. The *? instance for this type produces a human-readable description.futharkAdd information about what is being type-checked to the current context. Liberal use of this combinator makes it easier to track type errors, as the strings are added to type errors signalled via .*futharkMark a name as bound. If the name has been bound previously in the program, report a type error.*futharkProclaim that we have made read-only use of the given variable. No-op unless the variable is array-typed.futhark5Proclaim that we have written to the given variables.futharkPermit consumption of only the specified names. If one of these names is consumed, the consumption will be rewritten to be a consumption of the corresponding alias set. Consumption of anything else will result in a type error.*futharkGiven the immediate aliases, compute the full transitive alias set (including the immediate aliases).*futharkcheckAnnotation loc s t1 t2 checks if t2 is equal to t1 . If not, a  is raised.futhark require ts se* causes a '(TypeError vn)' if the type of se* is not a subtype of one of the types in ts.futhark Variant of  working on variable names.futharkType check a program containing arbitrary type information, yielding either a type error or a program with complete type information.futharkRemove all aliases from the *.;None ?futharkIf Verbose, print log messages to standard error. If VeryVerbose, also print logs from individual passes."<None?^=None?EfutharkReshape the arguments to a function so that they fit the expected shape declarations. Not used to change rank of arguments. Assumes everything is otherwise type-correct.>Nonefuthark Convert a   to a Futhark expression. The provided function converts the leaves.futharkConvert an expression to a  . The provided function is used to convert expressions that are not trivially  s. This includes constants and variable names, which are passed as s.futharkConvert s of a given type.futhark5Applying a monadic transformation to the leaves in a  .futhark3Substituting names in a PrimExp with other PrimExps ?Nonefuthark8ignoring permutations, is the index function contiguous?*futhark.monotonously increasing, decreasing or unknown*futharkLMAD's representation consists of a general offset and for each dimension a stride, rotate factor, number of elements (or shape), permutation, and monotonicity. Note that the permutation is not strictly necessary in that the permutation can be performed directly on LMAD dimensions, but then it is difficult to extract the permutation back from an LMAD.LMAD algebra is closed under composition w.r.t. operators such as permute, repeat, index and slice. However, other operations, such as reshape, cannot always be represented inside the LMAD algebra.It follows that the general representation of an index function is a list of LMADS, in which each following LMAD in the list implicitly corresponds to an irregular reshaping operation.However, we expect that the common case is when the index function is one LMAD -- we call this the nice representation.)Finally, the list of LMADs is kept in an IxFun together with the shape of the original array, and a bit to indicate whether the index function is contiguous, i.e., if we instantiate all the points of the current index function, do we get a contiguous memory interval??By definition, the LMAD denotes the set of points (simplified):!{ o + Sigma_{j=0}^{k} ((i_j+r_j) : n_j)*s_j, forall i_j such that 0<=i_jfinally, the underlying memory is contiguous (and monotonous).If any of these conditions do not hold, then the reshape operation will conservatively add a new LMAD to the list, leading to a representation that provides less opportunities for further analysis.futharkReshape an index function.*futharkHandle the case where a rebase operation can stay within m + n - 1 LMADs, where m is the number of LMADs in the index function, and n is the number of LMADs in the new base. If both index function have only on LMAD, this means that we stay within the single-LMAD domain.We can often stay in that domain if the original ixfun is essentially a slice, e.g. `x[i, (k1,m,s1), (k2,n,s2)] = orig`.,XXX: TODO: handle repetitions in both lmads.2How to handle repeated dimensions in the original?(a) Shave them off of the last lmad of original (b) Compose the result from (a) with the first lmad of the new base (c) apply a repeat operation on the result of (b).However, I strongly suspect that for in-place update what we need is actually the INVERSE of the rebase function, i.e., given an index function new-base and another one orig, compute the index function ixfun0 such that:new-base == rebase ixfun0 ixfun, or equivalently: new-base == ixfun o ixfun0because then I can go bottom up and compose with ixfun0 all the index functions corresponding to the memory block associated with ixfun.futhark.Rebase an index function on top of a new base.futharkOffset index. Results in the index function corresponding to indexing with i on the outermost dimension.futharkIf the memory support of the index function is contiguous and row-major (i.e., no transpositions, repetitions, rotates, etc.), then this should return the offset from which the memory-support of this index function starts.futharkSimilar restrictions to linearWithOffset except for transpositions, which are returned together with the offset.*futhark8Generalised iota with user-specified offset and strides.*futhark(Check monotonicity of an index function.futhark!Generalization (anti-unification)Anti-unification of two index functions is supported under the following conditions: 0. Both index functions are represented by ONE lmad (assumed common case!) 1. The support array of the two indexfuns have the same dimensionality (we can relax this condition if we use a 1D support, as we probably should!) 2. The contiguous property and the per-dimension monotonicity are the same (otherwise we might loose important information; this can be relaxed!) 3. Most importantly, both index functions correspond to the same permutation (since the permutation is represented by INTs, this restriction cannot be relaxed, unless we move to a gated-LMAD representation!)k06 is the existential to use for the shape of the array.futharkWhen comparing index functions as part of the type check in ExplicitMemory, we may run into problems caused by the simplifier. As index functions can be generalized over if-then-else expressions, the simplifier might hoist some of the code from inside the if-then-else (computing the offset of an array, for instance), but now the type checker cannot verify that the generalized index function is valid, because some of the existentials are computed somewhere else. To Work around this, we've had to relax the ExplicitMemory type-checker a bit, specifically, we've introduced this function to verify whether two index functions are "close enough" that we can assume that they match. We use this instead of `ixfun1 == ixfun2` and hope that it's good enough.@None-?8*futhark#Index a delayed array, if possible.*futharkTrue if consumed.*futhark#Index a delayed array, if possible.*futharkTrue if consumed.*futhark%Indexing a delayed array if possible.futhark'The result of indexing a delayed array.futharkA PrimExp based on the indexes (that is, without accessing any actual array).futharkThe indexing corresponds to another (perhaps more advantageous) array.futhark?Which names are available just before the most enclosing loop?futhark/We are in a situation where we should simplifyhoistun-existentialise memory as much as possible - typically, inside a kernel.futhark!In symbol table and not consumed.*futharkUpdating the ranges of all symbols whenever we enter a branch is presently too expensive, and disabled here.*futharkRefines the ranges in the symbol table with ranges extracted from branch conditions. cond# is the condition of the if-branch.futhark>Hide definitions of those entries that satisfy some predicate.futharkHide these definitions, if they are protected by certificates in the set of names.00ANone  ->? futharkLike , but just for s.futharkThe essential parts of a 4 factored out (everything except the input arrays).futhark Race factor RF means that only 1/RF bins are used.futhark7A combination of scan, reduction, and map. The first . is the size of the input arrays. The first / pair is for scan and its neutral elements. The second is for the reduction. The final lambda is for the map part, and finally comes the input arrays.futhark1How many reduction results are produced by these s?futhark:Combine multiple reduction operators to a single operator.futharkConstruct a lambda that takes parameters of the given types and simply returns them unchanged.futhark'Is the given lambda an identity lambda?futhark3A lambda with no parameters that returns no values.futhark/A mapper that simply returns the SOAC verbatim.futharkMap a monadic action across the immediate children of a SOAC. The mapping does not descend recursively into subexpressions and is done left-to-right.futhark2Get Stream's accumulators as a sub-expression list55BNone?9futharkTurns a binding of a redomap into two seperate bindings, a map binding and a reduce" binding (returned in that order).$Reuses the original pattern for the reduce&, and creates a new pattern with new s for the result of the map.Only handles a  with an empty futharkTurn a Screma into simpler Scremas that are all simple scans, reduces, and maps. This is used to handle Scremas that are so complicated that we cannot directly generate efficient parallel code for them. In essense, what happens is the opposite of horisontal fusion. CNone>futhark&The lore for the basic representation. DNone-?futharkThe constraints that a monad must uphold in order to be used for first-order transformation.futharkFirst transform any nested  or  elements, then apply  if the expression is a SOAC.futharkTransform a single  into a do-loop. The body of the lambda is untouched, and may or may not contain further s depending on the given lore.futhark+Recursively first-order-transform a lambda.ENone?futhark1Interchange Scan With Inner Map. Tries to turn a  scan(map) into a @map(scan)futhark3Interchange Reduce With Inner Map. Tries to turn a  reduce(map) into a @map(reduce)FNoneNone >futharkA mapping from external variable names to the corresponding internalised subexpressions.futharkExtra parameters to pass when calling this function. This corresponds to the closure of a locally defined function.futhark;Add a function definition to the program being constructed.futharkExecute the given action if / is true, otherwise just return an empty list.futharkExecute the given action if / is true, otherwise just return an empty list. GNonebfutharkThe call graph is a mapping from a function name, i.e., the caller, to a set of the names of functions called *directly* (not transitively!) by the function.>We keep track separately of the functions called by constants.futhark.Is the given function known to the call graph?futhark(Does the first function call the second?futhark/Is the function called in any of the constants?futhark&All functions called by this function.futharkbuildCallGraph prog build the program's call graph.*futharkbuildCallGraph ftable fg fname updates fg% with the contributions of function fname.HNone -2>? futhark=A host-level operation; parameterised by what else it can do.futharkA segmented operation.futhark)A simple size-level query or computation.futhark!SplitSpace o w i elems_per_thread.Computes how to divide array elements to threads in a kernel. Returns the number of elements in the chunk that the current thread should take.w5 is the length of the outer dimension in the array. i: is the current thread index. Each thread takes at most elems_per_thread elements. If the order o is , thread with index i should receive elements i*elems_per_tread, i*elems_per_thread + 1, ..., i*elems_per_thread + (elems_per_thread-1). If the order o is  stride$, the thread will receive elements =i, i+stride, i+2*stride, ..., i+(elems_per_thread-1)*stride.futhark'Produce some runtime-configurable size.futharkThe maximum size of some class.futhark:Compare size (likely a threshold) with some integer value.futhark)CalcNumGroups w max_num_groups group_size calculates the number of GPU workgroups to use for an input of the given size. The Name is a size name. Note that w% is an i64 to avoid overflow issues.futharkLike , but just for s.futharkThe KernelSpace must always have at least two dimensions, implying that the result of a SegRed is always an array.futharkIndex space of a .futharkFlat physical index corresponding to the dimensions (at code generation used for a thread ID or similar).futharkAt which level the *body* of a  executes.futharkDo we need group-virtualisation when generating code for the segmented operation? In most cases, we do, but for some simple kernels, we compute the full number of groups in advance, and then virtualisation is an unnecessary (but generally very small) overhead. This only really matters for fairly trivial but very wide map kernels where each thread performs constant-time work on scalars.futharkEach "worker" in the kernel returns this. Whether this is a result-per-thread or a result-per-group depends on the .futhark8Metadata about whether there is a subtle point to this . This is used to protect things like tiling, which might otherwise be removed by the simplifier because they're semantically redundant. This has no semantic effect and can be ignored at code generation.futharkDon't simplify this one!futharkGo nuts.futharkThe results produced are only used within the same physical thread later on, and can thus be kept in registers.futharkThe body of a Kernel.futharkIn case this operator is semantically a vectorised operator (corresponding to a perfect map nest in the SOACS representation), these are the logical "dimensions". This is used to generate more efficient code.futharkIn case this operator is semantically a vectorised operator (corresponding to a perfect map nest in the SOACS representation), these are the logical "dimensions". This is used to generate more efficient code.futhark"How an array is split into chunks.futhark&The type of a histogram produced by a /. This can be different from the type of the HistDest5s in case we are dealing with a segmented histogram.futhark1How many reduction results are produced by these s?futhark!A mapper that simply returns the  verbatim. INone> 9 /JNone?*futharkMap from variable names to defining expression. We use this to hackily determine whether something is transposed or otherwise funky in memory (and we'd prefer it not to be). If we cannot find it in the map, we just assume it's all good. HACK and FIXME, I suppose. We really should do this at the memory level.KNoneLNone?j*futharkInt64*futharkInt32futharkLike , but cap the thread count to the input size. This is more efficient for small kernels, e.g. summing a small array.