Modulefirst-class-families-0.8.2.0Haskell2010

Fcf

First-class type families

For example, here is a regular type family:

type family   FromMaybe (a :: k) (m :: Maybe k) :: k
type instance FromMaybe a 'Nothing  = a
type instance FromMaybe a ('Just b) = b

With Fcf, it translates to a data declaration:

data FromMaybe :: k -> Maybe k -> Exp k
type instance Eval (FromMaybe a 'Nothing)  = a
type instance Eval (FromMaybe a ('Just b)) = b

Fcfs can be higher-order.
The kind constructor Exp is a monad: there's (=<<) and Pure.

Essential language extensions for Fcf:

{-# LANGUAGE
    DataKinds,
    PolyKinds,
    TypeFamilies,
    TypeOperators,
    UndecidableInstances #-}

Contents

First-class type families
Functional combinators
Operations on common types
Pairs
Either
Maybe
Lists
Bool
Case splitting
Nat
Overloaded operations
Miscellaneous

Synopsis

type Exp
family Eval
type @@
data Pure
data Pure1
data Pure2
data Pure3
data Pure4
data Pure5
data Pure6
data Pure7
data Pure8
data Pure9
data =<<
data >>=
data <=<
type LiftM
data LiftM2
data LiftM3
data Join
data <$>
data <*>
data Flip
data ConstFn
data $
data Uncurry
data Fst
data Snd
data ***
data UnEither
data IsLeft
data IsRight
data UnMaybe
data FromMaybe
data IsNothing
data IsJust
data ++
data Head
data Last
data Tail
data Cons
data Snoc
data Cons2
data Init
data Uncons
data Unsnoc
data Singleton
data Null
data Length
data Reverse
data Intersperse
data Intercalate
data Foldr
data UnList
data Concat
data ConcatMap
data Unfoldr
data Replicate
data Take
data Drop
data SplitAt
data TakeWhile
data DropWhile
data Span
data Break
data Tails
data IsPrefixOf
data IsSuffixOf
data IsInfixOf
data Elem
data Lookup
data Find
data Filter
data Partition
data FindIndex
data SetIndex
data ZipWith
data Zip
data Unzip
data UnBool
data ||
data &&
data Not
data Case
data Match
type -->
type Is
type Any
type Else
data +
data -
data *
data ^
data <=
data >=
data <
data >
data Map
data Bimap
data Error
data Constraints
data TyEq
family Stuck
class IsBool
family If
data Assert
data AssertNot

Packagefirst-class-families-0.8.2.0
Exports107
LanguageHaskell2010
LicenceMIT
SourceFcf.hs

First-class type families

typetype Exp a = a -> Type

Source#

Kind of type-level expressions indexed by their result type.

familytype family Eval (e :: Exp a) :: a

Source#

Expression evaluator.

