Feldspar.Core.Expr

This module gives a representation core programs as typed expressions (see Expr / Data).

Documentation

data Expr a where

Typed core language expressions. A value of type Expr a is a representation of a program that computes a value of type a.

Constructors

Val :: a -> Expr a

Variable :: Expr a

Value :: Storable a => a -> Expr a

Function :: String -> (a -> b) -> Expr (a -> b)

Application :: Expr (a -> b) -> Data a -> Expr b

NoInline :: String -> Ref (a :-> b) -> Data a -> Expr b

IfThenElse :: Data Bool -> (a :-> b) -> (a :-> b) -> Data a -> Expr b

While :: (a :-> Bool) -> (a :-> a) -> Data a -> Expr a

Parallel :: Storable a => Data Length -> (Int :-> a) -> Expr [a]

data Data a

A wrapper around Expr to allow observable sharing (see Feldspar.Core.Ref) and for memoizing size information.

Constructors

Typeable a => Data

Fields

dataSize :: Size a

dataRef :: Ref (Expr a)

Instances

Eq (Data a)

(Fractional' a, Numeric a) => Fractional (Data a)

Numeric a => Num (Data a)

Ord (Data a)

Storable a => Show (Data a)

Storable a => RandomAccess (Data [a])

Storable a => Computable (Data a)

Storable a => Computable (Vector (Data a))

Storable a => Computable (Vector (Vector (Data a)))

ElemWise (Data a)

FromFloat (Data Float)

FixFloatLike (Data Float)

Numeric a => Mul (Data a) (Matrix a)

Numeric a => Mul (Data a) (DVector a)

Numeric a => Mul (Data a) (Data a)

Numeric a => Mul (DVector a) (Data a)

Numeric a => Mul (Matrix a) (Data a)

RandomAccess (Data Int -> Data a)

data a :-> b

Constructors

Typeable a => Lambda (Data a -> Data b) (Data a) (Data b)

dataType :: forall a. Data a -> Tuple StorableType

dataId :: Data a -> Unique

dataToExpr :: Data a -> Expr a

exprToData :: Typeable a => Size a -> Expr a -> Data a

freshVar :: Typeable a => Size a -> Data a

lambda :: Typeable a => Size a -> (Data a -> Data b) -> a :-> b

apply :: (a :-> b) -> Data a -> Data b

resultSize :: (a :-> b) -> Size b

(|$|) :: Expr (a -> b) -> Data a -> Expr b

_function :: Typeable b => String -> (Size a -> Size b) -> (a -> b) -> Data a -> Data b

_function2 :: Typeable c => String -> (Size a -> Size b -> Size c) -> (a -> b -> c) -> Data a -> Data b -> Data c

_function3 :: Typeable d => String -> (Size a -> Size b -> Size c -> Size d) -> (a -> b -> c -> d) -> Data a -> Data b -> Data c -> Data d

_function4 :: Typeable e => String -> (Size a -> Size b -> Size c -> Size d -> Size e) -> (a -> b -> c -> d -> e) -> Data a -> Data b -> Data c -> Data d -> Data e

tup2 :: (Typeable a, Typeable b) => Data a -> Data b -> Data (a, b)

tup3 :: (Typeable a, Typeable b, Typeable c) => Data a -> Data b -> Data c -> Data (a, b, c)

tup4 :: (Typeable a, Typeable b, Typeable c, Typeable d) => Data a -> Data b -> Data c -> Data d -> Data (a, b, c, d)

get21 :: Typeable a => Data (a, b) -> Data a

get22 :: Typeable b => Data (a, b) -> Data b

get31 :: Typeable a => Data (a, b, c) -> Data a

get32 :: Typeable b => Data (a, b, c) -> Data b

get33 :: Typeable c => Data (a, b, c) -> Data c

get41 :: Typeable a => Data (a, b, c, d) -> Data a

get42 :: Typeable b => Data (a, b, c, d) -> Data b

get43 :: Typeable c => Data (a, b, c, d) -> Data c

get44 :: Typeable d => Data (a, b, c, d) -> Data d

class Typeable (Internal a) => Computable a where

Computable types. A computable value completely represents a core program, in such a way that internalize . externalize preserves semantics, but not necessarily syntax.

The terminology used in this class comes from thinking of the Data type as the "internal" core language and the Feldspar.Core API as the "external" core language.

Associated Types

type Internal a

Data (Internal a) is the internal representation of the type a.

