express-1.0.10: src/Data/Express/Fixtures.hs
-- |
-- Module : Data.Express.Fixtures
-- Copyright : (c) 2019-2021 Rudy Matela
-- License : 3-Clause BSD (see the file LICENSE)
-- Maintainer : Rudy Matela <rudy@matela.com.br>
--
-- Defines some 'Expr' fixtures to facilitate testing and playing around on
-- the REPL (GHCI).
--
-- * Instead of having to write:
--
-- > > value "&&" (&&) :$ (value "not" not :$ val True) :$ val False
-- > not True && False :: Bool
--
-- Using this module, we can just write:
--
-- > > not' true -&&- false
-- > not True && False :: Bool
--
-- * Instead of having to write:
--
-- > > value "+" ((+)::Int->Int->Int) :$ (value "*" ((*)::Int->Int->Int) :$ var "x" (undefined::Int) :$ var "y" (undefined::Int)) :$ (value "*" ((*)::Int->Int->Int) :$ val (1::Int) :$ val (2::Int))
-- > x * y + 1 * 2 :: Int
--
-- Using this module, we can just write:
--
-- > > xx -*- yy -+- one -*- two
-- > x * y + 1 * 2 :: Int
--
-- * Instead of having to write:
--
-- > > value "||" (||) :$ (value "==" ((==)::Int->Int->Bool) :$ val (3::Int) :$ (value "+" ((+)::Int->Int->Int) :$ var "y" (undefined::Int) :$ val (1::Int))) :$ (value "not" not :$ val False)
-- > 3 == y + 1 || not False :: Bool
--
-- We can just write:
--
-- > > (three -==- yy -+- one) -||- not' false
-- > x == y + 1 || not False :: Bool
--
-- This exports over a hundred symbols
-- to be used mainly when writing unit tests
-- or playing around on GHCi.
--
-- Since the 'Expr' type only allows monomorphic values,
-- encoded polymorphic values are monomorphized
-- usually to the 'Int' type.
--
-- /Beware:/ lifted 'Expr' functions sometimes work for different types.
-- The current version does not have a rationale for types that are included:
-- you have to either try around on the REPL or look at the source to really know.
module Data.Express.Fixtures
(
-- * Convenience re-export
module Data.Express
-- * Functions and values encoded as Expr or functions of Exprs
-- | The naming rules are:
--
-- * 'Int's are encoded using their English names,
-- e.g.: 'zero', 'one', 'two';
--
-- * 'Char's are encoded using their English names,
-- e.g.: 'bee', 'cee', 'dee';
--
-- * 0-argument constructors are encoded in lowercase,
-- e.g.: 'false', 'true', 'nothing', 'just';
--
-- * lifted constructors are lowercased,
-- e.g.: 'just';
--
-- * lifted functions are primed
-- e.g.: 'id'', 'negate'', 'head'';
--
-- * lifted operators are surrounded by dashes,
-- e.g.: '-+-', '-*-', '-&&-', '-||-', '-:-'.
--
-- * operators are encoded using their English names,
-- e.g.: 'plus', 'times', 'cons';
--
-- * encoded functions are followed by @E@,
-- e.g.: 'idE', 'notE', 'absE';
--
-- * variables have the first character duplicated,
-- e.g.: 'xx', 'yy', 'xxs';
--
-- * encoded values may have the element type appended,
-- e.g.: 'idInt', 'idBool', 'justInt', 'nilChar'.
--
-- Unqualified polymorphic constructors and functions
-- have their element types bound to 'Int'.
--
-- There are exceptions to the above rules such as:
-- when a name would conflict with a Prelude function.
-- (e.g.: 'orE' and 'andE')
-- ** Booleans
, b_, pp, qq, rr, pp'
, false
, true
, notE
, orE
, andE
, implies
, not'
, (-||-)
, (-&&-)
, (-==>-)
, (-==-)
, (-/=-)
, (-<=-)
, (-<-)
, compare'
, if'
, caseBool
, caseOrdering
-- ** Integers
, i_, xx, yy, zz, xx'
, ii, jj, kk, ii'
, ll, mm, nn
, zero, one, two, three, four, five, six
, seven, eight, nine, ten, eleven, twelve
, minusOne, minusTwo
, idE, negateE, absE, signumE
, idInt
, idBool
, idChar
, idInts
, idBools
, idString
, id', const', negate', abs', signum'
, plus, times, minus
, (-+-), (-*-)
, divE, modE, quotE, remE
, div', mod', quot', rem'
, ff, ffE
, gg, ggE
, hh, hhE
, oo, ooE
, question
, (-?-)
, (-$-)
, odd'
, even'
-- ** Chars
, c_, cs_
, cc, dd, ccs
, ae, bee, cee, dee, zed, zee
, space, lineBreak
, ord'
, ordE
-- ** Lists
, is_
, xxs
, yys
, zzs
, nil
, emptyString
, nilInt
, nilBool
, nilChar
, cons
, consInt
, consBool
, consChar
, (-:-)
, unit
, (-++-)
, head'
, tail'
, null'
, length'
, init'
, elem'
, sort'
, insert'
, bs_, pps, qqs
, and', or'
, sum', product'
, appendInt
-- ** Maybes
, nothing
, nothingInt
, nothingBool
, just
, justInt
, justBool
-- ** Tuples
, comma
, pair
, (-|-)
, triple
, quadruple
, quintuple
, sixtuple
-- ** Ratios
, (-%-)
-- ** Higher order
, compose
, mapE
, (-.-)
, map'
-- ** Enum
, enumFrom', (-..)
, enumFromTo', (-..-)
, enumFromThen', (-...)
, enumFromThenTo', (-...-)
)
where
import Data.Express
import Data.Maybe
import Data.Typeable (Typeable, typeOf)
import Data.Char
import Data.List
import Data.Ratio
int :: Int
int = undefined
bool :: Bool
bool = undefined
char :: Char
char = undefined
string :: String
string = undefined
-- | 'Expr' representing a hole of 'Bool' type.
--
-- > > b_
-- > _ :: Bool
b_ :: Expr
b_ = hole bool
-- | 'Expr' representing a variable @p :: `Bool`@.
--
-- > > pp
-- > p :: Bool
pp :: Expr
pp = var "p" bool
-- | 'Expr' representing a variable @q :: `Bool`@.
--
-- > > qq
-- > q :: Bool
qq :: Expr
qq = var "q" bool
-- | 'Expr' representing a variable @r :: `Bool`@.
--
-- > > rr
-- > r :: Bool
rr :: Expr
rr = var "r" bool
-- | 'Expr' representing a variable @p' :: `Bool`@.
--
-- > > pp'
-- > p' :: Bool
pp' :: Expr
pp' = var "p'" bool
-- | 'False' encoded as an 'Expr'.
--
-- > > false
-- > False :: Bool
false :: Expr
false = val False
-- | 'True' encoded as an 'Expr'.
--
-- > > true
-- > True :: Bool
true :: Expr
true = val True
-- | The function 'not' encoded as an 'Expr'.
--
-- > > notE
-- > not :: Bool -> Bool
notE :: Expr
notE = value "not" not
-- | The function 'and' encoded as an 'Expr'.
--
-- > > andE
-- > (&&) :: Bool -> Bool -> Bool
andE :: Expr
andE = value "&&" (&&)
-- | The function 'or' encoded as an 'Expr'.
--
-- > > orE
-- > (||) :: Bool -> Bool -> Bool
orE :: Expr
orE = value "||" (||)
-- | The function @==>@ lifted over 'Expr's.
