h&Vk'      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKL M N OPQRSTUVWXYZ[ \ ] ^ _ ` 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 { | } ~                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " " # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $$$$$$$$%%%%%%%%%%%%%%%%%%%%%!%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%"%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#&#&#&#&#&#&#&#&#&#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#'#.$ Safe-Inferredb#'''''% Safe-Inferred()/04buLMNORPQSTUVWXYZ[\]^_'`a'bcde'f'g'h'i'j'k'lmno'p'q'r's't'uvwx'y'z'{'|'}~'''''''''''''''''''''''''''''''''''''-(C) 2013-2014 Richard Eisenberg, Jan StolarekBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/05esingletons-baseConjunction of singletonssingletons-baseDisjunction of singletonssingletons-baseNegation of a singletonsingletons-baseConditional over singletons$VWXYZ$VWXYZ32(C) 2013 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/01;m singletons-baseOne way to compute Boolean equality for types of any kind. This will return '8 if the two arguments are known to be the same type and '* if they are known to be apart. Examples: >>>  ' ' ' >>>  ' (' a) ' >>>  a a '  is most suited for data types that are not inductively defined. Four concrete examples of this are Natural, &', &(, and )*. One cannot implement boolean equality for these types by pattern matching alone, so  is a good fit instead.The downside to  is that it can fail to reduce if it is unable to determine if two types are equal or apart. Here is one such example:  (' a) (' b) /What should this reduce to? It depends on what a and b are.  has no way of knowing what these two types are, and as a result, this type will be stuck. This is a pitfall that you can run into if you use  to implement boolean equality for an inductive data type like '. For this reason, it is usually recommended to implement boolean equality for inductive data types using pattern matching and recursion, not .9Note that this definition is slightly different from the +, type family from Data.Type.Equality in base, as +, attempts to distinguish applications of type constructors from other types. As a result, a == a does not reduce to ' for every a, but  a a does reduce to ' for every a-. The latter behavior is more desirable for  singletons$' purposes, so we use it instead of +,. (C) 2013 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/qnsingletons-base A variant of ' whose underlying ' is restricted to kind ' rep (for some ' rep).'singletons-base#A choice of singleton for the kind ' rep (for some ' rep0), an instantiation of which is the famous kind '.Conceivably, one could generalize this instance to `Sing @k` for any kind k, and remove all other  instances. We don't adopt this design, however, since it is far more convenient in practice to work with explicit singleton values than 's (for instance, 's are more difficult to pattern match on, and require extra runtime checks).>We cannot produce explicit singleton values for everything in ' rep6, however, since it is an open kind, so we reach for ' in this one particular case.(C) 2013 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/014;rOPQRSTUOPQRUTS-(C) 2019 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/0s'''''''((((((((( (C) 2013 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/0tLMNbcdefghijklmnopqrstuvwxyz{|}~LM}~uvlmbcN|{zyxwtsrqponkjihgfed (C) 2017 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/0v.(C) 2014 Jan StolarekBSD-style (see LICENSE)%Jan Stolarek (jan.stolarek@p.lodz.pl) experimental non-portable Safe-Inferred()/0v((((((      (C) 2016 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/0xu&& -(C) 2013-2014 Richard Eisenberg, Jan StolarekBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/0y!!/(C) 2018 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/014;{((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))********************************************************************************************************************************++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,-------------------------------------------(C) 2018 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/014;(C) 2019 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/01+0(C) 2014 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()./0~ singletons-baseThe promotion of -3. This version is more poly-kinded for easier use.singletons-baseGiven a singleton for Nat, call something requiring a KnownNat instance.singletons-baseGiven a singleton for Symbol, call something requiring a  KnownSymbol instance.singletons-baseGiven a singleton for Char, call something requiring a  KnownChar instance.singletons-baseThe promotion of -3. This version is more poly-kinded for easier use.singletons-baseThe singleton for -singletons-baseThe promotion of -.singletons-baseThe singleton for -.singletons-baseThe singleton for -.singletons-baseThe singleton analogue of  for s.singletons-baseThe singleton analogue of 2Note that, because of historical reasons in GHC's  API, * is incompatible (unification-wise) with  and the , , , and  instances for . (a  b) ~ 'True does not imply anything about a  b or any other  /  relationships.(Be aware that " in the paragraph above refers to  from the  typeclass, exported from Data.Ord.Singletons, and not the - from  GHC.TypeNats*. The latter is simply a type alias for (a  b) ~ 'True.)This is provided here for the sake of completeness and for compatibility with libraries with APIs built around . New code should use -+, exposed through this library through the  and  instances for .(84(C) 2014 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()./0singletons-baseThis bogus instance is helpful for people who want to define functions over Symbols that will only be used at the type level or as singletons.-singletons-baseAdapted from GHC's source code.Compute the logarithm of a number in the given base, rounded down to the closest integer.       7777-(C) 2013-2014 Richard Eisenberg, Jan StolarekBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/08001(C) 2014 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/01;&                ((C) 2014 Jan Stolarek, Richard EisenbergBSD-style (see LICENSE)%Jan Stolarek (jan.stolarek@p.lodz.pl) experimental non-portable Safe-Inferred()/01;% % (C) 2018 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/0 singletons-baseA drop-in replacement for -*. This also exists at the value-level as  . singletons-base Convert a   to a - from  GHC.TypeLits. singletons-base A type-level   ` which uses  as its text kind. singletons-baseA value-level   ` which uses - as its text type. singletons-base%A description of a custom type error.This is a variation on -; that is parameterized over what text type is used in the  % constructor. Instantiating it with - gives you  , and instantiating it with  gives you  . singletons-baseShow the text as is. singletons-basePretty print the type. ShowType :: k -> ErrorMessage singletons-base4Put two pieces of error message next to each other. singletons-base8Stack two pieces of error message on top of each other. singletons-base Convert an   into a human-readable -. singletons-baseThe value-level counterpart to  .