Methods

internalize :: a -> Data (Internal a)

Convert to internal representation

externalize :: Data (Internal a) -> a

Convert to external representation

Instances

Storable a => Computable (Data a)

Storable a => Computable (Vector (Data a))

Storable a => Computable (Vector (Vector (Data a)))

(Computable a, Computable b) => Computable (a, b)

(Computable a, Computable b, Computable c) => Computable (a, b, c)

(Computable a, Computable b, Computable c, Computable d) => Computable (a, b, c, d)

lowerFun :: (Computable a, Computable b) => (a -> b) -> Data (Internal a) -> Data (Internal b)

Lower a function to operate on internal representation.

liftFun :: (Computable a, Computable b) => (Data (Internal a) -> Data (Internal b)) -> a -> b

Lift a function to operate on external representation.

evalE :: Expr a -> a

The semantics of expressions

evalD :: Data a -> a

The semantics of Data

evalF :: (a :-> b) -> a -> b

eval :: Computable a => a -> Internal a

The semantics of any Computable type

value :: Storable a => a -> Data a

A program that computes a constant value

array :: Storable a => Size a -> a -> Data a

Like value but with an extra Size argument that can be used to increase the size beyond the given data.

Example 1:

 array (10 :> 20 :> universal) [] :: Data [[Int]]

gives an uninitialized 10x20 array of Int elements.

Example 2:

 array (10 :> 20 :> universal) [[1,2,3]] :: Data [[Int]]

gives a 10x20 array whose first row is initialized to [1,2,3].

arrayLen :: Storable a => Data Length -> [a] -> Data [a]

unit :: Data ()

true :: Data Bool

false :: Data Bool

size :: forall a. Storable a => Data [a] -> [Range Length]

Returns the size of each level of a multi-dimensional array, starting with the outermost level.

cap :: (Storable a, Size a ~ Range b, Ord b) => Range b -> Data a -> Data a

function :: (Storable a, Storable b) => String -> (Size a -> Size b) -> (a -> b) -> Data a -> Data b

Constructs a one-argument primitive function.

function fun szf f:

• fun is the name of the function.
• szf computes the output size from the input size.
• f gives the evaluation semantics.

function2 :: (Storable a, Storable b, Storable c) => String -> (Size a -> Size b -> Size c) -> (a -> b -> c) -> Data a -> Data b -> Data c

A two-argument primitive function

function3 :: (Storable a, Storable b, Storable c, Storable d) => String -> (Size a -> Size b -> Size c -> Size d) -> (a -> b -> c -> d) -> Data a -> Data b -> Data c -> Data d

A three-argument primitive function

function4 :: (Storable a, Storable b, Storable c, Storable d, Storable e) => String -> (Size a -> Size b -> Size c -> Size d -> Size e) -> (a -> b -> c -> d -> e) -> Data a -> Data b -> Data c -> Data d -> Data e

A four-argument primitive function

getIx :: Storable a => Data [a] -> Data Int -> Data a

Look up an index in an array (see also !)

setIx :: Storable a => Data [a] -> Data Int -> Data a -> Data [a]

setIx arr i a:

Replaces the value at index i in the array arr with the value a.

class RandomAccess a where

Associated Types

type Element a

The type of elements in a random access structure

Methods

(!) :: a -> Data Int -> Element a

Index lookup in a random access structure

Instances

Storable a => RandomAccess (Data [a])

RandomAccess (Vector a)

RandomAccess (Stream a)

RandomAccess (Data Int -> Data a)

noInline :: (Computable a, Computable b) => String -> (a -> b) -> a -> b

Constructs a non-primitive, non-inlined function.

The normal way to make a non-primitive function is to use an ordinary Haskell function, for example:

 myFunc x = x * 4 + 5

However, such functions are inevitably inlined into the program expression when applied. noInline can be thought of as a way to protect a function against inlining (but later transformations may choose to inline anyway).

Ideally, it should be posssible to reuse such a function several times, but at the moment this does not work. Every application of a noInline function results in a new copy of the function in the core program.

ifThenElse :: (Computable a, Computable b) => Data Bool -> (a -> b) -> (a -> b) -> a -> b

ifThenElse cond thenFunc elseFunc:

Selects between the two functions thenFunc and elseFunc depending on whether the condition cond is true or false.

whileSized :: Computable state => Size (Internal state) -> Size (Internal state) -> (state -> Data Bool) -> (state -> state) -> state -> state

while :: Computable state => (state -> Data Bool) -> (state -> state) -> state -> state

While-loop

while cont body :: state -> state:

• state is the type of the state.
• cont determines whether or not to continue based on the current state.
• body computes the next state from the current state.
• The result is a function from initial state to final state.

parallel :: Storable a => Data Length -> (Data Int -> Data a) -> Data [a]

Parallel array

parallel l ixf:

• l is the length of the resulting array (outermost level).
• ifx is a function that maps each index in the range [0 .. l-1] to its element.

Since there are no dependencies between the elements, the compiler is free to compute the elements in any order, or even in parallel.