*futharkGiven a chunked fold lambda that takes its initial accumulator value as parameters, bind those parameters to the neutral element instead.futharkSegment indexes and sizes.MNone >? *futhark"Description of distribution to do.*futhark*Also related to avoiding identity mapping.futharkNote: first element is *outermost* nesting. This is different from the similar types elsewhere!futharkFirst pair element is the very innermost ("current") target. In the list, the outermost target comes first. Invariant: Every element of a pattern must be present as the result of the immediately enclosing target. This is ensured by & by removing unused pattern elements.*futharkFirst pair element is the very innermost ("current") nest. In the list, the outermost nest comes first.*futharkBoth parameters and let-bound.futharkAdd new outermost nesting, pushing the current outermost to the list, also taking care to swap patterns if necessary.futharkAdd new innermost nesting, pushing the current outermost to the list. It is important that the  has the right order (non-permuted compared to what is expected by the outer nests).futharkFlatten a kernel nesting to: The index space.:The kernel inputs - note that some of these may be unused.&&NNone?futharkAn encoding of a sequential do-loop with no existential context, alongside its result pattern.futharkGiven a (parallel) map nesting and an inner sequential loop, move the maps inside the sequential loop. The result is several statements - one of these will be the loop, which will then contain statements with Map expressions.ONone?PNone?#*futharkThe variance table keeps a mapping from a variable name (something produced by a ) to the kernel thread indices that name depends on. If a variable is not present in this table, that means it is bound outside the kernel (and so can be considered invariant to all dimensions).*futharkInformation about a loop that has been tiled inside a kernel, as well as the kinds of changes that we would then like to perform on the kernel.*futharkStatements that we insert directly into every thread-private SegMaps. This is for things that cannot efficiently be computed once in advance in the prelude SegMap, primarily (exclusively?) array slicing operations.*futharkMove statements from prelude to postlude if they are not used in the tiled statement anyway.*futharkPartition prelude statements preceding a tiled loop (or something containing a tiled loop) into three categories:1) Group-level statements that are invariant to the threads in the group.2) Thread-variant statements that should be computed once with a segmap_thread_scalar.3) Thread-variant statements that should be recomputed whenever they are needed.The third category duplicates computation, so we only want to do it when absolutely necessary. Currently, this is necessary for results that are views of an array (slicing, rotate, etc), because these cannot be efficiently represented by a scalar segmap (they'll be manifested in memory).QNone?$HfutharkName of result.futharkType of result.  RNone ->?$futhark>Apply the in-place lowering optimisation to the given program.SNone?%*futharkGiven a statement, compute how often each of its free variables are used. Not accurate: what we care about are only 1, and greater than 1.TNone?,futhark2A collection of both top-down and bottom-up rules.*futhark A collection of bottom-up rules.*futharkA collection of top-down rules.futharkContext for a rule applied during bottom-up traversal of the program. Takes a symbol table and usage table as arguments.futharkContext for a rule applied during top-down traversal of the program. Takes a symbol table as argument.*futharkA collection of rules grouped by which forms of statements they may apply to.futharkA simplification rule takes some argument and a statement, and tries to simplify the statement.futharkAn efficient way of encoding whether a simplification rule should even be attempted.futharkGive it a shot.futhark Don't bother.futhark6The monad in which simplification rules are evaluated.*futhark Execute a  action. If succesful, returns the result and a list of new bindings. Even if the action fail, there may still be a monadic effect - particularly, the name source may have been modified.futhark1Construct a rule book from a collection of rules.futharksimplifyStm lookup bnd) performs simplification of the binding bnd. If simplification is possible, a replacement list of bindings is returned, that bind at least the same names as the original binding (and possibly more, for intermediate results).futharksimplifyStm uses bnd) performs simplification of the binding bnd. If simplification is possible, a replacement list of bindings is returned, that bind at least the same names as the original binding (and possibly more, for intermediate results). The first argument is the set of names used after this binding.""UNone?.futhark?A function that, given a variable name, returns its definition.futhark+foldClosedForm look foldfun accargs arrargs, determines whether each of the results of foldfun# can be expressed in a closed form.futhark+loopClosedForm pat respat merge bound bodys determines whether the do-loop can be expressed in a closed form.*futhark Lambda-boundVNone?3'*futharkA simple rule is a top-down rule that can be expressed as a pure function.*futhark9A function that, given a subexpression, returns its type.futharkA set of standard simplification rules. These assume pure functional semantics, and so probably should not be applied after memory block merging.futharkTurn copy(x) into x iff x? is not used after this copy statement and it can be consumed.>This simplistic rule is only valid before we introduce memory.*futharkMove out results of a conditional expression whose computation is either invariant to the branches (only done for results in the context), or the same in both branches.*futharkIf we are copying a scratch array (possibly indirectly), just turn it into a scratch by itself.*futharkRemove the return values of a branch, that are not actually used after a branch. Standard dead code removal can remove the branch if *none* of the return values are used, but this rule is more precise.WNone->?8 futharkMake a hoisted Op safe. The SubExp is a boolean that is true when the value of the statement will actually be used.futhark+Blocker for hoisting out of parallel loops.futhark-Blocker for hoisting out of sequential loops.futhark%Blocker for hoisting out of branches.futhark(gets the sizes of arrays from a binding.*futharkMark that we have changed something and it would be a good idea to re-run the simplifier.*futharkWe are willing to hoist potentially unsafe statements out of branches, but they most be protected by adding a branch on top of them. (This means such hoisting is not worth it unless they are in turn hoisted out of a loop somewhere.)*futharkWe are willing to hoist potentially unsafe statements out of loops, but they most be protected by adding a branch on top of them.*futharkStatements that are not worth hoisting out of loops, because they are unsafe, and added safety (by *%) may inhibit further optimisation..futharkSimplify a single . The [Diet] only covers the value elements, because the context cannot be consumed.*futharkSimplify a single . The [Diet] only covers the value elements, because the context cannot be consumed.*futharkBranch condition.futhark1Which side of the branch are we protecting here? /XNone?:futhark Simplify a  $, including copy propagation. If a   refers to a name that is a , the node turns into a  .futharkLike , but where leaves may be s.YNone  ->?E\futharkThe memory return of a function, which must always indicate where returned arrays are located.futharkThe return of a body, which must always indicate where returned arrays are located.futharkThe memory return of an expression. An array is annotated with Maybe MemReturn, which can be interpreted as the expression either dictating exactly where the array is located when it is returned (if *8), or able to put it whereever the binding prefers (if )).This is necessary to capture the difference between an expression that is just an array-typed variable, in which the array being "returned" is located where it already is, and a copy expression, whose entire purpose is to store an existing array in some arbitrary location. This is a consequence of the design decision never to have implicit memory copies.futharkA description of the memory properties of an array being returned by an operation.futharkThe array is located in a memory block that is already in scope.futhark8The operation returns a new (existential) memory block.futhark?Memory information for an array bound somewhere in the program.futhark7Located in this memory block with this index function.futharkA summary of the memory information for every let-bound identifier, function parameter, and return value. Parameterisered over uniqueness, dimension, and auxiliary array information.futharkA primitive value.futharkA memory block.futharkThe array is stored in the named memory block, and with the given index function. The index function maps indices in the array to element offset, not byte offsets! To translate to byte offsets, multiply the offset with the size of the array element type.futhark9An index function that may contain existential variables.futhark>The index function representation used for memory annotations.futharkAllocate a memory block. This really should not be an expression, but what are you gonna do...futhark.A lore containing explicit memory information.*futhark/Helper function for index function unification.0The first return value maps a VName (wrapped in ) to its Int (wrapped in ). In case of duplicates, it is mapped to the *first* Int that occurs.5The second return value maps each Int (wrapped in an ) to a   : with the Int at which its associated VName first occurs.futharkThe return information of an expression. This can be seen as the "return type with memory annotations" of the expression. ZNone-9>?Nr*futhark1Monad for adding allocations to a single pattern.*futhark2Monad for adding allocations to an entire program.*futharkAggressively try to reuse memory in do-loops - should be True inside kernels, False outside.*futharkWhen allocating memory, put it in this memory space. This is primarily used to ensure that group-wide statements store their results in local memory.*futharkA mapping from chunk names to their maximum size. XXX FIXME HACK: This is part of a hack to add loop-invariant allocations to reduce kernels, because memory expansion does not use range analysis yet (it should).*futharkThe subexpression giving the number of elements we should allocate space for. See * comment.[None ->?Ou*futharkThe booleans indicate whether we should also play with the initial merge values.*futharkFirst name is the memory block to copy to, second is the name of the array copy.\None>?PfutharkThe operations that permit CSE.*futhark*Perform CSE within any nested expressions.futhark+Perform CSE on every function in a program.futhark!Perform CSE on a single function.futharkPerform CSE on some statements.]None-?SfutharkSimplify the given program. Even if the output differs from the output, meaningful simplification may not have taken place - the order of bindings may simply have been rearranged.futhark.Run a simplification operation to convergence.futharkSimplify the given function. Even if the output differs from the output, meaningful simplification may not have taken place - the order of bindings may simply have been rearranged. Runs in a loop until convergence.futharkSimplify just a single .futharkSimplify a list of s.^None-?T%futhark*Run copy propagation on an entire program.futhark(Run copy propagation on some statements.futhark#Run copy propagation on a function._None >?W&*futharkNever constructed.*futharkGetting the roots of what to hoist, for now only variable names that represent shapes/sizes.*futharkRemove all arguments to the map that are simply replicates. These can be turned into free variables instead.*futharkLike * , but for .*futhark0Remove inputs that are not used inside the SOAC.*futharkSome of the results of a reduction (or really: Redomap) may be dead. We remove them here. The trick is that we need to look at the data dependencies to see that the "dead" result is not actually used for computing one of the live ones.*futharkIf we are writing to an array that is never used, get rid of it.`None>?Wz!!aNone>?ZfutharkConvert the statements inside a map nest to kernel statements, attempting to parallelise any remaining (top-level) parallel statements. Anything that is not a map, scan or reduction will simply be sequentialised. This includes sequential loops that contain maps, scans or reduction. In the future, we could probably do something more clever. Make sure that the amount of parallelism to be exploited does not exceed the group size. Further, as a hack we also consider the size of all intermediate arrays as "parallelism to be exploited" to avoid exploding local memory.We distinguish between "minimum group size" and "maximum exploitable parallelism".bNone>?\futharkTransform a program using SOACs to a program using explicit kernels, using the kernel extraction transformation.*futhark(Returns the sizes of nested parallelism.*futharkIntra-group parallelism is worthwhile if the lambda contains non-map nested parallelism, or any nested parallelism inside a loop.*futharkA lambda is worth sequentialising if it contains nested parallelism of an interesting kind.cNone ->?\dNone ->?_*futharkGetting the roots of what to hoist, for now only variable names that represent array and memory-block sizes.*futharkIf a branch is returning some existential memory, but the size of the array is not existential, then we can create a block of the proper size and always return there.*futharkIf we are copying something that is itself a copy, just copy the original one instead.*futharkIf the destination of a copy is the same as the source, just remove it.eNone?_CfNone?`*futhark:A map from memory block names to new index function bases.*futharkA description of allocations that have been extracted, and how much memory (and which space) is needed.