Instances206Eval, …

type Eval MEmpty_ = MEmptyDefined in first-class-families-0.8.2.0 · Fcf.Class.Monoid
type Eval (Bimap f g '(x, y)) = '(Eval (f x), Eval (g y))Defined in first-class-families-0.8.2.0 · Fcf.Class.Bifunctor
type Eval (Bimap f g ('Left x)) = 'Left (Eval (f x))Defined in first-class-families-0.8.2.0 · Fcf.Class.Bifunctor
type Eval (Bimap f g ('Right y)) = 'Right (Eval (g y))Defined in first-class-families-0.8.2.0 · Fcf.Class.Bifunctor
type Eval (First f2 x) = Eval (Bimap f2 Pure x)Defined in first-class-families-0.8.2.0 · Fcf.Class.Bifunctor
type Eval (Second g x) = Eval (Bimap Pure g x)Defined in first-class-families-0.8.2.0 · Fcf.Class.Bifunctor
type Eval (All p lst) = Eval (Foldr (Bicomap p Pure (&&)) 'True lst)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (And lst) = Eval (Foldr (&&) 'True lst)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Any p lst) = Eval (Foldr (Bicomap p Pure (||)) 'False lst)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Concat xs) = Eval (FoldMap Pure xs)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (ConcatMap f xs) = Eval (FoldMap f xs)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (FoldMap f 'Nothing) = MEmptyDefined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (FoldMap f '[]) = MEmptyDefined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (FoldMap f ('Left _a)) = MEmptyDefined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (FoldMap f ('Right x)) = Eval (f x)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (FoldMap f ('Just x)) = Eval (f x)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (FoldMap f (x ': xs)) = Eval (f x) <> Eval (FoldMap f xs)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Foldr f y 'Nothing) = yDefined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Foldr f y '[]) = yDefined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Foldr f y ('Left _a)) = yDefined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Foldr f y ('Right x)) = Eval (f x y)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Foldr f y ('Just x)) = Eval (f x y)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Foldr f y (x ': xs)) = Eval (f x (Eval (Foldr f y xs)))Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Or lst) = Eval (Foldr (||) 'False lst)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Sum ns) = Eval (Foldr (+) 0 ns)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Map f 'Nothing) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f '(x, a2)) = '(x, Eval (f a2))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f '(x, y, a2)) = '(x, y, Eval (f a2))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f '(x, y, z, a2)) = '(x, y, z, Eval (f a2))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f '(x, y, z, w, a2)) = '(x, y, z, w, Eval (f a2))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f ('Left x)) = 'Left xDefined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f ('Right a3)) = 'Right (Eval (f a3))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f ('Just a3)) = 'Just (Eval (f a3))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f (a2 ': as)) = Eval (f a2) ': Eval (Map f as)Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Compare 'Nothing 'Nothing) = 'EQDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare 'Nothing ('Just _b)) = 'LTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare 'EQ 'GT) = 'LTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare 'EQ 'LT) = 'GTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare 'False 'True) = 'GTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare 'GT 'EQ) = 'GTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare 'GT 'LT) = 'GTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare 'LT 'EQ) = 'LTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare 'LT 'GT) = 'LTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare 'True 'False) = 'GTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare '(a3, a4) '(b1, b2)) = Eval (Compare a3 b1) <> Eval (Compare a4 b2)Defined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare '(a4, a5, a6) '(b1, b2, b3)) = (Eval (Compare a4 b1) <> Eval (Compare a5 b2)) <> Eval (Compare a6 b3)Defined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare '[] '[]) = 'EQDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare '[] (_y ': _ys)) = 'LTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare ('Left _a) ('Right _b)) = 'LTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare ('Left a2) ('Left b2)) = Eval (Compare a2 b2)Defined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare ('Right _a) ('Left _b)) = 'GTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare ('Right a3) ('Right b)) = Eval (Compare a3 b)Defined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare ('Just _a) 'Nothing) = 'GTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare ('Just a2) ('Just b)) = Eval (Compare a2 b)Defined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare (_x ': _xs) '[]) = 'GTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare (x ': xs) (y ': ys)) = Eval (Compare x y) <> Eval (Compare xs ys)Defined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare a a) = 'EQDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare a a) = 'EQDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare a b) = CmpSymbol a bDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare a b) = CmpNat a bDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (Compare a b) = 'EQDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (ConstFn a2 _b) = a2Defined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Flip f y x) = Eval (f x y)Defined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Join e) = Eval (Eval e)Defined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (LiftM2 f x y) = Eval (f (Eval x) (Eval y))Defined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (LiftM3 f x y z) = Eval (f (Eval x) (Eval y) (Eval z))Defined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Pure x) = xDefined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Pure1 