--
-- > > false -==>- true
-- > False ==> True :: Bool
--
-- > > evl $ false -==>- true :: Bool
-- > True
(-==>-) :: Expr -> Expr -> Expr
e1 -==>- e2 = implies :$ e1 :$ e2
infixr 0 -==>-
-- | The @==>@ operator encoded as an 'Expr'
implies :: Expr
implies = value "==>" (==>)
where
False ==> _ = True
True ==> p = p
-- | The function 'not' lifted over the 'Expr' type.
--
-- > > not' false
-- > not False :: Bool
--
-- > > evalBool $ not' false
-- > True
--
-- > > not' pp
-- > not p :: Bool
not' :: Expr -> Expr
not' pp = notE :$ pp
-- | The function '&&' lifted over the 'Expr' type.
--
-- > > pp -&&- qq
-- > p && q :: Bool
--
-- > > false -&&- true
-- > False && True :: Bool
--
-- > > evalBool $ false -&&- true
-- > False
(-&&-) :: Expr -> Expr -> Expr
pp -&&- qq = andE :$ pp :$ qq
infixr 3 -&&-
-- | The function '||' lifted over the 'Expr' type.
--
-- > > pp -||- qq
-- > p || q :: Bool
--
-- > > false -||- true
-- > False || True :: Bool
--
-- > > evalBool $ false -||- true
-- > True
(-||-) :: Expr -> Expr -> Expr
pp -||- qq = orE :$ pp :$ qq
infixr 2 -||-
-- | A typed hole of 'Int' type.
--
-- > > i_
-- > _ :: Int
i_ :: Expr
i_ = hole int
-- | A variable @x@ of 'Int' type.
--
-- > > xx
-- > x :: Int
xx :: Expr
xx = var "x" int
-- | A variable @y@ of 'Int' type.
--
-- > > yy
-- > y :: Int
yy :: Expr
yy = var "y" int
-- | A variable @z@ of 'Int' type.
--
-- > > zz
-- > z :: Int
zz :: Expr
zz = var "z" int
-- | A variable @x'@ of 'Int' type.
--
-- > > xx'
-- > x' :: Int
xx' :: Expr
xx' = var "x'" int
-- | A variable @i@ of 'Int' type.
--
-- > > ii
-- > i :: Int
ii :: Expr
ii = var "i" int
-- | A variable @j@ of 'Int' type.
--
-- > > jj
-- > j :: Int
jj :: Expr
jj = var "j" int
-- | A variable @k@ of 'Int' type.
--
-- > > kk
-- > k :: Int
kk :: Expr
kk = var "k" int
-- | A variable @i'@ of 'Int' type.
--
-- > > ii'
-- > i' :: Int
ii' :: Expr
ii' = var "i'" int
-- | A variable @l@ of 'Int' type.
--
-- > > ll
-- > l :: Int
ll :: Expr
ll = var "l" int
-- | A variable @m@ of 'Int' type.
--
-- > > mm
-- > m :: Int
mm :: Expr
mm = var "m" int
-- | A variable @n@ of 'Int' type.
--
-- > > nn
-- > n :: Int
nn :: Expr
nn = var "n" int
-- | The value @0@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > zero
-- > 0 :: Int
zero :: Expr
zero = val (0 :: Int)
-- | The value @1@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > one
-- > 1 :: Int
one :: Expr
one = val (1 :: Int)
-- | The value @2@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > two
-- > 2 :: Int
two :: Expr
two = val (2 :: Int)
-- | The value @3@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > three
-- > 3 :: Int
three :: Expr
three = val (3 :: Int)
-- | The value @4@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > four
-- > 4 :: Int
four :: Expr
four = val (4 :: Int)
-- | The value @5@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > five
-- > 5 :: Int
five :: Expr
five = val (5 :: Int)
-- | The value @6@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > six
-- > 6 :: Int
six :: Expr
six = val (6 :: Int)
-- | The value @7@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > seven
-- > 7 :: Int
seven :: Expr
seven = val (7 :: Int)
-- | The value @8@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > eight
-- > 8 :: Int
eight :: Expr
eight = val (8 :: Int)
-- | The value @9@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > nine
-- > 9 :: Int
nine :: Expr
nine = val (9 :: Int)
-- | The value @10@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > ten
-- > 10 :: Int
ten :: Expr
ten = val (10 :: Int)
-- | The value @11@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > eleven
-- > 11 :: Int
eleven :: Expr
eleven = val (11 :: Int)
-- | The value @12@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > twelve
-- > 12 :: Int
twelve :: Expr
twelve = val (12 :: Int)
-- | The value @-1@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > minusOne
-- > -1 :: Int
minusOne :: Expr
minusOne = val (-1 :: Int)
-- | The value @-2@ bound to the 'Int' type encoded as an 'Expr'.
--
-- > > minusOne
-- > -2 :: Int
minusTwo :: Expr
minusTwo = val (-2 :: Int)
-- | A variable function @f@ of 'Int -> Int' type lifted over the 'Expr' type.
--
-- > > ff xx
-- > f x :: Int
--
-- > > ff one
-- > f 1 :: Int
ff :: Expr -> Expr
ff = (ffE :$)
-- | A variable @f@ of 'Int -> Int' type encoded as an 'Expr'.
--
-- > > ffE
-- > f :: Int -> Int
ffE :: Expr
ffE = var "f" (undefined :: Int -> Int)
-- | A variable function @g@ of 'Int -> Int' type lifted over the 'Expr' type.
--
-- > > gg yy
-- > g y :: Int
--
-- > > gg minusTwo
-- > gg (-2) :: Int
gg :: Expr -> Expr
gg = (ggE :$)
-- | A variable @g@ of 'Int -> Int' type encoded as an 'Expr'.
--
-- > > ggE
-- > g :: Int -> Int
ggE :: Expr
ggE = var "g" (undefined :: Int -> Int)
-- | A variable function @h@ of 'Int -> Int' type lifted over the 'Expr' type.
--
-- > > hh zz
-- > h z :: Int
hh :: Expr -> Expr
hh = (hhE :$)
-- | A variable @h@ of 'Int -> Int' type encoded as an 'Expr'.
--
-- > > hhE
-- > h :: Int -> Int
hhE :: Expr
hhE = var "h" (undefined :: Int -> Int)
-- | A variable binary operator @?@ lifted over the 'Expr' type.
-- Works for 'Int', 'Bool', 'Char', @[Int]@ and 'String'.
--
-- > > xx -?- yy
-- > x ? y :: Int
--
-- > > pp -?- qq
-- > p ? q :: Bool
--
-- > > xx -?- qq
-- > *** Exception: (-?-): cannot apply `(?) :: * -> * -> *` to `x :: Int' and `q :: Bool'. Unhandled types?
(-?-) :: Expr -> Expr -> Expr
ex -?- ey = fromMaybe err $ ($$ ey) $ headOr err $ mapMaybe ($$ ex)
[ var "?" (undefined :: Int -> Int -> Int)
, var "?" (undefined :: Bool -> Bool -> Bool)
, var "?" (undefined :: Char -> Char -> Char)
, var "?" (undefined :: [Int] -> [Int] -> [Int])
, var "?" (undefined :: String -> String -> String)
]
where
err = error $ "(-?-): cannot apply `(?) :: * -> * -> *` to `"
++ show ex ++ "' and `" ++ show ey ++ "'. Unhandled types?"
-- | A variable binary operator @?@ encoded as an 'Expr' (cf. '-?-')
--
-- > > question :$ xx :$ yy
-- > x ? y :: Int
--
-- > > question :$ pp :$ qq
-- > p ? q :: Bool
question :: Expr
question = var "?" (undefined :: Int -> Int -> Int)
-- | A variable binary operator @o@ lifted over the 'Expr' type.