-Note that this is not quite as expressive as  ,, as it is unable to print the contents of  % constructors (it will simply print "" in their place). singletons-baseThe singleton for  .-Note that this is not quite as expressive as  , as it is unable to handle   constructors at all.   6 5 6 5      2(C) 2018 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/014;---- ------------------------------------------------------------------------..................... .............. . . . . . . . . . . . . . . . . . . . . . . . ......................................................................////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111111111111111111111111111111111111     3(C) 2019 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/01111111111111111111111114-(C) 2013-2014 Richard Eisenberg, Jan StolarekBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/0 111111111111111111111111111111111111111111111111111111111111 1 11 11 1122222 22 22 22 2 22 2222 2 2 2 2 2222 2 2 2 2 2 222222222 2222222222222 2 222222222222222222222222222222 2 2 2 2 2 2 2 2 2 222222222222222 2 2 2 2 2 2 2 2 2 22222222222 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 33333333333 3 333333 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3333333 3 3 3 3 3 3 3 3 33333333333333333 3 3 3 3 3 3333333333444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444445555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555566666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777778888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;22  222222     ::5(C) 2016 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/0o;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<=================================================(C) 2017 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/014;singletons-baseThe shows7 functions return a function that prepends the output  to an existing . This allows constant-time concatenation of results using function composition.singletons-base=, but with an extra underscore so that its promoted counterpart () will not clash with the Show class.;;(C) 2018 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/014;I     (C) 2020 Ryan ScottBSD-style (see LICENSE)'Richard Eisenberg (rae@cs.brynmawr.edu) experimental non-portable Safe-Inferred()/014  (C) 2018 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/014; (C) 2018 Ryan ScottBSD-style (see LICENSE)'Richard Eisenberg (rae@cs.brynmawr.edu) experimental non-portable Safe-Inferred()/014' [\]^_`a [\]a`_^(C) 2018 Ryan ScottBSD-style (see LICENSE)'Richard Eisenberg (rae@cs.brynmawr.edu) experimental non-portable Safe-Inferred()/014  (C) 2018 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/014;44(C) 2018 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/014;     -(C) 2013-2014 Richard Eisenberg, Jan StolarekBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred                                                                                  (C) 2018 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/01; (C) 2016 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/01Ⱦ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""""""""""""""""""""""" 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(C) 2021 Ryan ScottBSD-style (see LICENSE)'Richard Eisenberg (rae@cs.brynmawr.edu) experimental non-portable Safe-Inferred()/01M$$$$$$$$$$$$$$ (C) 2017 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/01$$$$$$$$$$$$(C) 2013 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred ()/04Θ  (C) 2018 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/01;/%%%%%%%%(C) 2013 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred==============================================================================>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZbcdefghijklmnopqrstuvwxyz{|}~ $$$$$$BC1%,#$+*;:76.-?>'&54)(980/A@32=>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNORPQSTUVWXYZbcdefghijklmnopqrstuvwxyz{|}~ $$$$$$$%%"(C) 2021 Ryan ScottBSD-style (see LICENSE)'Richard Eisenberg (rae@cs.brynmawr.edu) experimental non-portable Safe-Inferred()/01m %%%%%%%% %%%%%%%%%9 %9 %9 %9 (C) 2018 Ryan ScottBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred()/01;>%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%>%%%>%%%%%%%%%(C) 2013 Richard EisenbergBSD-style (see LICENSE) Ryan Scott experimental non-portable Safe-Inferred==============================================================================>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>LMNOPQRSTUVWXYZbcdefghijklmnopqrstuvwxyz{|}~ VWXOPQRLM}~uvlmbc                             ZYUTSN|{zyxwtsrqponkjihgfed     #(C) 2021 Ryan ScottBSD-style (see LICENSE)'Richard Eisenberg (rae@cs.brynmawr.edu) experimental non-portable Safe-Inferred()/01Q&&&&&&&&&&>67869:69;<=(>?@<='67A67B67C67D69E69F69G69HIJK6LM6NO69P69Q67R6ST6UV6UW6XY6XZ6X[6X\]^_`ab`ac`acdefdegdhidhjdhkdhldhmdhndhodhpdhqdhrdhsdhtdhudhvdwxdwydwzdw{dw|dw}dw~dwdwdwdwdwdwdwdwdwdwdwdw``````dd%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%,                                                 ....O...................................................../////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////M0000000000000000000000000000                                                            1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 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 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 222 2 2 2 2 222 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 44444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444                                                                                                                                                                                                                                                                                                                                                                                           ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !   ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 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69 ++ 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