f x) = f xDefined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Pure2 f x y) = f x yDefined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Pure3 f x y z) = f x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Pure4 f w x y z) = f w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Pure5 f v w x y z) = f v w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Pure6 f2 u v w x y z) = f2 u v w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Pure7 f2 t u v w x y z) = f2 t u v w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Pure8 f2 s t u v w x y z) = f2 s t u v w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Pure9 f2 r s t u v w x y z) = f2 r s t u v w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (Not 'False) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (Not 'True) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (UnBool fal tru 'False) = Eval falDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (UnBool fal tru 'True) = Eval truDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (FromMaybe _a ('Just b)) = bDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (FromMaybe a2 'Nothing) = a2Defined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (Fst '(a2, _b)) = a2Defined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsJust 'Nothing) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsJust ('Just _a)) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsLeft ('Left _a)) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsLeft ('Right _a)) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsNothing 'Nothing) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsNothing ('Just _a)) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsRight ('Left _a)) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsRight ('Right _a)) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (Snd '(_a, b)) = bDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (UnEither f g ('Left x)) = Eval (f x)Defined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (UnEither f g ('Right y)) = Eval (g y)Defined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (UnMaybe y f 'Nothing) = Eval yDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (UnMaybe y f ('Just x)) = Eval (f x)Defined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (Uncurry f '(x, y)) = Eval (f x y)Defined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (Bicomap f g r x y) = Eval (r (Eval (f x)) (Eval (g y)))Defined in first-class-families-0.8.2.0 · Fcf.Data.Function
type Eval (On r f x y) = Eval (r (Eval (f x)) (Eval (f y)))Defined in first-class-families-0.8.2.0 · Fcf.Data.Function
type Eval (Break p lst) = Eval (Span (Not <=< p) lst)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Cons a2 as) = a2 ': asDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Cons2 '(a3, b) '(as, bs)) = '(a3 ': as, b ': bs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Drop n as) = Drop_ n asDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (DropWhile p '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (DropWhile p (x ': xs)) = Eval (If (Eval (p x)) (DropWhile p xs) (Pure (x ': xs)))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Elem a2 as) = Eval (IsJust =<< FindIndex (TyEq a2) as)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Filter _p '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Filter p (a2 ': as)) = Eval (If (Eval (p a2)) ('(:) a2 <$> Filter p as) (Filter p as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Find _p '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Find p (a2 ': as)) = Eval (If (Eval (p a2)) (Pure ('Just a2)) (Find p as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (FindIndex _p '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (FindIndex p (a2 ': as)) = Eval (If (Eval (p a2)) (Pure ('Just 0)) (Map ((+) 1) =<< FindIndex p as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Head '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Head (a2 ': _as)) = 'Just a2Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Init '[a2]) = 'Just '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Init '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Init (a2 ': b ': as)) = Eval (Map (Cons a2) =<< Init (b ': as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Intercalate xs xss) = Eval (Concat =<< Intersperse xs xss)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Intersperse _1 '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Intersperse sep (x ': xs)) = x ': Eval (PrependToAll sep xs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (IsInfixOf xs ys) = Eval (Any (IsPrefixOf xs) =<< Tails ys)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (IsPrefixOf xs ys) = IsPrefixOf_ xs ysDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (IsSuffixOf xs ys) = Eval (IsPrefixOf (Reverse @@ xs) (Reverse @@ ys))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Last '[a2]) = 'Just a2Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Last '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Last (a2 ': b ': as)) = Eval (Last (b ': as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Length '[]) = 0Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Length (a2 ': as)) = 1 + Eval (Length as)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Lookup a as) = Eval (Map Snd (Eval (Find (TyEq a <=< Fst) as)))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Null '[]) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Null (a2 ': as)) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (NumIter a s) = If (Eval (s > 0)) ('Just '(a, s - 1)) 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (PartHelp p a2 '(xs, ys)) = If (Eval (p a2)) '(a2 ': xs, ys) '(xs, a2 ': ys)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Partition p lst) = Eval (Foldr (PartHelp p) '('[], '[]) lst)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (PrependF x '(xs, y)) = '(x ': xs, y)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (PrependToAll _1 '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (PrependToAll sep (x ': xs)) = sep ': x ': Eval (PrependToAll sep xs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Replicate n a2) = Eval (Unfoldr (NumIter a2) n)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Rev '[] ys) = ysDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Rev (x ': xs) ys) = Eval (Rev xs (x ': ys))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Reverse l) = Eval (Rev l '[])Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (SetIndex n a' as) = SetIndexImpl n a' asDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Singleton x) = '[x]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Snoc lst a) = Eval (lst ++ '[a])Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Span p lst) = '(Eval (TakeWhile p lst), Eval (DropWhile p lst))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (SplitAt n xs) = '(Eval (Take n xs), Eval (Drop n xs))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Tail '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Tail (_a ': as)) = 'Just asDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Tails '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Tails (a2 ': as)) = (a2 ': as) ': Eval (Tails as)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Take n as) = Take_ n asDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (TakeWhile p '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (TakeWhile p (x ': xs)) = Eval (If (Eval (p x)) ('(:) x <$> TakeWhile p xs) (Pure '[]))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (UnList y f xs) = Eval (Foldr f y xs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Uncons '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Uncons (a ': xs)) = 'Just '(a, xs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Unfoldr f c) = Eval (UnfoldrCase f (f @@ c))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (UnfoldrCase _1 'Nothing) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (UnfoldrCase f ('Just ab)) = Eval (Fst ab) ': Eval (Unfoldr f (Eval (Snd ab)))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Unsnoc '[x]) = 'Just '('[], x)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Unsnoc '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Unsnoc (x ': y ': ys)) = Eval (Map (PrependF x) =<< Unsnoc (y ': ys))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Unzip as) = Eval (Foldr Cons2 '('[], '[]) (Eval as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Zip as bs) = Eval (ZipWith (Pure2 '((,))) as bs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (ZipWith _f '[] _bs) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (ZipWith _f _as '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (ZipWith f (a2 ': as) (b2 ': bs)) = Eval (f a2 b2) ': Eval (ZipWith f as bs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Assert msg mcond k) = Eval (If (Eval mcond) (Pure k) (TError msg))Defined in first-class-families-0.8.2.0 · Fcf.Utils
type Eval (AssertNot err mcond k) = Eval (Assert err (Not =<< mcond) k)Defined in first-class-families-0.8.2.0 · Fcf.Utils
type Eval (Case ms a) = Case_ ms aDefined in first-class-families-0.8.2.0 · Fcf.Utils
type Eval (Constraints '[]) = ()Defined in first-class-families-0.8.2.0 · Fcf.Utils
type Eval (Constraints (a ': as)) = (a, Eval (Constraints as))Defined in first-class-families-0.8.2.0 · Fcf.Utils
type Eval (Error msg) = TypeError ('Text msg)Defined in first-class-families-0.8.2.0 · Fcf.Utils
type Eval (TError msg) = TypeError msgDefined in first-class-families-0.8.2.0 · Fcf.Utils
type Eval (TyEq a b) = TyEqImpl a bDefined in first-class-families-0.8.2.0 · Fcf.Utils
type Eval ('False && b) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval ('False || b) = bDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval ('True && b) = bDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval ('True || b) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval ((<=<) f g x) = Eval (f (Eval (g x)))Defined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval ((***) f f' '(b2, b'2)) = '(Eval (f b2), Eval (f' b'2))Defined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (a && 'False) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (a && 'True) = aDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (a || 'False) = aDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (a || 'True) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (a * b) = a * bDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat
type Eval (a + b) = a + bDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat
type Eval (a - b) = a - bDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat
type Eval (a < b) = Eval (Not =<< (a >= b))Defined in first-class-families-0.8.2.0 · Fcf.Data.Nat
type Eval (a <= b) = a <=? bDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat
type Eval (a > b) = Eval (Not =<< (a <= b))Defined in first-class-families-0.8.2.0 · Fcf.Data.Nat
type Eval (a >= b) = b <=? aDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat
type Eval (a ^ b) = a ^ bDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat
type Eval (a2 < b) = Compare a2 b ~== 'LTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (a2 <= b) = Compare a2 b ~/= 'GTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (a2 > b) = Compare a2 b ~== 'GTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (a2 >= b) = Compare a2 b ~/= 'LTDefined in first-class-families-0.8.2.0 · Fcf.Class.Ord
type Eval (e >>= k) = Eval (k (Eval e))Defined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (f $ a3) = Eval (f a3)Defined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (f <$> e) = f (Eval e)Defined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (f <*> e) = Eval f (Eval e)Defined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (k =<< e) = Eval (k (Eval e))Defined in first-class-families-0.8.2.0 · Fcf.Combinators
type Eval (x .<> y) = x <> yDefined in first-class-families-0.8.2.0 · Fcf.Class.Monoid
type Eval (x & f) = Eval (f x)Defined in first-class-families-0.8.2.0 · Fcf.Data.Function
type Eval (xs ++ ys) = xs <> ysDefined in first-class-families-0.8.2.0 · Fcf.Data.List