-- Works for 'Int', 'Bool', 'Char', @[Int]@ and 'String'.
--
-- > > xx `oo` yy
-- > x `o` y :: Int
--
-- > > pp `oo` qq
-- > p `o` q :: Bool
--
-- > > xx `oo` qq
-- > *** Exception: (-?-): cannot apply `o :: * -> * -> *` to `x :: Int' and `q :: Bool'. Unhandled types?
oo :: Expr -> Expr -> Expr
ex `oo` ey = fromMaybe err $ ($$ ey) $ headOr err $ mapMaybe ($$ ex)
[ var "`o`" (undefined :: Int -> Int -> Int)
, var "`o`" (undefined :: Bool -> Bool -> Bool)
, var "`o`" (undefined :: Char -> Char -> Char)
, var "`o`" (undefined :: [Int] -> [Int] -> [Int])
, var "`o`" (undefined :: String -> String -> String)
]
where
err = error $ "oo: cannot apply `o :: * -> * -> *` to `"
++ show ex ++ "' and `" ++ show ey ++ "'. Unhandled types?"
-- | A variable binary function @o@ encoded as an 'Expr' (cf. 'oo')
--
-- > > ooE :$ xx :$ yy
-- > x `o` y :: Int
--
-- > > ooE :$ pp :$ qq
-- > p `o` q :: Bool
ooE :: Expr
ooE = var "`o`" (undefined :: Int -> Int -> Int)
-- | The operator '+' for the 'Int' type for use on 'Expr's. (See also 'plus'.)
--
-- > > two -+- three
-- > 2 + 3 :: Int
--
-- > > minusOne -+- minusTwo -+- zero
-- > ((-1) + (-2)) + 0 :: Int
--
-- > > xx -+- (yy -+- zz)
-- > x + (y + z) :: Int
(-+-) :: Expr -> Expr -> Expr
e1 -+- e2 = plus :$ e1 :$ e2
infixl 6 -+-
-- | The operator '+' for the 'Int' type. (See also '-+-'.)
--
-- > > plus
-- > (+) :: Int -> Int -> Int
--
-- > > plus :$ one
-- > (1 +) :: Int -> Int
--
-- > > plus :$ xx :$ yy
-- > x + y :: Int
plus :: Expr
plus = value "+" ((+) :: Int -> Int -> Int)
-- | The operator '*' for the 'Int' type lifted over the 'Expr' type. (See also 'times'.)
--
-- > > three -*- three
-- > 3 * 3 :: Int
--
-- > > one -*- two -*- three
-- > (1 * 2) * 3 :: Int
--
-- > > two -*- xx
-- > 2 * x :: Int
(-*-) :: Expr -> Expr -> Expr
e1 -*- e2 = times :$ e1 :$ e2
infixl 7 -*-
-- | The operator '*' for the 'Int' type. (See also '-*-'.)
--
-- > > times
-- > (*) :: Int -> Int -> Int
--
-- > > times :$ two
-- > (2 *) :: Int -> Int
--
-- > > times :$ xx :$ yy
-- > x * y :: Int
times :: Expr
times = value "*" ((*) :: Int -> Int -> Int)
-- | The subtraction '-' operator encoded as an 'Expr'.
--
-- > > minus :$ one
-- > (1 -) :: Int -> Int
--
-- > > minus :$ one :$ zero
-- > 1 - 0 :: Int
minus :: Expr
minus = value "-" ((-) :: Int -> Int -> Int)
-- | The function 'div' for the 'Int' type lifted over the 'Expr' type. (See also 'mod'.)
--
-- > > six `div'` four
-- > 6 `div` 4 :: Int
div' :: Expr -> Expr -> Expr
ex `div'` ey = divE :$ ex :$ ey
-- | Integer division 'div' encoded as an 'Expr'.
--
-- > > divE :$ two
-- > (2 `div`) :: Int -> Int
--
-- > > divE :$ two :$ three
-- > 2 `div` 3 :: Int
divE :: Expr
divE = value "`div`" (div :: Int -> Int -> Int)
-- | The function 'mod' for the 'Int' type lifted over the 'Expr' type. (See also 'div'.)
--
-- > > six `mod'` four
-- > 6 `mod` 4 :: Int
mod' :: Expr -> Expr -> Expr
ex `mod'` ey = modE :$ ex :$ ey
-- | Integer modulo 'mod' encoded as an 'Expr'.
--
-- > > modE :$ two
-- > (2 `mod`) :: Int -> Int
--
-- > > modE :$ two :$ three
-- > 2 `mod` 3 :: Int
modE :: Expr
modE = value "`mod`" (mod :: Int -> Int -> Int)
-- | The function 'quot' for the 'Int' type lifted over the 'Expr' type. (See also 'rem'.)
--
-- > > six `quot'` four
-- > 6 `quot` 4 :: Int
quot' :: Expr -> Expr -> Expr
ex `quot'` ey = quotE :$ ex :$ ey
-- | Integer quotient 'quot' encoded as an 'Expr'.
--
-- > > quotE :$ two
-- > (2 `quot`) :: Int -> Int
--
-- > > quotE :$ two :$ three
-- > 2 `quot` 3 :: Int
quotE :: Expr
quotE = value "`quot`" (quot :: Int -> Int -> Int)
-- | The function 'rem' for the 'Int' type lifted over the 'Expr' type. (See also 'quot'.)
--
-- > > six `rem'` four
-- > 6 `rem` 4 :: Int
rem' :: Expr -> Expr -> Expr
ex `rem'` ey = remE :$ ex :$ ey
-- | Integer remainder 'rem' encoded as an 'Expr'.
--
-- > > remE :$ two
-- > (2 `rem`) :: Int -> Int
--
-- > > remE :$ two :$ three
-- > 2 `rem` 3 :: Int
remE :: Expr
remE = value "`rem`" (rem :: Int -> Int -> Int)
-- | Constructs an application of 'id' as an 'Expr'.
-- Only works for 'Int', 'Bool', 'Char', 'String', @[Int]@, @[Bool]@.
--
-- > > id' yy
-- > id yy :: Int
--
-- > > id' one
-- > id 1 :: Int
--
-- > > evl (id' one) :: Int
-- > 1
--
-- > > id' pp
-- > id p :: Bool
--
-- > > id' false
-- > id' False :: Bool
--
-- > > evl (id' true) :: Bool
-- > True :: Bool
id' :: Expr -> Expr
id' e = headOr err $ mapMaybe ($$ e)
[ idInt
, idBool
, idChar
, idInts
, idBools
, idString
]
where
err = error $ "id': unhandled type " ++ show (typ e)
-- | The function 'id' for the 'Int' type encoded as an 'Expr'. (See also 'id''.)
--
-- > > idE :$ xx
-- > id x :: Int
--
-- > > idE :$ zero
-- > id 0 :: Int
--
-- > > evaluate $ idE :$ zero :: Maybe Int
-- > Just 0
idE :: Expr
idE = idInt
-- | The function 'id' encoded as an 'Expr'. (cf. 'id'')
idInt,idBool,idChar,idInts,idBools,idString :: Expr
idInt = value "id" (id :: Id Int)
idBool = value "id" (id :: Id Bool)
idChar = value "id" (id :: Id Char)
idInts = value "id" (id :: Id [Int])
idBools = value "id" (id :: Id [Bool])
idString = value "id" (id :: Id String)
type Id a = a -> a
-- | The 'const' function lifted over the 'Expr' type.