+futharkExtract allocations from Thread statements with extractThreadAllocations.gNone`futharkThe assertion-resolver pass.hNone?c+futhark"inlineInFunDef constf fdmap caller inlines in calleer the functions in fdmap that are called as constf/. At this point the preconditions are that if fdmap8 is not empty, and, more importantly, the functions in fdmap" do not call any other functions.futharkInline  NotConstFun3 functions and remove the resulting dead functions.futharkremoveDeadFunctions prog removes the functions that are unreachable from the main function from the program.iNone>s+futhark8The reason why some expression cannot be converted to a  value.futhark,The expression is not a (tuple-)SOAC at all.futhark/A definite representation of a SOAC expression.futharkOne array input to a SOAC - a SOAC may have multiple inputs, but all are of this form. Only the array inputs are expressed with this type; other arguments, such as initial accumulator values, are plain expressions. The transforms are done left-to-right, that is, the first element of the  list is applied first.futhark0A view of the last transformation to be applied.futhark1A view of the first transformation to be applied.futhark:A sequence of array transformations, heavily inspired by Data.Seq. You can decompose it using viewF and viewL, and grow it by using  and . These correspond closely to the similar operations for sequences, except that appending will try to normalise and simplify the transformation sequence.The data type is opaque in order to enforce normalisation invariants. Basically, when you grow the sequence, the implementation will try to coalesce neighboring permutations, for example by composing permutations and removing identity transformations.futharkA single, simple transformation. If you want several, don't just create a list, use  instead.futhark*A permutation of an otherwise valid input.futhark(A reshaping of an otherwise valid input.futhark#A reshaping of the outer dimension.futhark2A reshaping of everything but the outer dimension.futhark2Replicate the rows of the array a number of times.futharkThe empty transformation list.futhark#Is it an empty transformation list?futhark7Decompose the input-end of the transformation sequence.futhark8Decompose the output-end of the transformation sequence.futhark6Add a transform to the end of the transformation list.futharkfuthark"Phantom type for a count of bytes.futhark%Phantom type for a count of elements.futharkA function call argument.futharkThe volatility of a memory access or variable. Feel free to ignore this for backends where it makes no sense (anything but C and similar low-level things)futharkCreate an array containing the given values. The lifetime of the array will be the entire application. This is mostly used for constant arrays, but also for some bookkeeping data, like the synchronisation counts used to implement reduction.futhark+Memory space must match the corresponding .futharkIndicate that some memory block will never again be referenced via the indicated variable. However, it may still be accessed through aliases. It is only safe to actually deallocate the memory block if this is the last reference. There is no guarantee that all memory blocks will be freed with this statement. Backends are free to ignore it entirely.futharkDestination, offset in destination, destination space, source, offset in source, offset space, number of bytes.futharkMust be in same space.futharkHas the same semantics as the contained code, but the comment should show up in generated code for ease of inspection.futharkPrint the given value to the screen, somehow annotated with the given string as a description. If no type/value pair, just print the string. This has no semantic meaning, but is used entirely for debugging. Code generators are free to ignore this statement.futharkThe contents of a statically declared constant array. Such arrays are always unidimensional, and reshaped if necessary in the code that uses them.futharkPrecisely these values.futharkThis many zeroes.futhark!Type alias for namespace control.futharkA imperative function, containing the body as well as its low-level inputs and outputs, as well as its high-level arguments and results. The latter are only used if the function is an entry point.futhark^ An externally visible value. This can be an opaque value (covering several physical internal values), or a single value that can be used externally.futharkThe string is a human-readable description with no other semantics.futhark0A description of an externally meaningful value.futharkAn array with memory block, memory block size, memory space, element type, signedness of element type (if applicable), and shape.futhark-A scalar value with signedness if applicable.futhark%A collection of imperative constants.futhark7The constants that are made available to the functions.futharkSetting the value of the constants. Note that this must not contain declarations of the names defined in .futhark%A collection of imperative functions.futhark3A collection of imperative functions and constants.futharkConvert a count of elements into a count of bytes, given the per-element size.futharkTurn a  into a int32 .  pNonefutharkSet all uses of 3 in the given definitions to another memory space.qNone ->?W&futharkCompile things to .futharkCompile to an , where the type (must must still be a primitive) is deduced monadically.futhark*Compile where we know the type in advance.futhark)The symbol table used during compilation.+futharkUser-extensible environment.+futhark.Name of the function we are compiling, if any.+futharkThe  is *# if a copy if required. If it is ), then a copy/assignment of a memory block somewhere takes care of this array.+futharkWhen compiling an expression, this is a description of where the result should end up. The integer is a reference to the construct that gave rise to this destination (for patterns, this will be the tag of the first name in the pattern). This can be used to make the generated code easier to relate to the original code.futhark;Every non-scalar variable must be associated with an entry.futhark3When an array is dared, this is where it is stored.futhark,An alternate way of compiling an allocation.futharkHow to compile an .futharkHow to compile some .futharkHow to compile an .futharkAn operations set for which the expression compiler always returns  CompileExp.futharkExecute a code generation action, returning the code that was emitted.futharkExecute a code generation action, wrapping the generated code within a  with the given description.futhark$Emit some generated imperative code.futhark&Emit a function in the generated code.futhark+Check if a function of a given name exists.+futhark+Note: a hack to be used only for functions.+futharkLike , but does not create new declarations. Note: a hack to be used only for functions.+futhark Another hack.+futharkRemove the array targets.futharkGet the current symbol table.futharkRun an action with a modified symbol table. All changes to the symbol table will be reverted once the action is done!+futharkUse an  if possible, otherwise .+futharkCopy from here to there; both destination and source may be indexeded.+futharkLike , but the target is a + instead of a variable name.futharkCopy from here to there; both destination and source be indexeded. If so, they better be arrays of enough dimensions. This function will generally just Do What I Mean, and Do The Right Thing. Both destination and source must be in scope.futharkAs , but implicitly es the indexes.futharkcompileAlloc pat size space allocates n bytes of memory in space, writing the result to dest, which must be a single +,futharkThe number of bytes needed to represent the array in a straightforward contiguous format.futharkLike , but permute the in-memory representation of the indices as specified.futhark Uses linear/iota index function.futhark Uses linear/iota index function.futhark ASsignment.futhark(Constructing a non-entry point function.3rNonefuthark8Phantom type for identifying sequential imperative code.futharkA piece of imperative code.futharkAn imperative function.futharkAn imperative program.  sNonetNoneRfuthark8The target platform when compiling imperative code to a futharkHost-level OpenCL operation.futharkInformation about bounds checks and how sensitive it is to errors. Ordered by least demanding to most.futharkDoes not need to know if we are in a failing state, and also cannot fail.futharkNeeds to be told if there's a global failure, and that's it, and cannot fail.futhark&Needs all parameters, may fail itself.+futharkWhether a kernel can potentially fail (because it contains bounds checks and such).futhark%An argument to be passed to a kernel.futhark5Pass the value of this scalar expression as argument.futharkPass this pointer as argument.futhark,Create this much local memory per workgroup.futharkThe name of a kernel.futharkA piece of code calling OpenCL.futhark"A function calling OpenCL kernels.futharkSomething that can go wrong in a kernel. Part of the machinery for reporting error messages from within kernels.futhark"An program calling OpenCL kernels.futhark!Must be prepended to the program.futhark/So we can detect whether the device is capable.futharkRuntime-configurable constants.futhark!Assertion failure error messages.futharkHow many leading failure arguments we must pass when launching a kernel with these safety characteristics.  uNone ? futharkPerform a barrier and also check whether any threads have failed an assertion. Make sure all threads would reach all s if any of them do. A failing assertion will jump to the next following 8, so make sure it's not inside control flow or similar.futharkWhen we do a barrier or fence, is it at the local or global level?futhark2A generic kernel containing arbitrary kernel code.futhark,The host variables referenced by the kernel.futharkA short descriptive and _unique_ name - should be alphanumeric and without spaces.futharkIf true, this kernel does not need for check whether we are in a failing state, as it can cope. Intuitively, it means that the kernel does not depend on any non-scalar parameters to make control flow decisions. Replication, transpose, and copy kernels are examples of this.futhark3An expression whose variables are kernel constants.futhark'A run-time constant related to kernels.futharkCode inside a kernel.futhark&Host-level code that can call kernels.  vNonefuthark1Which form of transposition to generate code for.futhark6For small arrays that do not benefit from coalescing.futharkGenerate a transpose kernel. There is special support to handle input arrays with low width, low height, or both.Normally when transposing a [2][n] array we would use a FUT_BLOCK_DIM x FUT_BLOCK_DIM group to process a [2][FUT_BLOCK_DIM] slice of the input array. This would mean that many of the threads in a group would be inactive. We try to remedy this by using a special kernel that will process a larger part of the input, by using more complex indexing. In our example, we could use all threads in a group if we are processing (2/FUT_BLOCK_DIM)8 as large a slice of each rows per group. The variable mulx contains this factor for the kernel to handle input arrays with low height.*See issue #308 on GitHub for more details.These kernels are optimized to ensure all global reads and writes are coalesced, and to avoid bank conflicts in shared memory. Each thread group transposes a 2D tile of block_dim*2 by block_dim*2 elements. The size of a thread group is block_dim/2 by block_dim*2, meaning that each thread will process 4 elements in a 2D tile. The shared memory array containing the 2D tile consists of block_dim*2 by block_dim*2+1 elements. Padding each row with an additional element prevents bank conflicts from occuring when the tile is accessed column-wise.Note that input_size and output_size may not equal width*height if we are dealing with a truncated array - this happens sometimes for coalescing optimisations.wNone?futharkIs there an atomic  corresponding to this ?futharkThe mechanism that will be used for performing the atomic update. Approximates how efficient it will be. Ordered from most to least efficient.futhark Supported directly by primitive.futharkCan be done by efficient swaps.futharkRequires explicit locking.futharkA function for generating code for an atomic update. Assumes that the bucket is in-bounds.futhark+Locking strategy used for an atomic update.futharkArray containing the lock.futhark'Value for us to consider the lock free.futharkWhat to write when we lock it.futhark What to write when we unlock it.futharkA transformation from the logical lock index to the physical position in the array. This can also be used to make the lock array smaller.futharkAssign iterations of a for-loop to all threads in the kernel. The passed-in function is invoked with the (symbolic) iteration. For multidimensional loops, use .futharkAssign iterations of a for-loop to threads in the workgroup. The passed-in function is invoked with the (symbolic) iteration. For multidimensional loops, use .futharkIterate collectively though a multidimensional space, such that all threads in the group participate. The passed-in function is invoked with a (symbolic) point in the index space.futhark atomicUpdate, but where it is explicitly visible whether a locking strategy is necessary.+futharkfutharkThe result of compilation to C is four parts, which can be put together in various ways. The obvious way is to concatenate all of them, which yields a CLI program. Another is to compile the library part by itself, and use the header file to call into it.futharkUtility definitions that must be visible to both CLI and library parts.futharkConstruct the Python array being returned from an entry point.futhark;Create a static array of values - initialised at load time.futhark&Copy from one memory block to another.futharkAllocate a memory block of the given size in the given memory space, saving a reference in the given variable name.futharkRead a scalar from the given memory block with the given index and in the given memory space.futharkWrite a scalar to the given memory block with the given index and in the given memory space.futharkA substitute expression compiler, tried before the main compilation function.futharkA set of operations that fail for every operation involving non-default memory spaces. Uses plain pointers and malloc for memory management.futhark7A constructor that takes no arguments and does nothing.futharkA  where the function is a variable and every argument is a simple .futhark#The ctypes type corresponding to a .futhark#The ctypes type corresponding to a , taking sign into account.futhark"The Numpy type corresponding to a .futhark"The Numpy type corresponding to a , taking sign into account.33NoneNone?NoneX+futharkBoolean negation.+futharkBitwise complement.+futharkNumerical negation.+futharkAbsolute/numerical value.Nonefuthark&Whether an option accepts an argument.futharkSpecification if a single command line option. The option must have a long name, and may also have a short name.When the statement is being executed, the argument (if any) will be stored in the variable optarg.futharkGenerate option parsing code that accepts the given command line options. Will read from sys.argv.If option parsing fails for any reason, the entire process will terminate with error code 1.  