--
-- > > const' zero one
-- > const 0 1 :: Int
--
-- This works for the argument types 'Int', 'Char', 'Bool' and their lists.
const' :: Expr -> Expr -> Expr
const' e1 e2 = (:$ e2) . headOr err $ mapMaybe ($$ e1)
[ value "const" (const :: Int -> Int -> Int)
, value "const" (const :: Bool -> Bool -> Bool)
, value "const" (const :: Char -> Char -> Char)
, value "const" (const :: [Int] -> [Int] -> [Int])
, value "const" (const :: [Bool] -> [Bool] -> [Bool])
, value "const" (const :: String -> String -> String)
]
where
err = error $ "const': unhandled type " ++ show (typ e1)
-- | 'negate' over the 'Int' type lifted over the 'Expr' type.
--
-- > > negate' xx
-- > negate x :: Int
--
-- > > evl (negate' one) :: Int
-- > -1
negate' :: Expr -> Expr
negate' e = negateE :$ e
-- | 'negate' over the 'Int' type encoded as an 'Expr'
--
-- > > negateE
-- > negate :: Int -> Int
negateE :: Expr
negateE = value "negate" (negate :: Int -> Int)
-- | 'abs' over the 'Int' type lifted over the 'Expr' type.
--
-- > > abs' xx'
-- > abs x' :: Int
--
-- > > evl (abs' minusTwo) :: Int
-- > 2
abs' :: Expr -> Expr
abs' e = absE :$ e
-- | 'abs' over the 'Int' type encoded as an 'Expr'.
--
-- > > absE
-- > abs :: Int -> Int
absE :: Expr
absE = value "abs" (abs :: Int -> Int)
-- | 'signum' over the 'Int' type lifted over the 'Expr' type.
--
-- > > signum' xx'
-- > signum x' :: Int
--
-- > > evl (signum' minusTwo) :: Int
-- > -1
signum' :: Expr -> Expr
signum' e = signumE :$ e
-- | 'signum' over the 'Int' type encoded as an 'Expr'.
--
-- > > signumE
-- > signum :: Int -> Int
signumE :: Expr
signumE = value "signum" (signum :: Int -> Int)
-- | 'odd' with an 'Int' argument lifted over the 'Expr' type.
--
-- > > odd' (xx -+- one)
-- > odd (x + 1) :: Bool
--
-- > > evl (odd' two) :: Bool
-- > False
odd' :: Expr -> Expr
odd' = (oddE :$) where oddE = value "odd" (odd :: Int -> Bool)
-- | 'even' with an 'Int' argument lifted over the 'Expr' type.
--
-- > > even' (xx -+- two)
-- > even (x + 2) :: Bool
--
-- > > evl (even' two) :: Bool
-- > True
even' :: Expr -> Expr
even' = (evenE :$) where evenE = value "even" (even :: Int -> Bool)
-- | A hole of 'Char' type encoded as an 'Expr'.
--
-- > > c_
-- > _ :: Char
c_ :: Expr
c_ = hole char
-- | A hole of 'String' type encoded as an 'Expr'.
--
-- > > cs_
-- > _ :: [Char]
cs_ :: Expr
cs_ = hole [char]
-- | A variable named @c@ of type 'Char' encoded as an 'Expr'.
--
-- > > cc
-- > c :: Char
cc :: Expr
cc = var "c" char
-- | A variable named @c@ of type 'Char' encoded as an 'Expr'.
--
-- > > dd
-- > d :: Char
dd :: Expr
dd = var "d" char
-- | A variable named @cs@ of type 'String' encoded as an 'Expr'.
--
-- > > ccs
-- > cs :: [Char]
ccs :: Expr
ccs = var "cs" [char]
-- | The character @\'a\'@ encoded as an 'Expr'.
--
-- > > ae
-- > 'a' :: Char
--
-- > > evl ae :: Char
-- > 'a'
ae :: Expr
ae = val 'a'
-- The English name for letter 'a' is not really 'ae', but simply 'a'.
-- | The character @\'b\'@ encoded as an 'Expr'
--
-- > > bee
-- > 'b' :: Char
--
-- > > evl bee :: Char
-- > 'b'
bee :: Expr
bee = val 'b'
-- | The character @\'c\'@ encoded as an 'Expr'
--
-- > > cee
-- > 'c' :: Char
--
-- > > evl cee :: Char
-- > 'c'
cee :: Expr
cee = val 'c'
-- | The character @\'d\'@ encoded as an 'Expr'
--
-- > > dee
-- > 'd' :: Char
--
-- > > evl dee :: Char
-- > 'd'
dee :: Expr
dee = val 'd'
-- | The character @\'z\'@ encoded as an 'Expr'
--
-- > > zed
-- > 'z' :: Char
--
-- > > evl zed :: Char
-- > 'z'
--
-- (cf. 'zee')
zed :: Expr
zed = val 'z'
-- | The character @\'z\'@ encoded as an 'Expr'
--
-- > > zee
-- > 'z' :: Char
--
-- > > evl zee :: Char
-- > 'z'
--
-- (cf. 'zed')
zee :: Expr
zee = val 'z'
-- | The space character encoded as an 'Expr'
--
-- > > space
-- > ' ' :: Char
space :: Expr
space = val ' '
-- | The line break character encoded as an 'Expr'
--
-- > > lineBreak
-- > '\n' :: Char
lineBreak :: Expr
lineBreak = val '\n'
-- | The 'ord' function lifted over 'Expr'
--
-- > > ord' bee
-- > ord 'b' :: Int
--
-- > > evl (ord' bee)
-- > 98
ord' :: Expr -> Expr
ord' = (ordE :$)
-- | The 'ord' function encoded as an 'Expr'
ordE :: Expr
ordE = value "ord" ord
-- | A typed hole of @[Int]@ type encoded as an 'Expr'.
--
-- > > is_
-- > _ :: [Int]
is_ :: Expr
is_ = hole [int]
-- | A variable named @xs@ of type @[Int]@ encoded as an 'Expr'.
--
-- > > xxs
-- > xs :: [Int]
xxs :: Expr
xxs = var "xs" [int]
-- | A variable named @ys@ of type @[Int]@ encoded as an 'Expr'.
--
-- > > yys
-- > ys :: [Int]
yys :: Expr
yys = var "ys" [int]
-- | A variable named @zs@ of type @[Int]@ encoded as an 'Expr'.
--
-- > > yys
-- > ys :: [Int]
zzs :: Expr
zzs = var "zs" [int]
-- | An empty list of type @[Int]@ encoded as an 'Expr'.
--
-- > > nil
-- > [] :: [Int]
nil :: Expr
nil = nilInt
-- | An empty 'String' encoded as an 'Expr'.
--
-- > > emptyString
-- > "" :: String
emptyString :: Expr
emptyString = val ""
-- | The empty list '[]' encoded as an 'Expr'.
nilInt, nilBool, nilChar :: Expr
nilInt = val ([] :: [Int])
nilBool = val ([] :: [Bool])
nilChar = value "[]" ([] :: [Char])
-- | The list constructor with 'Int' as element type encoded as an 'Expr'.
--
-- > > cons
-- > (:) :: Int -> [Int] -> [Int]
--
-- > > cons :$ one :$ nil
-- > [1] :: [Int]
--
-- Consider using '-:-' and 'unit' when building lists of 'Expr'.
cons :: Expr
cons = consInt
-- | The list constructor @ : @ encoded as an 'Expr'.
consInt, consBool, consChar :: Expr
consInt = value ":" ((:) :: Cons Int)
consBool = value ":" ((:) :: Cons Bool)
consChar = value ":" ((:) :: Cons Char)
type Cons a = a -> [a] -> [a]
-- | 'unit' constructs a list with a single element.
-- This works for elements of type 'Int', 'Char' and 'Bool'.
--
-- > > unit one
-- > [1]
--
-- > > unit false
-- > [False]
unit :: Expr -> Expr
unit e = e -:- nil'
where
nil' | typ e == typ i_ = nil
| typ e == typ c_ = emptyString
| typ e == typ b_ = nilBool
-- | The list constructor lifted over the 'Expr' type.
-- Works for the element types 'Int', 'Char' and 'Bool'.
--
-- > > zero -:- one -:- unit two
-- > [0,1,2] :: [Int]
--
-- > > zero -:- one -:- two -:- nil
-- > [0,1,2] :: [Int]
--
-- > > bee -:- unit cee
-- > "bc" :: [Char]
(-:-) :: Expr -> Expr -> Expr
e1 -:- e2 = (:$ e2) . headOr err $ mapMaybe ($$ e1)
[ consInt
, consBool
, consChar
, value ":" ((:) :: Cons (Maybe Int))
]
where
err = error $ "(-:-): unhandled type " ++ show (typ e1)
infixr 5 -:-
-- | Append for list of 'Int's encoded as an 'Expr'.
appendInt :: Expr
appendInt = value "++" ((++) :: [Int] -> [Int] -> [Int])
-- | List concatenation lifted over the 'Expr' type.
-- Works for the element types 'Int', 'Char' and 'Bool'.
--
-- > > (zero -:- one -:- nil) -:- (two -:- three -:- nil)
-- > [0,1] -++- [2,3] :: [Int]
--
-- > > (bee -:- unit cee) -:- unit dee
-- > "bc" -++- "c" :: [Char]
(-++-) :: Expr -> Expr -> Expr
e1 -++- e2 = (:$ e2) . headOr err $ mapMaybe ($$ e1)
[ value "++" ((++) :: [Int] -> [Int] -> [Int])
, value "++" ((++) :: String -> String -> String)
, value "++" ((++) :: [Bool] -> [Bool] -> [Bool])
]
where
err = error $ "(-++-): unhandled type " ++ show (typ e1)
infixr 5 -++-
-- | List 'head' lifted over the 'Expr' type.
-- Works for the element types 'Int', 'Char' and 'Bool'.
--
-- > > head' $ unit one
-- > head [1] :: Int
--
-- > > head' $ unit bee
-- > head "b" :: Char
--
-- > > head' $ zero -:- unit two
-- > head [0,2] :: Int
--
-- > > evl $ head' $ unit one :: Int
-- > 1
head' :: Expr -> Expr
head' exs = headOr err $ mapMaybe ($$ exs)
[ value "head" (head :: [Int] -> Int)
, value "head" (head :: [Char] -> Char)
, value "head" (head :: [Bool] -> Bool)
]
where
err = error $ "head': cannot apply `head :: [a] -> a` to `" ++ show exs ++ "'."
-- | List 'tail' lifted over the 'Expr' type.
-- Works for the element types 'Int', 'Char' and 'Bool'.
--
-- > > tail' $ unit one
-- > tail [1] :: [Int]
--
-- > > tail' $ unit bee
-- > tail "b" :: [Char]
--
-- > > tail' $ zero -:- unit two
-- > tail [0,2] :: [Int]
--
-- > > evl $ tail' $ zero -:- unit two :: [Int]
-- > [2]
tail' :: Expr -> Expr
tail' exs = headOr err $ mapMaybe ($$ exs)
[ value "tail" (tail :: [Int] -> [Int])
, value "tail" (tail :: [Char] -> [Char])
, value "tail" (tail :: [Bool] -> [Bool])
]
where
err = error $ "tail': unhandled type " ++ show (typ exs)
-- | List 'null' lifted over the 'Expr' type.
-- Works for the element types 'Int', 'Char' and 'Bool'.
--
-- > > null' $ unit one
-- > null [1] :: Bool
--
-- > > null' $ nil
-- > null [] :: Bool
--
-- > > evl $ null' nil :: Bool
-- > True
null' :: Expr -> Expr
null' exs = headOr err $ mapMaybe ($$ exs)
[ value "null" (null :: [Int] -> Bool)
, value "null" (null :: [Char] -> Bool)
, value "null" (null :: [Bool] -> Bool)
]
where
err = error $ "null': unhandled type " ++ show (typ exs)
-- | List 'length' lifted over the 'Expr' type.
-- Works for the element types 'Int', 'Char' and 'Bool'.
--
-- > > length' $ unit one
-- > length [1] :: Int
--
-- > > length' $ unit bee
-- > length "b" :: Int
--
-- > > length' $ zero -:- unit two
-- > length [0,2] :: Int
--
-- > > evl $ length' $ unit one :: Int
-- > 1
length' :: Expr -> Expr
length' exs = headOr err $ mapMaybe ($$ exs)
[ value "length" (length :: [Int] -> Int)
, value "length" (length :: [Char] -> Int)
, value "length" (length :: [Bool] -> Int)
]
where
err = error $ "length': cannot apply `length :: [a] -> a` to `" ++ show exs ++ "'."
-- | List 'init' lifted over the 'Expr' type.
-- Works for the element types 'Int', 'Char' and 'Bool'.
--
-- > > init' $ unit one
-- > init [1] :: [Int]
--
-- > > init' $ unit bee
-- > init "b" :: [Char]
--
-- > > init' $ zero -:- unit two
-- > init [0,2] :: [Int]
--
-- > > evl $ init' $ zero -:- unit two :: [Int]
-- > [0]
init' :: Expr -> Expr
init' exs = headOr err $ mapMaybe ($$ exs)
[ value "init" (init :: [Int] -> [Int])
, value "init" (init :: [Char] -> [Char])
, value "init" (init :: [Bool] -> [Bool])
]
where
err = error $ "init': unhandled type " ++ show (typ exs)
-- | List 'sort' lifted over the 'Expr' type.
-- Works for the element types 'Int', 'Char' and 'Bool'.
--
-- > > sort' $ unit one
-- > sort [1] :: Int
--
-- > > sort' $ unit bee
-- > sort "b" :: Int
--
-- > > sort' $ zero -:- unit two
-- > sort [0,2] :: Int
--
-- > > evl $ sort' $ two -:- unit one :: [Int]
-- > [1,2]
sort' :: Expr -> Expr
sort' exs = headOr err $ mapMaybe ($$ exs)
[ value "sort" (sort :: [Int] -> [Int])
, value "sort" (sort :: [Char] -> [Char])
, value "sort" (sort :: [Bool] -> [Bool])
]
where
err = error $ "sort': unhandled type " ++ show (typ exs)
-- | List 'insert' lifted over the 'Expr' type.
-- Works for the element types 'Int', 'Char' and 'Bool'.
--
-- > > insert' zero nilInt
-- > insert 0 [] :: [Int]
--
-- > > insert' false (false -:- unit true)
-- > insert False [False,True] :: [Bool]
insert' :: Expr -> Expr -> Expr
insert' ex exs = (:$ exs) . headOr err $ mapMaybe ($$ ex)
[ value "insert" (insert :: Int -> [Int] -> [Int])
, value "insert" (insert :: Bool -> [Bool] -> [Bool])
, value "insert" (insert :: Char -> String -> String)
]
where
err = error $ "insert': unhandled type " ++ show (typ ex)
-- | List 'elem' lifted over the 'Expr' type.
-- Works for the element types 'Int', 'Char' and 'Bool'.