None 9futharkThe class generated by the code generator must have a constructor, although it can be vacuous.futhark0Unpack the array being passed to an entry point.futhark:Construct the C# array being returned from an entry point.futhark;Create a static array of values - initialised at load time.futhark&Copy from one memory block to another.futharkAllocate a memory block of the given size in the given memory space, saving a reference in the given variable name.futharkRead a scalar from the given memory block with the given index and in the given memory space.futharkWrite a scalar to the given memory block with the given index and in the given memory space.futharkA substitute expression compiler, tried before the main compilation function.futharkA set of operations that fail for every operation involving non-default memory spaces. Uses plain pointers and malloc for memory management.futhark7A constructor that takes no arguments and does nothing.futharkA  where the function is a variable and every argument is a simple .futhark A CallMethodfuthark#The ctypes type corresponding to a .futhark#The ctypes type corresponding to a , taking sign into account.+futharkSelect function to retrieve bytes from byte array as specific data type | The ctypes type corresponding to a .+futhark#The ctypes type corresponding to a .futhark#The ctypes type corresponding to a .futhark+Public names must have a consistent prefix.NoneNoneNone?None GfutharkPrelude embedded as ) values, one for every file.None2>?(futharkThe program described by a single Futhark file. May depend on other files.futharkA top-level binding.futhark)The contents of another file as a module.futharkFunctor application.futharkA type refinement.futharkAbstract type.futhark%A type parameter that must be a size.futhark%A type parameter that must be a type.futhark,The liftedness of a type parameter. By the Ord instance, Unlifted < SizeLifted < Lifted.futharkMay only be instantiated with a zero-order type of (possibly symbolically) known size.futharkMay only be instantiated with a zero-order type, but the size can be varying.futhark+May be instantiated with a functional type.futharkType DeclarationsfutharkFunction DeclarationsfutharkJust if this function is an entry point. If so, it also contains the externally visible interface. Note that this may not strictly be well-typed after some desugaring operations, as it may refer to abstract types that are no longer in scope.futharkInformation about the external interface exposed by an entry point. The important thing is that that we remember the original source-language types, without desugaring them at all. The annoying thing is that we do not require type annotations on entry points, so the types can be either ascribed or inferred.futharkPart of the type of an entry point. Has an actual type, and maybe also an ascribed type expression.futhark1Documentation strings, including source location.futharkA pattern as used most places where variables are bound (function parameters, let expressions, etc). futharkWhether the loop is a for -loop or a while-loop. futharkA case in a match expression. futharkAn entry in a record literal. futhark The Futhark expression language.In a value of type Exp f vn*, annotations are wrapped in the functor f, and all names are of type vn.This allows us to encode whether or not the expression has been type-checked in the Haskell type of the expression. Specifically, the parser will produce expressions of type Exp ! ., and the type checker will convert these to Exp ! , in which type information is always present and all names are unique. futharkA polymorphic integral literal. futharkA polymorphic decimal literal. futhark?A string literal is just a fancy syntax for an array of bytes. futharkA parenthesized expression. futharkTuple literals, e.g., {1+3, {x, y+z}}. futharkRecord literals, e.g.  {x=2,y=3,z}. futharkArray literals, e.g., [ [1+x, 3], [2, 1+4] ]7. Second arg is the row type of the rows of the array. futharkType ascription: e : t. futharkSize coercion: e :> t. futharkThe  Maybe VName is a possible existential size that is instantiated by this argument..The [VName] are the existential sizes that come into being at this call site. futhark;Numeric negation (ugly special case; Haskell did it first). futhark+0; first two types are operands, third is result. futhark2+*; first type is operand, second is result. futhark+2*; first type is operand, second is result. futharkField projection as a section: (.x.y.z). futharkArray indexing as a section: (.[i,j]). futharkExplore the Danger Zone and elide safety checks on array operations and other assertions during execution of this expression. Make really sure the code is correct. futharkFail if the first expression does not return true, and return the value of the second expression if it does. futharkAn n-ary value constructor. futharkA match expression. futhark6A name qualified with a breadcrumb of module accesses. futhark"An indexing of a single dimension. futhark&Whether a bound for an end-point of a  / or a range literal is inclusive or exclusive. futhark%May be "down to" if step is negative. futharkDefault binary operators. futharkA pseudo-operator standing in for any normal identifier used as an operator (they all have the same fixity). Binary Ops for Numbers futhark |> futhark<| Misc futharkAn identifier consists of its name and the type of the value bound to the identifier. futharkSimple Futhark values. Values are fully evaluated and their type is always unambiguous. futharkIt is assumed that the array is 0-indexed. The type is the full type. futhark;Information about which parts of a value/type are consumed. futhark$Consumes these fields in the record. futhark?A function that consumes its argument(s) like this. The final   should always be  , as there is no way for a function to consume its return value. futharkConsumes this value. futhark8Only observes value in this position, does not consume. futhark'A declaration of the type of something. futharkThe type declared by the user. futhark%The type deduced by the type checker. futharkAn unstructured type with type variables and possibly shape declarations - this is what the user types in the source program. futhark0A dimension declaration expression for use in a  . futharkThe size of the dimension is this name, which must be in scope. futharkThe size is a constant. futharkNo dimension declaration. futhark6A value type contains full, manifest size information. futharkA "structural" type with shape annotations and no aliasing information, used for declarations. futharkA type with aliasing information and shape annotations, used for describing the type patterns and expressions. futharkAliasing for a type, which is a set of the variables that are aliased. futharkA variable that is aliased. Can be still in-scope, or have gone out of scope and be free. In the latter case, it behaves more like an equivalence class. See uniqueness-error18.fut for an example of why this is necessary.!futharkAn expanded Futhark type is either an array, or something that can be an element of an array. When comparing types for equality, function parameter names are ignored. This representation permits some malformed types (arrays of functions), but importantly rules out arrays-of-arrays.!futharkTypes that can be elements of arrays. This representation does allow arrays of records of functions, which is nonsensical, but it convolutes the code too much if we try to statically rule it out.!futharkThe aliasing corresponds to the lexical closure of the function.!futhark0The name (if any) of a function parameter. The * and *5 instances always compare values of this type equal.!futhark?A type name consists of qualifiers (for error messages) and a  (for equality checking).!futharkThe size of an array type is a list of its dimension sizes. If )3, that dimension is of a (statically) unknown size.!futhark Declaration of a dimension size.!futharkThe size of the dimension is this name, which must be in scope. In a return type, this will give rise to an assertion.!futharkThe size is a constant.!futharkNo dimension declaration.!futhark unifyDims x y combines x and y to contain their maximum common information, and fails if they conflict.!futharkNon-array values.!futharkLow-level primitive types.!futharkSome information. The dual to !!futharkNo information functor. Usually used for placeholder type- or aliasing information.!futharkConvenience class for deriving * instances for the AST.!futhark.The number of dimensions contained in a shape.!futharkstripDims n shape strips the outer n dimensions from shape , returning )3 if this would result in zero or fewer dimensions.!futharkunifyShapes x y combines x and y to contain their maximum common information, and fails if they conflict. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! !!!!!!!!! !!!!!!!  !!!!!!! None>?J"futhark8A case (of a match expression) with no type annotations."futhark+A Futhark program with no type annotations."futhark'A declaration with no type annotations."futhark0A function declaration with no type annotations."futhark#A pattern with no type annotations."futhark*A type parameter with no type annotations."futhark2A module type expression with no type annotations."futhark-A module expression with no type annotations."futhark'An expression with no type annotations."futhark"An index with no type annotations."futhark'An identifier with no type annotations."futhark)A type declaration with no expanded type."futhark:A type with no aliasing information but shape annotations."futharkThe nature of something predefined. These can either be monomorphic or overloaded. An overloaded builtin is a list valid types it can be instantiated with, to the parameter and result type, with ), representing the overloaded parameter type."futhark Where does this dimension occur?#futharkImmediately in the argument to #.#futharkIn a function parameter type.#futharkIn a function return type.#futharkReturn the dimensionality of a type. For non-arrays, this is zero. For a one-dimensional array it is one, for a two-dimensional it is two, and so forth.#futhark5Return the shape of a type - for non-arrays, this is *.#futharkReturn any shape declarations in the type, with duplicates removed.#futhark*Change the shape of a type to be just the Rank.#futhark"Add size annotations that are all !.#futhark"Change all size annotations to be !.#futharkPerform a traversal (possibly including replacement) on sizes that are parameters in a function type, but also including the type immediately passed to the function.#futharkFigure out which of the sizes in a parameter type must be passed explicitly, because their first use is as something else than just an array dimension. # is like this function, but first decomposes into parameter types.#futharkFigure out which of the sizes in a binding type must be passed explicitly, because their first use is as something else than just an array dimension.#futhark Return the uniqueness of a type.#futharkunique t is *' if the type of the argument is unique.#futharkReturn the set of all variables mentioned in the aliasing of a type.#futharkdiet t< returns a description of how a function parameter of type t might consume its argument.#futharkConvert any type to one that has rank information, no alias information, and no embedded names.#futhark(Remove aliasing information from a type.#futhark,Replace no aliasing with an empty alias set.#futhark peelArray n t4 returns the type resulting from peeling the first n array dimensions from t . Returns Nothing if t has less than n dimensions.#futhark arrayOf t s u constructs an array type. The convenience compared to using the ! constructor directly is that t can itself be an array. If t is an n-dimensional array, and s is a list of length n, the resulting type is of an n+m6 dimensions. The uniqueness of the new array will be u, no matter the uniqueness of t.#futharkstripArray n t removes the n outermost layers of the array. Essentially, it is the type of indexing an array of type t with n indexes.#futharkCreate a record type corresponding to a tuple with the given element types.#futhark+Does this record map correspond to a tuple?#futhark0Construct a record map corresponding to a tuple.#futhark1Increasing field names for a tuple (starts at 0).#futharkSort fields by their name; taking care to sort numeric fields by their numeric value. This ensures that tuples and tuple-like records match.#futharkCombine the shape information of types as much as possible. The first argument is the orignal type and the second is the type of the transformed expression. This is necessary since the original type may contain additional information (e.g., shape restrictions) from the user given annotation.#futhark6Match the dimensions of otherwise assumed-equal types.#futharkSet the uniqueness attribute of a type. If the type is a record or sum type, the uniqueness of its components will be modified.#futharkt `setAliases` als returns t , but with als/ substituted for any already present aliasing.#futharkt `addAliases` f returns t5, but with any already present aliasing replaced by f applied to that aliasing.#futharkThe type of a basic value.#futharkThe type of the value.#futhark*The size of values of this type, in bytes.#futhark Construct a ! with the given number of ! dimensions.#futharkThe type is leaving a scope, so clean up any aliases that reference the bound variables, and turn any dimensions that name them into AnyDim instead.#futhark:Perform some operation on a given record field. Returns ) if that field does not exist.#futharkThe type of an Futhark term. The aliasing will refer to itself, if the term is a non-tuple-typed variable.#futharkExtract the parameter types and return type from a type. If the type is not an arrow type, the list of parameter types is empty.#futhark#The type names mentioned in a type.#futhark orderZero t is * if the argument type has order 0, i.e., it is not a function type, does not contain a function type as a subcomponent, and may not be instantiated with a function type.#futhark:Extract all the shape names that occur in a given pattern.#futhark7Extract all the shape names that occur in a given type.#futharkpatternOrderZero pat is *8 if all of the types in the given pattern have order 0.#futhark*The set of identifiers bound in a pattern.#futhark$The set of names bound in a pattern.#futhark8A mapping from names bound in a map to their identifier.#futhark(The type of values bound by the pattern.#futharkThe type matched by the pattern, including shape declarations if present.#futharkWhen viewed as a function parameter, does this pattern correspond to a named parameter of some type?