--
-- > > elem' false (false -:- unit true)
-- > elem False [False,True] :: Bool
--
-- > > evl $ elem' false (false -:- unit true) :: Bool
-- > True
elem' :: Expr -> Expr -> Expr
elem' ex exs = (:$ exs) . headOr err $ mapMaybe ($$ ex)
[ value "elem" (elem :: Int -> [Int] -> Bool)
, value "elem" (elem :: Bool -> [Bool] -> Bool)
, value "elem" (elem :: Char -> String -> Bool)
]
where
err = error $ "elem': unhandled type " ++ show (typ ex)
-- | '$' lifted over 'Expr's
--
-- > > absE -$- one
-- > abs $ 1 :: Int
--
-- Works for 'Int', 'Bool', 'Char' argument types and their lists.
(-$-) :: Expr -> Expr -> Expr
ef -$- ex = (:$ ex) . headOr err $ mapMaybe ($$ ef)
[ value "$" (($) :: Apply Int)
, value "$" (($) :: Apply Bool)
, value "$" (($) :: Apply Char)
, value "$" (($) :: Apply [Int])
, value "$" (($) :: Apply [Bool])
, value "$" (($) :: Apply [Char])
]
where
err = error $ "(-$-): unhandled type " ++ show (typ ef)
infixl 6 -$-
type Apply a = (a -> a) -> a -> a
-- | Constructs an equation between two 'Expr's.
--
-- > > xx -==- zero
-- > x == 0 :: Bool
--
-- > > cc -==- dee
-- > c == 'd' :: Bool
--
-- This works for the 'Int', 'Bool', 'Char' argument types and their lists.
(-==-) :: Expr -> Expr -> Expr
ex -==- ey = (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value "==" ((==) :: Comparison ())
, value "==" ((==) :: Comparison Int)
, value "==" ((==) :: Comparison Bool)
, value "==" ((==) :: Comparison Char)
, value "==" ((==) :: Comparison [Int])
, value "==" ((==) :: Comparison [Bool])
, value "==" ((==) :: Comparison [Char])
]
where
err = error $ "(-==-): unhandled type " ++ show (typ ex)
infix 4 -==-
type Comparison a = a -> a -> Bool
-- | Constructs an inequation between two 'Expr's.
--
-- > > xx -/=- zero
-- > x /= 0 :: Bool
--
-- > > cc -/=- ae
-- > c /= 'a' :: Bool
(-/=-) :: Expr -> Expr -> Expr
ex -/=- ey = (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value "/=" ((/=) :: Comparison ())
, value "/=" ((/=) :: Comparison Int)
, value "/=" ((/=) :: Comparison Bool)
, value "/=" ((/=) :: Comparison Char)
, value "/=" ((/=) :: Comparison [Int])
, value "/=" ((/=) :: Comparison [Bool])
, value "/=" ((/=) :: Comparison [Char])
]
where
err = error $ "(-/=-): unhandled type " ++ show (typ ex)
infix 4 -/=-
-- | Constructs a less-than-or-equal inequation between two 'Expr's.
--
-- > > xx -<=- zero
-- > x <= 0 :: Bool
--
-- > > cc -<=- ae
-- > c <= 'a' :: Bool
(-<=-) :: Expr -> Expr -> Expr
ex -<=- ey = (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value "<=" ((<=) :: Comparison ())
, value "<=" ((<=) :: Comparison Int)
, value "<=" ((<=) :: Comparison Bool)
, value "<=" ((<=) :: Comparison Char)
, value "<=" ((<=) :: Comparison [Int])
, value "<=" ((<=) :: Comparison [Bool])
, value "<=" ((<=) :: Comparison [Char])
]
where
err = error $ "(-<=-): unhandled type " ++ show (typ ex)
infix 4 -<=-
-- | Constructs a less-than inequation between two 'Expr's.
--
-- > > xx -<- zero
-- > x < 0 :: Bool
--
-- > > cc -<- bee
-- > c < 'b' :: Bool
(-<-) :: Expr -> Expr -> Expr
ex -<- ey = (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value "<" ((<) :: Comparison ())
, value "<" ((<) :: Comparison Int)
, value "<" ((<) :: Comparison Bool)
, value "<" ((<) :: Comparison Char)
, value "<" ((<) :: Comparison [Int])
, value "<" ((<) :: Comparison [Bool])
, value "<" ((<) :: Comparison [Char])
]
where
err = error $ "(-<-): unhandled type " ++ show (typ ex)
infix 4 -<-
-- | A function @if :: Bool -> a -> a -> a@ lifted over the 'Expr' type
-- that encodes if-then-else functionality.
-- This is properly displayed as an if-then-else.
--
-- > > if' pp zero xx
-- > (if p then 0 else x) :: Int
--
-- > > zz -*- if' pp xx yy
-- > z * (if p then x else y) :: Int
--
-- > > if' pp false true -||- if' qq true false
-- > (if p then False else True) || (if q then True else False) :: Bool
--
-- > > evl $ if' true (val 't') (val 'f') :: Char
-- > 't'
if' :: Expr -> Expr -> Expr -> Expr
if' ep ex ey = (:$ ey) . headOr err . mapMaybe ($$ ex) $ map (:$ ep)
[ value "if" (iff :: If ())
, value "if" (iff :: If Int)
, value "if" (iff :: If Bool)
, value "if" (iff :: If Char)
, value "if" (iff :: If [Int])
, value "if" (iff :: If [Bool])
, value "if" (iff :: If [Char])
]
where
err = error $ "if': unhandled type " ++ show (typ ex)
iff :: Bool -> a -> a -> a
iff p x y = if p then x else y
type If a = Bool -> a -> a -> a
-- | A function @case :: Bool -> a -> a -> a@ lifted over the 'Expr' type
-- that encodes case-of-False-True functionality.
-- This is properly displayed as a case-of-False-True expression.
--
-- > > caseBool pp zero xx
-- > (case p of False -> 0; True -> x) :: Int
--
-- > > zz -*- caseBool pp xx yy
-- > z * (case p of False -> x; True -> y) :: Int
--
-- > > caseBool pp false true -||- caseBool qq true false
-- > (caseBool p of False -> False; True -> True) || (caseBool q of False -> True; True -> False) :: Bool
--
-- > > evl $ caseBool true (val 'f') (val 't') :: Char
-- > 't'
--
-- By convention, the 'False' case comes before 'True'
-- as @False < True@ and @data Bool = False | True@.
--
-- When evaluating, this is equivalent to if with arguments reversed.
-- Instead of using this, you are perhaps better of using if encoded as an
-- expression. This is just here to be consistent with 'caseOrdering'.
caseBool :: Expr -> Expr -> Expr -> Expr
caseBool ep ex ey = (:$ ey) . headOr err . mapMaybe ($$ ex) $ map (:$ ep)
[ value "case" (caseB :: CaseB ())
, value "case" (caseB :: CaseB Int)
, value "case" (caseB :: CaseB Bool)
, value "case" (caseB :: CaseB Char)
, value "case" (caseB :: CaseB [Int])
, value "case" (caseB :: CaseB [Bool])
, value "case" (caseB :: CaseB [Char])
]
where
err = error $ "caseBool: unhandled type " ++ show (typ ex)
caseB :: Bool -> a -> a -> a
caseB p x y = case p of
False -> x
True -> y
type CaseB a = Bool -> a -> a -> a
-- | A function @case :: Ordering -> a -> a -> a -> a@ lifted over the 'Expr' type
-- that encodes case-of-LT-EQ-GT functionality.
-- This is properly displayed as a case-of-LT-EQ-GT expression.
-- (cf. 'caseBool')
--
-- > > caseOrdering (xx `compare'` yy) zero one two
-- > (case compare x y of LT -> 0; EQ -> 1; GT -> 2) :: Int
--
-- > > evl $ caseOrdering (val EQ) (val 'l') (val 'e') (val 'g') :: Char
-- > 'e'
--
-- By convention cases are given in 'LT', 'EQ' and 'GT' order
-- as @LT < EQ < GT@ and @data Ordering = LT | EQ | GT@.
caseOrdering :: Expr -> Expr -> Expr -> Expr -> Expr
caseOrdering eo ex ey ez = (:$ ez) . (:$ ey) . headOr err . mapMaybe ($$ ex) $ map (:$ eo)
[ value "case" (caseO :: CaseO ())
, value "case" (caseO :: CaseO Int)
, value "case" (caseO :: CaseO Bool)
, value "case" (caseO :: CaseO Char)
, value "case" (caseO :: CaseO [Int])
, value "case" (caseO :: CaseO [Bool])
, value "case" (caseO :: CaseO [Char])
]
where
err = error $ "caseOrdering: unhandled type " ++ show (typ ex)
caseO :: Ordering -> a -> a -> a -> a
caseO o x y z = case o of
LT -> x
EQ -> y
GT -> z
type CaseO a = Ordering -> a -> a -> a -> a
-- | Constructs an 'Expr'-encoded 'compare' operation between two 'Expr's.
--
-- > > xx `compare'` zero
-- > compare x 0 :: Ordering
--
-- > > compare' ae bee
-- > compare 'a' 'b' :: Ordering
compare' :: Expr -> Expr -> Expr
compare' ex ey = (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value "compare" (compare :: Compare ())
, value "compare" (compare :: Compare Int)
, value "compare" (compare :: Compare Bool)
, value "compare" (compare :: Compare Char)
, value "compare" (compare :: Compare [Int])
, value "compare" (compare :: Compare [Bool])
, value "compare" (compare :: Compare [Char])
]
where
err = error $ "(-<-): unhandled type " ++ show (typ ex)
type Compare a = a -> a -> Ordering
-- | 'Nothing' bound to the 'Maybe' 'Int' type encoded as an 'Expr'.
--
-- This is an alias to 'nothingInt'.
nothing :: Expr
nothing = nothingInt
-- | 'Nothing' bound to the 'Maybe' 'Int' type encoded as an 'Expr'.
nothingInt :: Expr
nothingInt = val (Nothing :: Maybe Int)
-- | 'Nothing' bound to the 'Maybe' 'Bool' type encoded as an 'Expr'.
nothingBool :: Expr
nothingBool = val (Nothing :: Maybe Bool)
-- | The 'Just' constructor of the 'Int' element type encoded as an 'Expr'.
justInt :: Expr
justInt = value "Just" (Just :: Int -> Maybe Int)
-- | The 'Just' constructor of the 'Bool' element type encoded as an 'Expr'.
justBool :: Expr
justBool = value "Just" (Just :: Bool -> Maybe Bool)
-- | The 'Just' constructor lifted over the 'Expr' type.
--
-- This works for the 'Bool' and 'Int' argument types.
--
-- > > just zero
-- > Just 0 :: Maybe Int
-- > > just false
-- > Just False :: Maybe Bool
just :: Expr -> Expr
just ex = headOr err $ mapMaybe ($$ ex)
[ justInt
, justBool
]
where
err = error $ "just: unhandled type " ++ show (typ ex)
-- | An infix synonym of 'pair'.
(-|-) :: Expr -> Expr -> Expr
(-|-) = pair
-- | The pair constructor lifted over 'Expr's.
--
-- This works for the 'Int' and 'Bool' element types
-- by differently from 'foldPair' by returning a well-typed expression.
pair :: Expr -> Expr -> Expr
pair x y = comma :$ x :$ y
where
comma = case (show $ typ x, show $ typ y) of
("Int", "Int") -> value "," ((,) :: Pair Int Int)
("Int", "Bool") -> value "," ((,) :: Pair Int Bool)
("Bool","Int") -> value "," ((,) :: Pair Bool Int)
("Bool","Bool") -> value "," ((,) :: Pair Bool Bool)
(t,t') -> error $ "(-:-): unhandled types " ++ t ++ " " ++ t'
type Pair a b = a -> b -> (a,b)
-- | The pair constructor (@ :: ... -> (Int,Int) @) encoded as an 'Expr'.
comma :: Expr
comma = value "," ((,) :: Pair Int Int)
-- | The triple/trio constructor lifted over 'Expr's.
--
-- This only works for the 'Int' element type.
triple :: Expr -> Expr -> Expr -> Expr
triple e1 e2 e3 = ccE :$ e1 :$ e2 :$ e3
where
ccE = value ",," ((,,) :: Int -> Int -> Int -> (Int,Int,Int))
-- | The quadruple constructor lifted over 'Expr's.
--
-- This only works for the 'Int' element type.
quadruple :: Expr -> Expr -> Expr -> Expr -> Expr
quadruple e1 e2 e3 e4 = cccE :$ e1 :$ e2 :$ e3 :$ e4
where
cccE = value ",,," ((,,,) :: Int -> Int -> Int -> Int -> (Int,Int,Int,Int))
-- | The quintuple constructor lifted over 'Expr's.
--
-- This only works for the 'Int' element type.
quintuple :: Expr -> Expr -> Expr -> Expr -> Expr -> Expr
quintuple e1 e2 e3 e4 e5 = ccccE :$ e1 :$ e2 :$ e3 :$ e4 :$ e5
where
ccccE = value ",,,," ((,,,,) :: Int -> Int -> Int -> Int -> Int -> (Int,Int,Int,Int,Int))
-- | The sixtuple constructor lifted over 'Expr's.
--
-- This only works for the 'Int' element type.
sixtuple :: Expr -> Expr -> Expr -> Expr -> Expr -> Expr -> Expr
sixtuple e1 e2 e3 e4 e5 e6 = cccccE :$ e1 :$ e2 :$ e3 :$ e4 :$ e5 :$ e6
where
cccccE = value ",,,,," ((,,,,,) :: Int -> Int -> Int -> Int -> Int -> Int -> (Int,Int,Int,Int,Int,Int))
-- | A typed hole of @[Bool]@ type encoded as an 'Expr'.
--
-- > > bs_
-- > _ :: [Bool]
bs_ :: Expr
bs_ = hole [bool]
-- | 'Expr' representing a variable @p' :: `[Bool]`@.
--
-- > > pps
-- > ps :: [Bool]
pps :: Expr
pps = var "ps" [bool]
-- | A typed hole of '[Bool]' type
--
-- > > qqs
-- > qs :: [Bool]
qqs :: Expr
qqs = var "qs" [bool]
-- | 'and' lifted over the 'Expr' type.
--
-- > > and' pps
-- > and ps :: Bool
--
-- > > evl (and' $ expr [False,True]) :: Bool
-- > False
and' :: Expr -> Expr
and' e = andE :$ e
where
andE = value "and" (and :: [Bool] -> Bool)
-- | 'or' lifted over the 'Expr' type.
--
-- > > or' pps
-- > or ps :: Bool
--
-- > > evl (or' $ expr [False,True]) :: Bool
-- > True
or' :: Expr -> Expr
or' e = orE :$ e
where
orE = value "or" (or :: [Bool] -> Bool)
-- | 'sum' of 'Int' elements lifted over the 'Expr' type.
--
-- > > sum' xxs
-- > sum xs :: Int
--
-- > > evl (sum' $ expr [1,2,3::Int]) :: Int
-- > 6
sum' :: Expr -> Expr
sum' e = sumE :$ e
where
sumE = value "sum" (sum :: [Int] -> Int)
-- | 'product' of 'Int' elements lifted over the 'Expr' type.