#futharkNames of primitive types to types. This is only valid if no shadowing is going on, but useful for tools.#futharkA map of all built-ins.#futharkThe largest tag used by an intrinsic - this can be used to determine whether a / refers to an intrinsic or a user-defined name.#futhark-Create a name with no qualifiers from a name.#futhark8Add another qualifier (at the head) to a qualified name.#futhark2Create a type name name with no qualifiers from a .#futhark*The modules imported by a Futhark program.#futhark-The modules imported by a single declaration.#futharkThe set of module types used in any exported (non-local) declaration.#futharkExtract a leading $((name, namespace, file), remainder) from a documentation comment string. These are formatted as `name`@namespace[@file]. Let us hope that this pattern does not occur anywhere else.#futharkGiven an operator name, return the operator that determines its syntactical properties.!!"""""""""""""""""""""###################################################################""""""#################################################"##################!!""""""""""""""None>?P#futharkClass for type constructors that represent annotations. Used in the prettyprinter to either print the original AST, or the computed attribute.#futharkExtract value, if any.#futharkA class for types that are variable names in the Futhark source language. This is used instead of a mere ) instance because in the compiler frontend we want to print VNames differently depending on whether the FUTHARK_COMPILER_DEBUGGING environment variable is set, yet in the backend we want to always print VNames with the tag. To avoid erroneously using the ) instance for VNames, we in fact only define it inside the modules for the core language (as an orphan instance).#futharkDepending on the environment variable FUTHARK_COMPILER_DEBUGGING, VNames are printed as either the name with an internal tag, or just the base name.############None QS#futharkA lexical token. It does not itself contain position information, so in practice the parser will consume tokens tagged with a source position.$futhark&A value tagged with a source location.+futhark+Suffix a zero if the last character is dot.#$$#$$$$$$$$$$$$$$$$$$$$$$$$$$$$#############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+None >Sw$futharkA parse error. Use +% to get a human-readable description.+futharkParse an Futhark expression incrementally from monadic actions, using the +' as the source name for error messages.$futharkParse either an expression or a declaration incrementally; favouring declarations in case of ambiguity. $$++++++++$+9 +9 NoneV$futhark/Parse an entire Futhark program from the given ) , using the +' as the source name for error messages.$futhark+Parse an Futhark expression from the given ) , using the +' as the source name for error messages.$futhark1Parse a Futhark module expression from the given ) , using the +' as the source name for error messages.$futhark%Parse an Futhark type from the given ) , using the +' as the source name for error messages.$futhark'Parse any Futhark value from the given ) , using the +( as the source name for error messages.$futharkParse several Futhark values (separated by anything) from the given ) , using the +( as the source name for error messages.#$$#$$$$$$$$$$$$$$$$$$$$$$$$$$$$#############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#$$#$$$$$$$$$$$$$$$$$$$$$$$$$$$$#############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$None\+$futhark,A type-checked case (of a match expression).$futhark.A known scalar type with no shape annotations.$futharkA type-checked type parameter.$futhark(A known type arg with shape annotations.$futhark)An Futhark program with type information.$futharkA type-checked specification.$futharkA type-checked declaration.$futhark&A type-checked module type expression.$futhark A type-checked module parameter.$futhark!A type-checked module expression.$futhark#A type-checked module type binding.$futharkA type-checked module binding.$futhark%A type binding with type information.$futhark(A type declaration with type information$futhark.An constant declaration with type information.$futhark A pattern with type information.$futhark$An expression with type information.$futharkAn index with type information.$futhark2An identifier with type- and aliasing information.  !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""########################################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$Nonefd$futhark6Modules produces environment with this representation.$futharkType parameters, list of parameter types (optinally named), and return type. The type parameters are in scope in both parameter types and the return type. Non-functional values have only a return type.$futhark2A binding from a name to its definition as a type.$futhark Representation of a module type.$futhark"Abstract types in the module type.$futharkA parametric functor consists of a set of abstract types, the environment of its parameter, and the resulting module type.$futharkRepresentation of a module, which is either a plain environment, or a parametric module ("functor" in SML).$futhark0A mapping of abstract types to their liftedness.$futharkThe space inhabited by a name.$futharkFunctions and values.$futharkA mapping from import names to imports. The ordering is significant.$futharkThe result of type checking some file. Can be passed to further invocations of the type checker.$futharkAbstract types.%futharkCanonical reference to a Futhark code file. Does not include the .fut extension. This is most often a path relative to the current working directory of the compiler.%futharkCreate an import name immediately from a file path specified by the user.%futhark We resolve '..' paths here and assume that no shenanigans are going on with symbolic links. If there is, too bad. Don't do that.%futhark Create a .fut file corresponding to an %.%futhark7Produce a human-readable canonicalized string from an %.($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%$%%%%%%(%%%%%$$%$%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$None 567k +futharkA mapping from type parameters to the shapes of the value to which they were initially bound.+futharkA TermValue with a )! type annotation is an intrinsic.+futhark.A polymorphic value that must be instantiated.%futhark A fully evaluated Futhark value.+futharkA shape is a tree to accomodate the case of records. It is parameterised over the representation of dimensions.+futhark*The monad in which evaluation takes place.%futhark,Does the value correspond to an empty array?%futharkString representation of an empty array with the provided element type. This is pretty ad-hoc - don't expect good results unless the element type is a primitive.+futharkCreate an array value; failing if that would result in an irregular array.+futhark+, but with 0 as 1.+futharkExpand type based on information that was not available at type-checking time (the structure of abstract types).%futharkThe initial environment contains definitions of the various intrinsic functions.%futharkExecute the named function on the given arguments; may fail horribly if these are ill-typed.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%None?nH%futharkThe names that are bound for some types, either implicitly or explicitly.%futhark)Determine the names bound for some types.%futharkAs %>, but returns components of a top-level tuple type piecemeal.%futharkHow many core language values are needed to represent one source language value of the given type?%futhark7Convert an external primitive to an internal primitive.%futharkConvert an external primitive value to an internal primitive value. %%%%%%%%%% %%%%%%%%%%None?n%futhark%A function for internalising lambdas.%%%%%%%%%%%%None? +futharkDefunctionalization monad. The Reader environment tracks both the current Env as well as the set of globally defined dynamic functions. This is used to avoid unnecessarily large closure environments.+futharkEnvironment mapping variable names to their associated static value.+futharkA static value stores additional information about the result of defunctionalization of an expression, aside from the residual expression.+futharkThe .s are shape parameters that are bound by the $.+futharkThe constructor that is actually present, plus the others that are not.+futharkAn expression or an extended  ; (with size parameters, which AST lambdas do not support).+futharkReturns the defunctionalization environment restricted to the given set of variable names and types.+futharkRun a computation in the defunctionalization monad. Returns the result of the computation, a new name source, and a list of lifted function declations.+futharkLooks up the associated static value for a given name in the environment.+futharkDefunctionalization of an expression. Returns the residual expression and the associated static value in the defunctionalization monad.+futharkSame as +%, except it ignores the static value.+futharkDefunctionalize the function argument to a SOAC by eta-expanding if necessary and then defunctionalizing the body of the introduced lambda.+futhark8Defunctionalize an indexing of a single array dimension.+futharkDefunctionalize a let-bound function, while preserving parameters that have order 0 types (i.e., non-functional).+futharkDefunctionalize an application expression at a given depth of application. Calls to dynamic (first-order) functions are preserved at much as possible, but a new lifted function is created if a dynamic function is only partially applied.+futhark Check if a + and a given application depth corresponds to a fully applied dynamic function.+futharkConverts a dynamic function + into a list of dimensions, a list of parameters, a function body, and the appropriate static value for applying the function at the given depth of partial application.+futharkConverts a pattern to an environment that binds the individual names of the pattern to their corresponding types wrapped in a + static value.+futhark6Create an environment that binds the shape parameters.+futharkCreate a new top-level value declaration with the given function name, return type, list of parameters, and body expression.+futharkGiven a closure environment, construct a record pattern that binds the closed over variables.+futharkGiven a closure environment pattern and the type of a term, construct the type of that term, where uniqueness is set to  for those arrays that are bound in the environment or pattern (except if they are unique there). This ensures that a lifted function can create unique arrays as long as they do not alias any of its parameters. XXX: it is not clear that this is a sufficient property, unfortunately.+futhark8Compute the corresponding type for a given static value.+futharkConstruct the type for a fully-applied dynamic function from its static value and the original types of its arguments.+futharkMatch a pattern with its static value. Returns an environment with the identifier components of the pattern mapped to the corresponding subcomponents of the static value.+futharkGiven a pattern and the static value for the defunctionalized argument, update the pattern to reflect the changes in the types.+futharkConvert a record (or tuple) type to a record static value. This is used for "unwrapping" tuples and records that are nested in + static values.+futhark3Compute the set of free variables of an expression.+futhark2Extract all the variable names bound in a pattern.+futharkDefunctionalize a top-level value binding. Returns the transformed result as well as an environment that binds the name of the value binding to the static value of the transformed body. The boolean is true if the function is a +.+futhark1Defunctionalize a list of top-level declarations.%futharkTransform a list of top-level value bindings. May produce new lifted function definitions, which are placed in front of the resulting list of declarations.%%None?W+futharkFlatten a pattern. Returns a list of identifiers. The structural type of each identifier is returned separately.%%%%%%%%None %%%%%%%%% %%%%%%%%%None  %futhark$Two values differ in some way. The *1 instance produces a human-readable explanation.,futhark?The position the value number and a flat index into the array.%futharkA representation of the simple values we represent in this module.%futhark/An efficiently represented Futhark value. Use ? to get a human-readable representation, and the instances of , and ," to obtain binary representations&futharkAn Unboxed vector.&futharkA textual description of the type of a value. Follows Futhark type notation, and contains the exact dimension sizes if an array.,futharkA character that can be part of a value. This doesn't work for string and character literals.&futhark/Parse Futhark values from the given bytestring.,futharkA human-readable description of how two values are not the same.&futharkCompare two sets of Futhark values for equality. Shapes and types must also match.&futharkAs & , but only reports one mismatch.%%%%%%%%&&&%%&&&&&&&%%%%%&&&%%&&&&%%&&&%None ?!&futhark/The result expected from a succesful execution.&futharkThese values are expected.&futharkCompute expected values from executing a known-good reference implementation.&futhark)How a test case is expected to terminate.&futhark;Execution suceeds, with or without expected result values.&futhark Execution fails with this error.&futharkGenerate a value of the given rank and primitive type. Scalars are considered 0-ary arrays.&futhark'A fixed non-randomised primitive value.&futharkSeveral Values - either literally, or by reference to a file, or to be generated on demand.&futhark6A condition for execution, input, and expected result.&futharkA warning test requires that a warning matching the regular expression is produced. The program must also compile succesfully.&futharkA structure test specifies a compilation pipeline, as well as metrics for the program coming out the other end.&futhark!How a program can be transformed.&futhark'The error expected for a negative test.&futhark/Input and output pairs for some entry point(s).&futharkHow to test a program.&futharkDescription of a test to be carried out on a Futhark program. The Futhark program is stored separately.,futhark?A prettyprinted representation of type of value produced by a &.&futhark;Read the test specification from the given Futhark program.&futharkLike &!, but kills the process on error.,futharkRead test specifications from the given path, which can be a file or directory containing .fut files and further directories.&futharkRead test specifications from the given paths, which can be a files or directories containing .fut files and further directories.&futharkLike &", but kills the process on errors.&futhark7Try to parse a several values from a byte string. The )' parameter is used for error messages.&futhark6Get the actual core Futhark values corresponding to a & specification. The +9 is the directory which file paths are read relative to.&futhark(Extract a pretty representation of some &. In the IO monad because this might involve reading from a file. There is no guarantee that the resulting byte string yields a readable value.,futharkThere is a risk of race conditions when multiple programs have identical &. In such cases, multiple threads in 'futhark test' might attempt to create the same file (or read from it, while something else is constructing it). This leads to a mess. To avoid this, we create a temporary file, and only when it is complete do we move it into place. It would be better if we could use file locking, but that does not work on some file systems. The approach here seems robust enough for now, but certainly it could be made even better. The race condition that remains should mostly result in duplicate work, not crashes or data corruption.,futharkCompute the expected size of the file. We use this to check whether an existing file is broken/truncated.&futharkWhen/if generating a reference output file for this run, what should it be called? Includes the "data/" folder.&futhark;Get the values corresponding to an expected result, if any.&futhark&The name we use for compiled programs.&futharkEnsure that any reference output files exist, or create them (by compiling the program with the reference compiler and running it on the input) if necessary.&futharkDetermine the --tuning options to pass to the program. The first argument is the extension of the tuning file, or ) if none should be used.>%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&>&&&&&&&&&&&&&&&&%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%None ?o&futharkHow to compile a benchmark.&futharkHow to run a benchmark.&futhark1Transform benchmark results to a JSON bytestring.&futhark0Decode benchmark results from a JSON bytestring.&futhark3Run the benchmark program on the indicated dataset.&futhark'Compile and produce reference datasets.&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&None>3&futharkMap a monadic action across the immediate children of an object. Importantly, the & action is not invoked for the object itself, and the mapping does not descend recursively into subexpressions. The mapping is done left-to-right.&futharkExpress a monad mapping operation on a syntax node. Each element of this structure expresses the operation to be performed on a given child.'futharkAn && that just leaves its input unchanged.'futharkRemove all annotations from an expression, but retain the name/scope information. &&&&&&&'''' &&&&&''&&''None?3'futhark7Information about what is at the given source location.'futharkWhat a name is bound to.'futharkWhere was a bound variable actually bound? That is, what is the location of its definition?,futhark*All bindings of everything in the program.'futharkInformation about what's at the given source position. Returns ) if there is nothing there, including if the source position is invalid. .-'''''''''' ''''''''''.-None,futhark5A pairing of a lexical closure and a module function.,futharkA non-parametric module.,futharkA substitution from names in the original program to names in the generated/residual program.,futhark(A general-purpose substitution of names.''None%'futhark,The warnings produced by the compiler. The *1 instance produces a human-readable description.''''None ?'futhark$The type checker runs in this monad.'futhark0Information about an error during type checking.,futhark5A note with extra information regarding a type error.'futhark$The name of the current file/import.,futharkExtract from a type either a function type comprising a list of parameter types and a return type, or a first-order type.$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$$$$$'$$$$$$$$$$$$''''''$$$$''None >? 'futharkClass of types which allow for substitution of types with no annotations for type variable names.'futharkA type substituion may be a substitution or a yet-unknown substitution (but which is certainly an overloaded primitive type!). The latter is used to remove aliases from types that are yet-unknown but that we know cannot carry aliases (see issue #682).'futharkunifyTypes uf t1 t2 attempts to unify t1 and t2". If unification cannot happen, )> is returned, otherwise a type that combines the aliasing of t1 and t2* is returned. Uniqueness is unified with uf.'futharkx `subtypeOf` y is true if x is a subtype of y (or equal to y ), meaning x is valid whenever y is.'futharkx ' y is true if x is not less unique than y.(futharkCheck for duplication of names inside a pattern group. Produces a description of all names used in the pattern group.,futharkCheck whether the type contains arrow types that define the same parameter. These might also exist further down, but that's not really a problem - we mostly do this checking to help the user, since it is likely an error, but it's easy to assign a semantics to it (normal name shadowing).(futhark?ά,futharkA data type for constructor patterns. This is used to make the code for detecting unmatched constructors cleaner, by separating the constructor-pattern cases from other cases.,futharkAn unmatched pattern. Used in in the generation of unmatched pattern warnings by the type checker.,futharkThe state is a set of constraints and a counter for generating type names. This is distinct from the usual counter we use for generating unique names, as these will be user-visible.,futharkMapping function arguments encountered to the sizes they ended up generating (when they could not be substituted directly). This happens for function arguments that are not constants or names.,futharkWhat was the source of some existential size? This is used for using the same existential variable if the same source is encountered in multiple locations.,futhark=Type checking happens with access to this environment. The , will be extended during type-checking as bindings come into scope.,futhark4Aliases in parameters indicate the lexical closure.,futhark2Whether something is a global or a local variable.,futharkThe consumption set is a Maybe so we can distinguish whether a consumption took place, but the variable went out of scope since, or no consumption at all took place.,futharkA null occurence is one that we can remove without affecting anything.,futharkA seminull occurence is one that does not contain references to any variables in scope. The big difference is that a seminull occurence may denote a consumption, as long as the array that was consumed is now out of scope.,futharkGet the type of an expression, with top level type variables substituted. Never call #; directly (except in a few carefully inspected locations)!,futharkGet the type of an expression, with all type variables substituted. Slower than ,', but sometimes necessary. Never call #; directly (except in a few carefully inspected locations)!,futharkWrap '; to also perform an observation of every size in the type.,futharkInstantiate a type scheme with fresh type variables for its type parameters. Returns the names of the fresh type variables, the instance list, and the instantiated type.,futharkCreate a new type name and insert it (unconstrained) in the substitution map.,futharkDetermine if the two types of identical, ignoring uniqueness. Mismatched dimensions are turned into fresh rigid type variables. Causes a '; if they fail to match, and otherwise returns one of them.,futhark require ts e causes a ' if  expType e is not one of the types in ts. Otherwise, simply returns e.,futhark%returnType ret_type arg_diet arg_type gives result of applying an argument the given types to a function with the given return type, consuming the argument with the given diet.,futharkt , d removes aliases (sets them to *) from the parts of t% that are denoted as consumed by the   d.(futharkType-check a top-level (or module-level) function definition. Despite the name, this is also used for checking constant definitions, by treating them as 0-ary functions.,futharkThis is "fixing" as in "setting them", not "correcting them". We only make very conservative fixing.,futharkExtract all the shape names that occur in positive position (roughly, left side of an arrow) in a given type.,futhark5The set of in-scope variables that are being aliased.,futharkVerify certain restrictions on function parameters, and bail out on dubious constructions.These restrictions apply to all functions (anonymous or otherwise). Top-level functions have further restrictions that are checked during let-generalisation.,futharkFind at all type variables in the given type that are covered by the constraints, and produce type parameters that close over them.The passed-in list of type parameters is always prepended to the produced list of type parameters.,futhark?Proclaim that we have made read-only use of the given variable.,futhark4Proclaim that we have written to the given variable.,futharkProclaim that we have written to the given variable, and mark accesses to it and all of its aliases as invalid inside the given computation.,futharkMake all bindings nonunique.((((None J,futhark"All names defined anywhere in the $.)futhark,Refine the given type name in the given env.))))))))None ?)futharkType check a program containing no type information, yielding either a type error or a program with complete type information. Accepts a mapping from file names (excluding extension) to previously type checker results. The + is used to resolve relative imports.)futharkType check a single expression containing no type information, yielding either a type error or the same expression annotated with type information. Also returns a list of type parameters, which will be nonempty if the expression is polymorphic. See also ).)futharkType check a single declaration containing no type information, yielding either a type error or the same declaration annotated with type information along the Env produced by that declaration. See also ).)futharkType check a single module expression containing no type information, yielding either a type error or the same expression annotated with type information along the Env produced by that declaration. See also ).)futharkAn initial environment for the type checker, containing intrinsics and such.'')))))))))'')None ?!)futharkPre-typechecked imports, including a starting point for the name source.)futhark'Files that should be implicitly opened.,futhark?A little monad for reading and type-checking a Futhark program.)futharkA basis that contains no imports, and has a properly initialised name source.)futharkRead Futhark files from some basis, and printing log messages if the first parameter is True.,futharkRead and type-check a Futhark library (multiple files, relative to the same search path), including all imports.)futhark(Read and type-check Futhark imports (no .fut extension; may refer to baked-in prelude). This is an exotic operation that probably only makes sense in an interactive environment.$$$%$%'))))))))))$$$%$%'))))))None ?)futhark Warn if True.)futharkIf true, error on any warnings.)futharkIf True, ignore unsafe.)futhark=Read and type-check a Futhark program, including all imports.)futharkRead and type-check a collection of Futhark files, including all imports.)futhark-Not verbose, and terminates process on error.$$$%%$'))))))))))))))))))))) ))))))))))))) Safe-InferredP,,,,,,,,None=)futharkThe version of Futhark that we are using. This is equivalent to the version defined in the .cabal file.)futhark/The version of Futhark that we are using, as a )))))None)futharkA command line option that either purely updates a configuration, or performs an IO action (and stops).)futharkGenerate a main action that parses the given command line options (while always adding )).,futhark*Short-hand for 'liftIO . hPutStrLn stderr')futharkCommon definitions for -v and -h', given the list of all other options.))))))None޴)futhark,Are we compiling a library or an executable?)futhark2An option that modifies the configuration of type cfg.)futhark,Run a parameterised Futhark compiler, where cfg6 is a user-given configuration type. Call this from main.,futhark"The configuration of the compiler.)futharkInitial configuration.futhark&Options that affect the configuration.futhark,The short action name (e.g. "compile to C").futharkThe longer action description.futharkThe pipeline to use.futhark1The action to take on the result of the pipeline.futhark Program namefutharkCommand line arguments.))))))))))None?))None? ))None?-))None?P))None?s))None?ߖ))None?