--
-- > > product' xxs
-- > product xs :: Int
--
-- > > evl (product' $ expr [1,2,3::Int]) :: Int
-- > 6
product' :: Expr -> Expr
product' e = productE :$ e
where
productE = value "product" (product :: [Int] -> Int)
headOr :: a -> [a] -> a
headOr x [] = x
headOr _ (x:_) = x
-- | The '%' constructor lifted over 'Expr's.
--
-- > > val (2 :: Integer) -%- val (3 :: Integer)
-- > 2 % 3 :: Ratio Integer
--
-- This only accepts 'Expr's bound to the 'Integer' type.
(-%-) :: Expr -> Expr -> Expr
en -%- ed = value "%" ((%) :: Integer -> Integer -> Rational) :$ en :$ ed
-- | Function composition encoded as an 'Expr':
--
-- > > compose
-- > (.) :: (Int -> Int) -> (Int -> Int) -> Int -> Int
compose :: Expr
compose = value "." ((.) :: Compose Int)
-- | Function composition '.' lifted over 'Expr'.
--
-- > > absE -.- negateE
-- > abs . negate :: Int -> Int
--
-- > > absE -.- negateE :$ one
-- > (abs . negate) 1 :: Int
--
-- This works for 'Int', 'Bool', 'Char' and their lists.
(-.-) :: Expr -> Expr -> Expr
ex -.- ey = (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value "." ((.) :: Compose ())
, value "." ((.) :: Compose Int)
, value "." ((.) :: Compose Bool)
, value "." ((.) :: Compose Char)
, value "." ((.) :: Compose [Int])
, value "." ((.) :: Compose [Bool])
, value "." ((.) :: Compose [Char])
]
where
err = error $ "(-.-): unhandled type " ++ show (typ ex)
type Compose a = (a -> a) -> (a -> a) -> (a -> a)
-- | 'map' over the 'Int' element type encoded as an 'Expr'
--
-- > > mapE
-- > map :: (Int -> Int) -> [Int] -> [Int]
mapE :: Expr
mapE = value "map" (map :: Map Int)
-- | 'map' lifted over 'Expr's.
--
-- > > map' absE (unit one)
-- > map abs [1] :: [Int]
map' :: Expr -> Expr -> Expr
map' ef exs = (:$ exs) . headOr err $ mapMaybe ($$ ef)
[ value "map" (map :: Map ())
, value "map" (map :: Map Int)
, value "map" (map :: Map Bool)
, value "map" (map :: Map Char)
, value "map" (map :: Map [Int])
, value "map" (map :: Map [Bool])
, value "map" (map :: Map [Char])
]
where
err = error $ "map': unhandled type " ++ show (typ ef)
type Map a = (a -> a) -> [a] -> [a]
-- | 'enumFrom' lifted over 'Expr's.
--
-- > > enumFrom' zero
-- > enumFrom 0 :: [Int]
--
-- Works for 'Int's, 'Bool's and 'Char's.
enumFrom' :: Expr -> Expr
enumFrom' ex = headOr err $ mapMaybe ($$ ex)
[ value "enumFrom" (enumFrom :: EnumFrom Int)
, value "enumFrom" (enumFrom :: EnumFrom Bool)
, value "enumFrom" (enumFrom :: EnumFrom Char)
]
where
err = error $ "enumFrom': unhandled type " ++ show (typ ex)
type EnumFrom a = (a -> [a])
-- | 'enumFrom' lifted over 'Expr's named as @".."@ for pretty-printing.
--
-- > > (-..) one
-- > [1..] :: [Int]
--
-- Works for 'Int's, 'Bool's and 'Char's.
(-..) :: Expr -> Expr
(-..) ex = headOr err $ mapMaybe ($$ ex)
[ value ".." (enumFrom :: EnumFrom Int)
, value ".." (enumFrom :: EnumFrom Bool)
, value ".." (enumFrom :: EnumFrom Char)
]
where
err = error $ "(-..): unhandled type " ++ show (typ ex)
-- | 'enumFromTo' lifted over 'Expr's
--
-- > > enumFromTo' zero four
-- > enumFromTo 0 4 :: [Int]
enumFromTo' :: Expr -> Expr -> Expr
enumFromTo' ex ey = (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value "enumFromTo" (enumFromTo :: EnumFromTo Int)
, value "enumFromTo" (enumFromTo :: EnumFromTo Bool)
, value "enumFromTo" (enumFromTo :: EnumFromTo Char)
]
where
err = error $ "enumFromTo': unhandled type " ++ show (typ ex)
type EnumFromTo a = (a -> a -> [a])
-- | 'enumFromTo' lifted over 'Expr's but named as @".."@ for pretty-printing.
--
-- > > zero -..- four
-- > [0..4] :: [Int]
(-..-) :: Expr -> Expr -> Expr
ex -..- ey = (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value ".." (enumFromTo :: EnumFromTo Int)
, value ".." (enumFromTo :: EnumFromTo Bool)
, value ".." (enumFromTo :: EnumFromTo Char)
]
where
err = error $ "-..-: unhandled type " ++ show (typ ex)
-- | 'enumFromThen' lifted over 'Expr's
--
-- > > enumFromThen' zero ten
-- > enumFromThen 0 10 :: [Int]
enumFromThen' :: Expr -> Expr -> Expr
enumFromThen' ex ey = (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value "enumFromThen" (enumFromThen :: EnumFromThen Int)
, value "enumFromThen" (enumFromThen :: EnumFromThen Bool)
, value "enumFromThen" (enumFromThen :: EnumFromThen Char)
]
where
err = error $ "enumFromThen': unhandled type " ++ show (typ ex)
type EnumFromThen a = (a -> a -> [a])
-- | 'enumFromThen' lifted over 'Expr's but named as @",.."@ for pretty printing.
--
-- > > zero -... ten
-- > [0,10..] :: [Int]
(-...) :: Expr -> Expr -> Expr
ex -... ey = (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value ",.." (enumFromThen :: EnumFromThen Int)
, value ",.." (enumFromThen :: EnumFromThen Bool)
, value ",.." (enumFromThen :: EnumFromThen Char)
]
where
err = error $ "-..-: unhandled type " ++ show (typ ex)
-- | 'enumFromThenTo' lifted over 'Expr's.
--
-- > > enumFromThenTo' zero two ten
-- > enumFromThenTo 0 2 10 :: [Int]
enumFromThenTo' :: Expr -> Expr -> Expr -> Expr
enumFromThenTo' ex ey ez = (:$ ez) . (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value "enumFromThenTo" (enumFromThenTo :: EnumFromThenTo Int)
, value "enumFromThenTo" (enumFromThenTo :: EnumFromThenTo Bool)
, value "enumFromThenTo" (enumFromThenTo :: EnumFromThenTo Char)
]
where
err = error $ "enumFromThenTo': unhandled type " ++ show (typ ex)
type EnumFromThenTo a = (a -> a -> a -> [a])
-- | 'enumFromThenTo' lifted over 'Expr's but named as @",.."@ for pretty-printing.
--
-- > > (zero -...- two) ten
-- > [0,2..10] :: [Int]
(-...-) :: Expr -> Expr -> Expr -> Expr
(ex -...- ey) ez = (:$ ez) . (:$ ey) . headOr err $ mapMaybe ($$ ex)
[ value ",.." (enumFromThenTo :: EnumFromThenTo Int)
, value ",.." (enumFromThenTo :: EnumFromThenTo Bool)
, value ",.." (enumFromThenTo :: EnumFromThenTo Char)
]
where
err = error $ "-..-: unhandled type " ++ show (typ ex)