߹))None ?j,futhark/Extra options passed to the programs being run.,futhark>Exclude those test cases that have tags we do not wish to run.))None ?))None))None ,futhark$The monad in which futhark-pkg runs.,futhark5Install the packages listed in the build list in the lib directory of the current working directory. Since we are touching the file system, we are going to be very paranoid. In particular, we want to avoid corrupting the lib- directory if something fails along the way.The procedure is as follows:1) Create a directory 'lib~new'. Delete an existing 'lib~new' if necessary..2) Populate 'lib~new' based on the build list. 3) Rename lib; to 'lib~old'. Delete an existing 'lib~old' if necessary.4) Rename 'lib~new' to lib+5) If the current package has package path p#, move 'lib~old/p' to 'lib~new/p'.6) Delete 'lib~old'.Since POSIX at least guarantees atomic renames, the only place this can fail is between steps 3, 4, and 5. In that case, at least the 'lib~old' will still exist and can be put back by the user.))None?))))None9 ,futharkA human-readable description of the representation expected or contained, usable for error messages.,futharkNothing is distinct from a empty pipeline - it means we don't even run the internaliser.,futharkIf true, prints programs as raw ASTs instead of their prettyprinted form.,futhark3What to do with the program after it has been read.,futharkJust print it.,futhark(Run the type checker; print type errors.,futharkRun this pipeline.,futhark,Partially evaluate away the module language.,futharkDefunctorise and monomorphise.,futhark0Defunctorise, monomorphise, and defunctionalise.,futharkGet a Futhark pipeline from the configuration - an empty one if none exists.)futharkEntry point. Non-interactive, except when reading interpreter input from standard input.))None ,futharkClosed interval, as in  System.Random.))None ))None))None ?,futharkNumerically stable mean,futhark Standard deviation of population,futharkPopulation variance,futharkCentral moments))None ?P,futharkDepth-first list of thresholds to tune in order, and a corresponding assignment of ancestor thresholds to ensure that they are used.))None V,futharkWe keep a mapping of the names we have actually documented, so we can generate an index.,futharkLocal module types that show up in the interface. These should be documented, but clearly marked local.,futharkA set of names that we should not generate links to, because they are uninteresting. These are for example type parameters.,futharkThe header documentation (which need not be present) can contain an abstract and further sections.))None ~))None ?,futhark)Are we currently stopped at a breakpoint?,futhark$Skip breakpoints at these locations.,futharkThe currently loaded file.,futharkRepresentation of breaking at a breakpoint, to allow for navigating through the stack frames and such.,futhark>Index of the current breakpoint (with 0 being the outermost).)),                                                                                                                                                                                                                                                                                                                                                                                           ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 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$fEqBodyT $fShowBodyT $fOrdBodyT$fEqStm $fShowStm$fOrdStmnewDimnewDimsnewShape shapeCoerce repeatShapes repeatDims reshapeOuter reshapeInner shapeCoercion fuseReshape informReshape reshapeIndexunflattenIndex flattenIndex sliceSizes paramType paramDeclType paramIdent patElemIdent patElemTypesetPatElemLorepatternElements patternIdentspatternContextIdentspatternValueIdents patternNamespatternContextNamespatternValueNames patternTypespatternValueTypes patternSize basicPattern PrettyLore ppExpLore PrettyAnnotppAnnotbindingAnnotationppTuple'$fPrettyDimIndex$fPrettyDimChange$fPrettyErrorMsg$fPrettyBasicOp $fPrettyParam$fPrettyParam0$fPrettyParam1$fPrettyPatElemT$fPrettyPatElemT0$fPrettyPatternT$fPrettyCertificates$fPrettySubExp $fPrettyIdent$fPrettyTypeBase$fPrettyTypeBase0$fPrettyTypeBase1 $fPrettySpace$fPrettyShapeBase $fPrettyExt$fPrettyShapeBase0$fPrettyCommutativity$fPrettyNoUniqueness $fPrettyVName$fPrettyAnnot()$fPrettyAnnotParam$fPrettyAnnotPatElemT $fPrettyProg$fPrettyFunDef$fPrettyLambdaT $fPrettyExpT $fPrettyStm $fPrettyBodyT $fPrettySeq ExtendedScope SameScopeScopedscopeOf LocalScope localScopeHasScope lookupType lookupInfoaskScope asksScopeScopeNameInfoLetInfo FParamInfo LParamInfo IndexInfo inScopeOfscopeOfPatternscopeOfPatElemscopeOfLParamsscopeOfFParams castScope castNameInfo extendedScope$fTypedNameInfo$fHasScopeloreRWST$fHasScopeloreRWST0$fHasScopeloreExceptT$fHasScopeloreReaderT$fLocalScopeloreRWST$fLocalScopeloreRWST0$fLocalScopeloreReaderT$fLocalScopeloreExceptT$fScopedloreLambdaT$fScopedloreLoopForm$fScopedlore(,)$fScopedloreFunDef$fScopedloreStm$fScopedloreSeq$fScopedlore[]$fHasScopeloreExtendedScope$fFunctorExtendedScope$fApplicativeExtendedScope$fMonadExtendedScope$fMonadReaderMapExtendedScope$fShowNameInfoWalker walkOnSubExp walkOnBody walkOnVName walkOnRetTypewalkOnBranchType walkOnFParam walkOnLParamwalkOnOpMapper mapOnSubExp mapOnBody mapOnVName mapOnRetTypemapOnBranchType mapOnFParam mapOnLParammapOnOpidentityMappermapExpM mapOnLoopFormmapExp mapOnTypeidentityWalkerwalkExpMTypedOpopType subExpTypemapType primOpType expExtTypeexpExtTypeSize bodyExtType$fHasScopeloreFeelBad$fApplicativeFeelBad$fFunctorFeelBad $fTypedOp()FreeAttr precomputedFreeInfreeIn'FVNamesnameIn namesFromList namesToListoneNamenamesIntersectionnamesIntersect namesSubtractmapNamesfvBindfvNamefvNamesfreeInStmsAndResfreeIn boundInBody boundByStm boundByStms boundByLambda $fPrettyNames $fMonoidNames$fSemigroupNames $fSemigroupFV $fMonoidFV$fFreeInIfAttr$fFreeInStmAux$fFreeInCertificates$fFreeInPatternT$fFreeInDimIndex$fFreeInDimChange$fFreeInLoopForm$fFreeInPatElemT $fFreeInParam$fFreeInTypeBase $fFreeInExt$fFreeInShapeBase $fFreeInSpace$fFreeInSubExp $fFreeInIdent $fFreeInVName $fFreeInMaybe $fFreeInBool $fFreeInNames $fFreeInSeq $fFreeIn[] $fFreeIn(,,) $fFreeIn(,) $fFreeInInt $fFreeIn() $fFreeInFV$fFreeAttrMaybe $fFreeAttr[] $fFreeAttr(,) $fFreeAttr() $fFreeInStm $fFreeInExpT $fFreeInBodyT$fFreeInLambdaT$fFreeInFunDef $fEqNames $fShowNames NumThreadsCountunCount SizeClass SizeThreshold SizeGroup SizeNumGroupsSizeTileSizeLocalMemory SizeBespoke KernelPath$fPrettySizeClass$fTraversableCount$fFoldableCount$fFunctorCount $fEqCount $fOrdCount $fShowCount $fNumCount$fIntegralExpCount $fFreeInCount $fPrettyCount $fEqSizeClass$fOrdSizeClass$fShowSizeClassPrimExpLeafExpValueExpBinOpExpCmpOpExpUnOpExp ConvOpExpFunExpprimExpSizeAtLeastconstFoldPrimExp.&&..||..<..<=..==..>..>=..&..|..^. evalPrimExp primExpTypecoerceIntPrimExptruefalse leafExpTypes$fPrettyPrimExp$fIntegralExpPrimExp$fFractionalPrimExp $fNumPrimExp$fFreeInPrimExp$fTraversablePrimExp$fFoldablePrimExp$fFunctorPrimExp $fEqPrimExp $fOrdPrimExp $fShowPrimExp Substitutable SubstitutesubstituteNames Substitutions$fSubstituteFV$fSubstitutePrimExp$fSubstituteDimIndex$fSubstituteDimChange$fSubstituteIdent$fSubstituteTypeBase$fSubstituteNames$fSubstituteExt$fSubstituteShapeBase$fSubstitute()$fSubstituteRank$fSubstituteCertificates$fSubstitutePatternT$fSubstituteParam$fSubstituteStmAux$fSubstitutePatElemT$fSubstituteSubExp$fSubstituteVName$fSubstituteBool$fSubstituteMaybe$fSubstitute(,,,)$fSubstitute(,,)$fSubstitute(,)$fSubstituteSeq$fSubstitute[]$fSubstituteNameInfo$fSubstituteLambdaT$fSubstituteBodyT$fSubstituteStm$fSubstituteExpTleastGeneralGeneralization VNameSourcenewNameblankNameSource newNameSource$fMonoidVNameSource$fSemigroupVNameSource$fLiftLiftedRepVNameSource$fEqVNameSource$fOrdVNameSourceMonadFreshNames getNameSource putNameSourcemodifyNameSourcenewNameFromStringnewVNamenewIdent newIdent'newParam$fMonadFreshNamesExceptT$fMonadFreshNamesMaybeT$fMonadFreshNamesWriterT$fMonadFreshNamesWriterT0$fMonadFreshNamesReaderT$fMonadFreshNamesRWST$fMonadFreshNamesRWST0$fMonadFreshNamesStateT$fMonadFreshNamesStateT0 RenameableRenamerenameRenameM renameProg renameExp renameStm renameBody renameLambda renamePatternsubstituteRename renamingStms$fRenameDimIndex $fRename() $fRenameExt$fRenameShapeBase $fRenameRank $fRenameNames$fRenameTypeBase$fRenameStmAux$fRenameCertificates$fRenamePatElemT$fRenamePatternT $fRenameParam$fRenameSubExp $fRenameIdent $fRenameBool $fRenameMaybe $fRename(,,) $fRename(,) $fRename[] $fRenameVName$fRenameLambdaT $fRenameExpT $fRenameStm $fRenameBodyT$fRenameFunDef$fFunctorRenameM$fApplicativeRenameM$fMonadRenameM$fMonadFreshNamesRenameM$fMonadReaderRenameEnvRenameM AttributesexpTypesFromPatternIsOpsafeOpcheapOpisBuiltInFunctionbuiltInFunctions asBasicOpsafeExp subExpVars subExpVar shapeVarscommutativeLambdaentryPointSizedefAuxstmCertscertifyexpExtTypesFromPattern$fIsOp() CanBeAliased OpWithAliasesremoveOpAliases addOpAliases AliasedOp opAliases consumedInOp AliasesOf aliasesOfAliased bodyAliasesconsumedInBody vnameAliases subExpAliases primOpAliases expAliases consumedInStm consumedInExpconsumedByLambdapatternAliases$fAliasesOfPatElemT$fAliasesOfNames $fAliasedOp()$fCanBeAliased()Usages UsageTablewithoutlookupusedexpand isConsumed isInResultisUsedDirectlyusagesusage consumedUsage inResultUsage$fMonoidUsages$fSemigroupUsages$fSubstituteUsageTable$fMonoidUsageTable$fSemigroupUsageTable$fEqUsageTable$fShowUsageTable $fEqUsages $fOrdUsages $fShowUsages usageInStm RephraserrephraseExpLorerephraseLetBoundLorerephraseFParamLorerephraseLParamLorerephraseBodyLorerephraseRetTyperephraseBranchType rephraseOp rephraseProgrephraseFunDef rephraseExp rephraseStmrephrasePatternrephrasePatElem rephraseBodyrephraseLambdaMetricsM OpMetrics opMetrics AstMetricsseeninside progMetrics bodyMetricsbindingMetrics lambdaMetrics$fReadAstMetrics$fShowAstMetrics$fMonoidCountMetrics$fSemigroupCountMetrics $fOpMetrics()$fMonadMetricsM$fApplicativeMetricsM$fFunctorMetricsM!$fMonadWriterCountMetricsMetricsM DependenciesdataDependenciesfindNecessaryForReturned LookupVarScalExpValIdSNegSNotSAbsSPlusSMinusSTimesSPowMaxMinRelExpSLogAndSLogOrRelOp0LTH0LEQ0 scalExpType scalExpSizesubExpToScalExp toScalExp expandScalExp$fFreeInScalExp$fRenameScalExp$fSubstituteScalExp$fPrettyScalExp $fNumScalExp $fEqScalExp $fOrdScalExp $fShowScalExp $fEqRelOp0 $fOrdRelOp0 $fEnumRelOp0$fBoundedRelOp0 $fShowRelOp0 RangesRep ppRangesRepsimplify linFormScalE mkSuffConds pickSymToElim $fEqBTerm $fOrdBTerm $fShowBTerm $fEqNNumExp $fOrdNNumExp $fShowNNumExp CanBeRanged OpWithRangesremoveOpRanges addOpRangesRangedOpopRangesRangesOfrangesOfRangeOfrangeOfRanged ScalExpRangeRangeBound KnownBoundVarBound MinimumBound MaximumBound ScalarBoundboundToScalExp minimumBound maximumBound unknownRange expRanges$fPrettyKnownBound$fFreeAttrKnownBound$fFreeInKnownBound$fRenameKnownBound$fSubstituteKnownBound$fRangeOfSubExp$fRangeOfPatElemT $fRangeOf(,)$fRangesOfPatternT $fRangesOf[] $fRangedOp()$fRangesOfBodyT$fCanBeRanged()$fEqKnownBound$fOrdKnownBound$fShowKnownBoundRangesremoveProgRangesremoveExpRangesremoveBodyRangesremoveStmRangesremoveLambdaRangesremovePatternRangesaddRangesToPattern mkRangedBodymkPatternRanges mkBodyRanges$fAliasesOf(,)$fAliasesOf(,)0 $fRangesOf(,)$fAliasedRanges$fPrettyLoreRanges$fAttributesRanges$fAnnotationsRangesRangeM rangeAnalysis analyseFun analyseBody analyseStms analyseExp analyseLambda runRangeMPasspassNamepassDescription passFunctionPassMrunPassM liftEither liftEitherMpassLongOptionparPass'intraproceduralTransformationWithConstsintraproceduralTransformation$fMonadFreshNamesPassM$fMonadLoggerPassM$fFunctorPassM$fApplicativePassM $fMonadPassM MonadBinderLore mkExpAttrMmkBodyM mkLetNamesMaddStmaddStms collectStms certifyingBindablemkExpPat mkExpAttrmkBody mkLetNamesmkLetMletBindletBind_mkLet letBindNames letBindNames_ collectStms_bodyBind insertStms insertStmBinderBinderT BinderOps mkExpAttrBmkBodyB mkLetNamesBbindableMkExpAttrBbindableMkBodyBbindableMkLetNamesB runBinderT runBinderT_ runBinderT' runBinderT'_ runBinder runBinder_ joinBinder runBodyBinder addBinderStmscollectBinderStmscertifyingBinder$fMonadErroreBinderT$fMonadWriterwBinderT$fMonadStatesBinderT$fMonadReaderrBinderT$fMonadBinderBinderT$fLocalScopeloreBinderT$fHasScopeloreBinderT$fMonadFreshNamesBinderT$fMonadTransBinderT$fFunctorBinderT$fMonadBinderT$fApplicativeBinderTAliasesAndConsumed BodyAliasing ConsumedInExp VarAliasesNames'unNamesAliasesremoveScopeAliasesremoveProgAliasesremoveFunDefAliasesremoveExpAliasesremoveStmAliasesremoveLambdaAliasesremovePatternAliasesaddAliasesToPattern mkAliasedBodymkPatternAliases mkBodyAliasesconsumedInStms trackAliasesmkAliasedLetStm$fBinderOpsAliases$fAttributesAliases$fBindableAliases$fPrettyLoreAliases$fAliasedAliases$fFreeAttrNames'$fPrettyNames'$fFreeInNames'$fSubstituteNames'$fRenameNames' $fOrdNames' $fEqNames'$fMonoidNames'$fSemigroupNames'$fAnnotationsAliases $fShowNames' AliasTable aliasAnalysis CanBeWise OpWithWisdomremoveOpWisdom ExpWisdom VarWisdomvarWisdomAliasesvarWisdomRangeWiseremoveScopeWisdomaddScopeWisdomremoveFunDefWisdomremoveStmWisdomremoveLambdaWisdomremoveBodyWisdomremoveExpWisdomremovePatternWisdomaddWisdomToPattern mkWiseBody mkWiseLetStm mkWiseExpAttr$fFreeInVarWisdom$fSubstituteVarWisdom$fRenameVarWisdom$fRenameExpWisdom$fSubstituteExpWisdom$fFreeAttrExpWisdom$fFreeInExpWisdom$fFreeAttrBodyWisdom$fFreeInBodyWisdom$fSubstituteBodyWisdom$fRenameBodyWisdom $fCanBeWise()$fBindableWise $fAliasedWise$fPrettyLoreWise$fAttributesWise$fAnnotationsWise$fEqBodyWisdom$fOrdBodyWisdom$fShowBodyWisdom $fEqExpWisdom$fOrdExpWisdom$fShowExpWisdom $fEqVarWisdom$fOrdVarWisdom$fShowVarWisdomToExptoExp letSubExpletExp letInPlace letSubExps letTupExp letTupExp'eSubExpeIfeIf'eBinOpeCmpOpeConvOpeNoteSignumeCopyeAsserteBodyeLambdaeDivRoundingUpeRoundToMultipleOf eSliceArray eOutOfBounds eWriteArrayeBlankasIntSasIntZ foldBinOp binOpLambda cmpOpLambdasliceDim fullSlicesliceAt fullSliceNum isFullSliceifCommon resultBody resultBodyM insertStmsM mapResultinstantiateShapesinstantiateShapes'removeExistentialssimpleMkLetNames $fToExpVName $fToExpSubExp Checkable checkExpLore checkBodyLorecheckFParamLorecheckLParamLorecheckLetBoundLore checkRetType matchPattern primFParammatchReturnTypematchBranchType CheckableOpcheckOpTypeM Occurences TypeError ErrorCaseUnexpectedTypeReturnTypeErrorDupDefinitionError DupParamErrorDupPatternErrorInvalidPatternErrorUnknownVariableErrorUnknownFunctionErrorParameterMismatch SlicingError BadAnnotation ReturnAliasedUniqueReturnAliased NotAnArrayPermutationErrorbadcontextmessageconsumecollectOccurences checkOpWithconsumeOnlyParamsbinding lookupVar lookupAliasesrequirerequireI checkProg checkSubExp checkStms checkBodycheckExpcheckSOACArrayArgs checkType checkExtTypecheckStmmatchExtPatternmatchExtReturnTypematchExtBranchTypeargType argAliases noArgAliasescheckArg checkLambdarequirePrimExp$fMonoidConsumption$fSemigroupConsumption$fHasScopeAliasesTypeM$fShowTypeError$fShowErrorCase $fMonadTypeM$fFunctorTypeM$fApplicativeTypeM$fMonadReaderEnvTypeM$fMonadWriterConsumptionTypeM$fMonadStateNamesTypeM$fShowConsumption $fEqOccurence$fShowOccurence $fEqUsage $fOrdUsage $fShowUsagePipelinePipelineConfigpipelineVerbosepipelineValidateAction actionNameactionDescriptionactionProcedureFutharkM Verbosity NotVerboseVerbose VeryVerbose runFutharkMinternalErrorS runPassesonePasspasses$fMonadLoggerFutharkM$fMonadFreshNamesFutharkM$fCategoryTYPEPipeline$fApplicativeFutharkM$fFunctorFutharkM$fMonadFutharkM!$fMonadErrorCompilerErrorFutharkM $fMonadStateFutharkStateFutharkM$fMonadReaderFutharkEnvFutharkM$fMonadIOFutharkM $fEqVerbosity$fOrdVerbosityIndexSubstitutionsIndexSubstitutionsubstituteIndices shapeBody argShapesensureResultShapeensureResultExtShapeensureResultExtShapeNoCtxensureExtShape ensureShapeensureArgShapes primExpToExpprimExpToSubExpprimExpFromExpprimExpFromSubExpMprimExpFromSubExpreplaceInPrimExpMreplaceInPrimExpsubstituteInPrimExp$fToExpPrimExpIxFun ixfunLMADs ixfunContigsubstituteInIxFunisDirectshapeindexiotapermuterepeatrotateslicereshaperankrebase offsetIndexlinearWithOffsetrearrangeWithOffsetisLinear closeEnough$fPrettyMonotonicity$fTraversableLMAD$fFoldableLMAD $fFunctorLMAD $fFreeInLMAD $fRenameLMAD$fSubstituteLMAD $fPrettyLMAD$fTraversableIxFun$fFoldableIxFun$fFunctorIxFun $fFreeInIxFun $fRenameIxFun$fSubstituteIxFun $fPrettyIxFun $fShowIxFun $fEqIxFun $fShowLMAD$fEqLMAD $fShowLMADDim $fEqLMADDim$fShowMonotonicity$fEqMonotonicityIndexOpindexOpIndexed IndexedArray SymbolTable loopDepthbindingsavailableAtClosestLoopsimplifyMemory fromScopetoScopedeepenindexedAddCerts entryType asScalExp bindingDepth valueRangeentryStmentryLetBoundAttrelem lookupStm lookupExp lookupBasicOp lookupSubExp lookupScalExp availableindex' rangesRep insertFParams insertLParaminsertArrayLParam insertLoopVar updateBounds setUpperBound setLowerBound isAtLeasthideIf hideCertified$fFreeInIndexed$fMonoidSymbolTable$fSemigroupSymbolTable $fIndexOp() SOACMappermapOnSOACSubExpmapOnSOACLambdamapOnSOACVNameReduceredComm redLambda redNeutralScan ScremaForm StreamFormParallel SequentialHistOp histWidthhistRaceFactorhistDest histNeutralhistOpSOACStreamScatterHistScrema CmpThreshold redResults singleReduce scremaTypemkIdentityLambdaisIdentityLambdanilFn scanomapSOAC redomapSOACscanSOAC reduceSOACmapSOACisScanomapSOAC isScanSOAC isRedomapSOAC isReduceSOAC isMapSOACidentitySOACMappermapSOACMsoacType typeCheckSOACgetStreamAccumsgetStreamOrderppScremappHist$fPrettyReduce $fPrettySOAC$fOpMetricsSOAC $fIndexOpSOAC$fRangedOpSOAC $fIsOpSOAC$fAliasedOpSOAC $fTypedOpSOAC$fCanBeWiseSOAC$fCanBeRangedSOAC$fCanBeAliasedSOAC $fRenameSOAC$fSubstituteSOAC $fFreeInSOAC$fEqSOAC $fOrdSOAC $fShowSOAC$fEqScremaForm$fOrdScremaForm$fShowScremaForm $fEqReduce $fOrdReduce $fShowReduce$fEqStreamForm$fOrdStreamForm$fShowStreamForm $fEqHistOp $fOrdHistOp $fShowHistOpnonuniqueParamsredomapToMapAndReduce dissectScremasequentialStreamWholeArraypartitionChunkedFoldParameters$partitionChunkedKernelFoldParametersSOACS$fPrettyLoreSOACS$fBinderOpsSOACS$fBindableSOACS$fCheckableSOACS$fCheckableOpSOACS$fAttributesSOACS$fAnnotationsSOACS TransformertransformFunDef transformStms transformBodytransformStmRecursively transformSOACtransformLambdaiswimirwim rwimPossible TryFusion tryFusion liftMaybe$fFunctorTryFusion$fApplicativeTryFusion$fAlternativeTryFusion$fMonadTryFusion$fMonadFailTryFusion$fMonadFreshNamesTryFusion$fHasScopeSOACSTryFusion$fLocalScopeSOACSTryFusionInternaliseTypeMDimTable InternaliseMInternaliseEnv envSubstsenvDoBoundsChecksenvSafeVarSubstitutionsFunInfoClosurerunInternaliseMsubstitutingVars lookupSubst addFunDeflookupFunction'lookupFunction lookupConst allConsts bindFunction bindConstantlocalConstsScope asserting assertingOneliftInternaliseMrunInternaliseTypeMwithDims lookupDim$fMonoidInternaliseResult$fSemigroupInternaliseResult$fMonadBinderInternaliseM$fFunctorInternaliseTypeM$fApplicativeInternaliseTypeM$fMonadInternaliseTypeM$$fMonadReaderTypeEnvInternaliseTypeM$fMonadStateIntInternaliseTypeM$fFunctorInternaliseM$fApplicativeInternaliseM$fMonadInternaliseM'$fMonadReaderInternaliseEnvInternaliseM($fMonadStateInternaliseStateInternaliseM$fMonadFreshNamesInternaliseM$fHasScopeSOACSInternaliseM$fLocalScopeSOACSInternaliseM CallGraphisFunInCallGraphcallscalledByConsts allCalledBybuildCallGraphHostOpSegOpSizeOpOtherOp SplitSpaceGetSize GetSizeMax CmpSizeLe CalcNumGroups SegOpMappermapOnSegOpSubExpmapOnSegOpLambdamapOnSegOpBodymapOnSegOpVNameSegMapSegRedSegScanSegHistSegSpacesegFlat unSegSpaceSegLevel SegThreadSegGroup segNumGroups segGroupSizesegVirtSegVirt SegNoVirt KernelResultReturns WriteReturns ConcatReturns TileReturnsResultManifestResultNoSimplifyResultMaySimplify ResultPrivate KernelBodykernelBodyLorekernelBodyStmskernelBodyResultSegRedOp segRedComm segRedLambda segRedNeutral segRedShape histShape SplitOrderingSplitContiguous SplitStridedhistType segRedResultskernelResultSubExpaliasAnalyseKernelBodyconsumedInKernelBody segSpaceDimsscopeOfSegSpacesegLevelsegSpacetypeCheckSegOpidentitySegOpMapper mapSegOpMtypeCheckHostOp$fRenameSplitOrdering$fSubstituteSplitOrdering$fFreeInSplitOrdering$fPrettyKernelResult$fRenameKernelResult$fSubstituteKernelResult$fFreeInKernelResult$fPrettyKernelBody$fRenameKernelBody$fSubstituteKernelBody$fFreeInKernelBody$fPrettySegLevel$fPrettySegSpace $fIsOpSegOp$fIndexOpSegOp$fRangedOpSegOp $fPrettySegOp$fOpMetricsSegOp$fAliasedOpSegOp$fTypedOpSegOp$fCanBeWiseSegOp$fCanBeAliasedSegOp$fCanBeRangedSegOp $fFreeInSegOp $fRenameSegOp$fSubstituteSegOp$fOpMetricsSizeOp$fPrettySizeOp$fFreeInSizeOp$fRangedOpSizeOp$fAliasedOpSizeOp$fTypedOpSizeOp $fIsOpSizeOp$fRenameSizeOp$fSubstituteSizeOp$fOpMetricsHostOp$fPrettyHostOp$fIndexOpHostOp$fCanBeWiseHostOp$fCanBeRangedHostOp$fCanBeAliasedHostOp$fFreeInHostOp$fRangedOpHostOp$fAliasedOpHostOp$fTypedOpHostOp $fIsOpHostOp$fRenameHostOp$fSubstituteHostOp $fEqHostOp $fOrdHostOp $fShowHostOp $fEqSizeOp $fOrdSizeOp $fShowSizeOp $fEqSegOp $fOrdSegOp $fShowSegOp $fEqSegSpace $fOrdSegSpace$fShowSegSpace $fEqSegLevel $fOrdSegLevel$fShowSegLevel $fEqSegVirt $fOrdSegVirt $fShowSegVirt$fEqKernelResult$fShowKernelResult$fOrdKernelResult$fEqResultManifest$fShowResultManifest$fOrdResultManifest $fEqSegRedOp $fOrdSegRedOp$fShowSegRedOp$fEqSplitOrdering$fOrdSplitOrdering$fShowSplitOrdering$fEqKernelBody$fShowKernelBody$fOrdKernelBodyKernels$fPrettyLoreKernels$fBinderOpsKernels$fBindableKernels$fCheckableKernels$fCheckableOpKernels$fAttributesKernels$fAnnotationsKernelsbabysitKernelsnonlinearInMemoryfirstOrderTransform KernelInputkernelInputNamekernelInputTypekernelInputArraykernelInputIndices MkSegLevelThreadRecommendation ManyThreadsNoRecommendationgetSize segThreadsegThreadCapped mkSegSpacesegRedsegScansegMap nonSegRed streamRed streamMapsegHist mapKernelreadKernelInputsoacsStmToKernelssoacsLambdaToKernels scopeForSOACsscopeForKernels$fShowKernelInput$fEqKernelSize$fOrdKernelSize$fShowKernelSize KernelNestNestingsNestingnestingLetBound nestingLoop LoopNesting MapNestingloopNestingPatternloopNestingCertificatesloopNestingWidthloopNestingParamsAndArrsTargetsTarget ppTargets singleTarget outerTarget innerTargetpushInnerTargetpopInnerTarget targetsScope ppLoopNesting ppNestings singleNestingpushInnerNestingletBindInInnerNesting ppKernelNestpushKernelNestingpushInnerKernelNesting newKernelkernelNestLoopsboundInKernelNestboundInKernelNestskernelNestWidthsconstructKernel flatKernel tryDistributetryDistributeStm$fFreeInLoopNesting$fScopedKernelsLoopNesting $fShowNesting$fShowLoopNestingBranchSeqLoopinterchangeLoopsinterchangeBranchunstream tileLoops$fMonoidPrivStms$fSemigroupPrivStms LowerUpdate DesiredUpdate updateName updateTypeupdateCertificates updateSource updateIndices updateValuelowerUpdateKernels$fFunctorDesiredUpdate$fShowLoopResultSummary$fShowDesiredUpdateinPlaceLowering$fMonoidBottomUp$fSemigroupBottomUp$fHasScopeAliasesForwardingM$fMonadFreshNamesForwardingM$fMonadForwardingM$fApplicativeForwardingM$fFunctorForwardingM$fMonadReaderTopDownForwardingM $fMonadWriterBottomUpForwardingM"$fMonadStateVNameSourceForwardingMsinkRuleBook BottomUpRuleBottomUpRuleOpBottomUpRuleDoLoopBottomUpRuleIfBottomUpRuleBasicOpBottomUpRuleGenericBottomUp TopDownRule TopDownRuleOpTopDownRuleDoLoop TopDownRuleIfTopDownRuleBasicOpTopDownRuleGenericTopDownSimplificationRule RuleGeneric RuleBasicOpRuleIf RuleDoLoopRuleOpRuleSimplifySkipRuleMcannotSimplifyruleBooktopDownSimplifyStmbottomUpSimplifyStm$fMonadBinderRuleM$fMonadFailRuleM $fMonoidRules$fSemigroupRules$fMonoidRuleBook$fSemigroupRuleBook$fFunctorRuleM$fApplicativeRuleM $fMonadRuleM$fMonadFreshNamesRuleM$fHasScopeloreRuleM$fLocalScopeloreRuleM$fMonadErrorRuleErrorRuleM VarLookupfoldClosedFormloopClosedForm standardRulesremoveUnnecessaryCopy SimplifiableSimplifiableLoreSimplifiedBody BlockPredSimpleM SimplifyOp SimpleOps mkExpAttrSmkBodyS mkLetNamesSprotectHoistedOpS simplifyOpSEnvenvRulesenvHoistBlockers HoistBlockers blockHoistPar blockHoistSeqblockHoistBranch getArraySizes isAllocationnoExtraHoistBlockersemptyEnvbindableSimpleOps runSimpleM asksEngineEnv askVtable localVtable bindLParams hoistStms neverBlocksisFalseorIfisOpblockIfhasFree isNotSafe simplifyBody simplifyStms simplifyParamsimplifyLambdasimplifyLambdaNoHoisting simplifyFun$fMonadFreshNamesSimpleM$fSimplifiableCertificates$fSimplifiableDimIndex$fSimplifiableTypeBase$fSimplifiableSpace$fSimplifiableExt$fSimplifiableShapeBase$fSimplifiableVName$fSimplifiableSubExp$fSimplifiable[]$fSimplifiableMaybe$fSimplifiableInt$fSimplifiable(,,)$fSimplifiable(,)$fLocalScopeWiseSimpleM$fHasScopeWiseSimpleM$fApplicativeSimpleM$fFunctorSimpleM$fMonadSimpleM$fMonadReader(,)SimpleM$fMonadState(,,)SimpleMsimplifyPrimExpsimplifyExtPrimExp FunReturns BodyReturns ExpReturns MemReturnReturnsInBlockReturnsNewBlockMemBindArrayInMemBoundMemInfoMemPrimMemMemMemArrayExtIxFunMemOpAllocInnerExplicitMemorishExplicitMemory isStaticIxFunexistentialiseIxFunnoUniquenessReturnsbodyReturnsToExpReturns lookupMemInfo subExpMemInfolookupArraySummary extReturns expReturns sliceInfo$fPrettyLoreExplicitMemory$fAttributesExplicitMemory$fCheckableOpExplicitMemory$fIndexOpMemOp$fCanBeWiseMemOp $fIsOpMemOp$fOpMetricsMemOp $fPrettyMemOp$fSubstituteMemOp $fRenameMemOp$fCanBeRangedMemOp$fRangedOpMemOp$fCanBeAliasedMemOp$fAliasedOpMemOp$fTypedOpMemOp $fFreeInMemOp$fCheckableExplicitMemory$fPrettyMemInfo$fSimplifiableMemInfo$fRenameMemInfo$fSubstituteMemInfo$fFreeInMemInfo$fDeclTypedMemInfo$fTypedMemInfo$fTypedMemInfo0$fFixExtMemInfo$fExtTypedMemInfo$fDeclExtTypedMemInfo$fSimplifiableMemBind$fFreeInMemBind$fPrettyMemBind$fSubstituteMemBind$fRenameMemBind $fOrdMemBind $fEqMemBind$fSimplifiableMemReturn$fFreeInMemReturn$fPrettyMemReturn$fFixExtMemReturn$fSubstituteMemReturn$fRenameMemReturn$fOrdMemReturn $fEqMemReturn$fIsBodyTypeMemInfo$fAnnotationsExplicitMemory$fIsRetTypeMemInfo$fOpReturnsExplicitMemory$fShowMemReturn $fShowMemBind $fEqMemInfo $fShowMemInfo $fOrdMemInfo $fEqMemOp $fOrdMemOp $fShowMemOparraySizeInBytesExpexplicitAllocationsexplicitAllocationsInStms simplifiable$fBinderOpsWise$fBinderOpsExplicitMemory$fSizeSubstMemOp$fSizeSubstHostOp"$fAllocatorExplicitMemoryPatAllocM$fAllocatorExplicitMemoryAllocM$fMonadBinderAllocM$fApplicativeAllocM$fFunctorAllocM $fMonadAllocM$fMonadFreshNamesAllocM$fHasScopetoloreAllocM$fLocalScopetoloreAllocM$fMonadReaderAllocEnvAllocM$fApplicativePatAllocM$fFunctorPatAllocM$fMonadPatAllocM$fHasScopelorePatAllocM$fMonadWriter[]PatAllocM$fMonadFreshNamesPatAllocM $fEqAllocStm $fOrdAllocStm$fShowAllocStm doubleBuffer'$fLocalScopeExplicitMemoryDoubleBufferM%$fHasScopeExplicitMemoryDoubleBufferM$fShowDoubleBuffer$fFunctorDoubleBufferM$fApplicativeDoubleBufferM$fMonadDoubleBufferM$fMonadReaderEnvDoubleBufferM$fMonadFreshNamesDoubleBufferMCSEInOp performCSEperformCSEOnFunDefperformCSEOnStms $fCSEInOpSOAC$fCSEInOpMemOp$fCSEInOpSegOp$fCSEInOpHostOp $fCSEInOp() simplifyProgsimplifySomethingcopyPropagateInProgcopyPropagateInStmscopyPropagateInFun simpleSOACS simplifySOACSsimplifyConsts simplifySOAC soacRules $fEqArrayOp $fOrdArrayOp $fShowArrayOp DistNestTDistAcc distTargetsdistStmsDistEnvdistNest distScopedistOnTopLevelStmsdistOnInnerMap distSegLevel KernelsStmsMapLoop mapLoopStmpostKernelsStmsaddStmsToKerneladdStmToKernel runDistNestT addKernels addKernel inNestingbodyContainsParallelismlambdaContainsParallelismincrementalFlatteningdistributeMapBodyStms distributedistributeSingleStm histKerneldetermineReduceOppermutationAndMissing distributeMap$fMonoidPostKernels$fSemigroupPostKernels$fMonoidDistRes$fSemigroupDistRes$fMonadLoggerDistNestT$fLocalScopeKernelsDistNestT$fHasScopeKernelsDistNestT$fMonadFreshNamesDistNestT$fMonadTransDistNestT$fFunctorDistNestT$fApplicativeDistNestT$fMonadDistNestT$fMonadReaderDistEnvDistNestT$fMonadWriterDistResDistNestTintraGroupParallelise 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checkNamedDim typeError ImportTableNotesaNoteunexpectedType undefinedTypeunappliedFunctorunknownVariableError underscoreUserunTypeM askImportName lookupMTy lookupImport checkName bindSpacedcheckQualNameWithEnvqualifyTypeVars badOnLeft anySignedTypeanyUnsignedType anyIntType anyFloatType anyNumberType anyPrimTypeintrinsicsNameMaptopLevelNameMap $fPrettyNote $fPrettyNotes$fPrettyTypeError$fMonadTypeCheckerTypeM$fMonadReaderContextTypeM$fMonadWriterWarningsTypeM$fMonadStateVNameSourceTypeM$fMonadErrorTypeErrorTypeM$fSemigroupNotes $fMonoidNotes applySubstSubst PrimSubst SizeSubstTypeSubsTypeSubDimSub unifyTypesU subuniqueOf checkTypeDecl checkTypeExpcheckForDuplicateNamescheckTypeParamstypeParamToArgsubstituteTypes substTypesAny$fFunctorSubst$fSubstitutablePatternBase$fSubstitutableShapeDecl$fSubstitutableDimDecl$fSubstitutableTypeBase$fSubstitutableTypeBase0 $fShowSubst $fShowTypeSub MonadUnifygetConstraintsputConstraintsmodifyConstraints newTypeVar newDimVarcurLevel matchError unifyErrorRigidityRigidNonrigid RigidSourceRigidArgRigidRet RigidLoop RigidSlice RigidRange RigidBound RigidCond RigidUnifyRigidOutOfScope Constraints Constraint NoConstraint ParamType Overloaded HasFieldsEquality HasConstrs ParamSizeSizeUnknowableSizeLevelUsage BreadCrumbs noBreadCrumbshasNoBreadCrumbsmkUsagemkUsage'dimNotes normTypeFullynormTypenormPatternTypeinstantiateEmptyArrayDimsunifyexpect mustBeOneOf equalityType zeroOrderTypemustHaveConstr mustHaveFieldanyDimOnMismatchunifyMostCommon mkTypeVarName doUnification$fPrettyBreadCrumb$fPrettyBreadCrumbs$fLocatedUsage $fPrettyUsage$fLocatedConstraint$fMonadUnifyUnifyM $fMonadUnifyM$fFunctorUnifyM$fApplicativeUnifyM$fMonadState(,)UnifyM$fMonadErrorTypeErrorUnifyM $fEqRigidity $fOrdRigidity$fShowRigidity$fShowConstraint$fEqRigidSource$fOrdRigidSource$fShowRigidSource transformDecs$fFunctorMonoM$fApplicativeMonoM $fMonadMonoM$fMonadReaderEnvMonoM$fMonadWriterSeqMonoM$fMonadFreshNamesMonoMinternaliseProg checkOneExp 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$fOrdTestCase $fEqTestCase$fShowTestCase $fEqTestMode$fShowTestMode$fShowProgConfig$fEqTestResult$fShowTestResult$fMonadLoggerPkgM$fMonadPkgRegistryPkgM$fMonadFailPkgM $fMonadPkgM $fFunctorPkgM$fApplicativePkgM $fMonadIOPkgM$fMonadReaderPkgConfigPkgM mainImports mainDataget$fPrettyUntypedPassState $fRepresentationUntypedPassState$fRepresentationUntypedAction$fEqOutputFormat$fOrdOutputFormat$fShowOutputFormat$fEqSkipReason$fShowDatasetResult renderFiles$fFunctorFutharkiM$fApplicativeFutharkiM$fMonadFutharkiM"$fMonadStateFutharkiStateFutharkiM$fMonadIOFutharkiM$fMonadErrorStopReasonFutharkiMGHC.BaserequiredInManifest GHC.MaybeNothingmap Data.EitherpartitionEithersGHC.ListsplitAtprocess-extras-0.7.4-d80760c7d8195098f70184cad6d2d976b4883dee588998b0bb0c189cce96e53aSystem.Process.ByteStringreadProcessWithExitCodeControl.Monad.IO.ClassMonadIOcurlmemoiseGetManifestRoughBuildList doSolveDeps text-1.2.3.2Data.Text.InternalTextText.PrettyPrint.Mainland.ClassPrettypprListpprpprPrecpprintinteger-wired-inGHC.Integer.TypeGHC.RealIntegralRationaldoSubdoUDivdoUModdoSQuotdoSRemdoSMindoUMindoSMaxdoUMaxdoShldoLShrdoAShrdoAnddoOrdoXorintToIntnegativeIshIntMonoidghc-prim GHC.Classes==mempty GHC.TypesTrue shapeMapping'OrdEqtransformers-0.5.6.2Control.Monad.Trans.ReaderReaderGHC.ErrerrorData.Functor.IdentityIdentity loopExtTypeFunctorData.Traversable TraversableGHC.NumNum Data.FoldablelengthControl.Monad.Failfail zeroIshExp oneIshExprenamerSubstitutionsmatcheswithoutUsminusAlgSimplifyEnvmaxSteps markInSolve scalExpRangeEitherLeft BodyWisdomControl.Monad.Trans.Writer.LazyWriter Consumption FunBindingGHC.ShowShowboundobserve expandAliasescheckAnnotationUnknownsubstituteInLMADhasContiguousPerm lmadShape lmadShapeBase sliceOneLMADreshapeCoercionreshapeOneLMAD rebaseNice makeRotIotaixfunMonotonicityRots freeVarIndexfreeVarConsumed letBoundIndexletBoundConsumed IndexArraynoUpdateBounds 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