typetype (@@) (f :: k1 -> Exp k) (x :: k1) = Eval (f x)

Source#

Apply and evaluate a unary type function.

Functional combinators

datadata Pure (b :: a) (c :: a)

Instances1Eval

type Eval (Pure x) = xDefined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata Pure1 (c :: a -> b) (d :: a) (e :: b)

Instances1Eval

type Eval (Pure1 f x) = f xDefined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata Pure2 (d :: a -> b -> c) (e :: a) (f :: b) (g :: c)

Instances1Eval

type Eval (Pure2 f x y) = f x yDefined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata Pure3 (e :: a -> b -> c -> d) (f :: a) (g :: b) (h :: c) (i :: d)

Instances1Eval

type Eval (Pure3 f x y z) = f x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata Pure4 (f :: a -> b -> c -> d -> e) (g :: a) (h :: b) (i :: c) (j :: d) (k :: e)

Instances1Eval

type Eval (Pure4 f w x y z) = f w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata Pure5 (g :: a -> b -> c -> d -> e -> f) (h :: a) (i :: b) (j :: c) (k :: d) (l :: e) (m :: f)

Instances1Eval

type Eval (Pure5 f v w x y z) = f v w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata Pure6 (h :: a -> b -> c -> d -> e -> f -> g) (i :: a) (j :: b) (k :: c) (l :: d) (m :: e) (n :: f) (o :: g)

Instances1Eval

type Eval (Pure6 f2 u v w x y z) = f2 u v w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators

data

data Pure7 (i :: a -> b -> c -> d -> e -> f -> g -> h) (j :: a) (k :: b) (l :: c) (m :: d) (n :: e) (o :: f) (p :: g) (q :: h)

Instances1Eval

type Eval (Pure7 f2 t u v w x y z) = f2 t u v w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators

data

data Pure8 (j :: a -> b -> c -> d -> e -> f -> g -> h -> i) (k :: a) (l :: b) (m :: c) (n :: d) (o :: e) (p :: f) (q :: g) (r :: h) (s :: i)

Instances1Eval

type Eval (Pure8 f2 s t u v w x y z) = f2 s t u v w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators

data

data Pure9 (k :: a -> b -> c -> d -> e -> f -> g -> h -> i -> j) (l :: a) (m :: b) (n :: c) (o :: d) (p :: e) (q :: f) (r :: g) (s :: h) (t :: i) (u :: j)

Instances1Eval

type Eval (Pure9 f2 r s t u v w x y z) = f2 r s t u v w x y zDefined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata (=<<) (c :: a -> Exp b) (d :: Exp a) (e :: b)

Instances1Eval

type Eval (k =<< e) = Eval (k (Eval e))Defined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata (>>=) (c :: Exp a) (d :: a -> Exp b) (e :: b)

Instances1Eval

type Eval (e >>= k) = Eval (k (Eval e))Defined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata (<=<) (d :: b -> Exp c) (e :: a -> Exp b) (f :: a) (g :: c)

Instances1Eval

type Eval ((<=<) f g x) = Eval (f (Eval (g x)))Defined in first-class-families-0.8.2.0 · Fcf.Combinators

typetype LiftM = (=<<)

datadata LiftM2 (d :: a -> b -> Exp c) (e :: Exp a) (f :: Exp b) (g :: c)

Instances1Eval

type Eval (LiftM2 f x y) = Eval (f (Eval x) (Eval y))Defined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata LiftM3 (e :: a -> b -> c -> Exp d) (f :: Exp a) (g :: Exp b) (h :: Exp c) (i :: d)

Instances1Eval

type Eval (LiftM3 f x y z) = Eval (f (Eval x) (Eval y) (Eval z))Defined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata Join (b :: Exp (Exp a)) (c :: a)

Instances1Eval

type Eval (Join e) = Eval (Eval e)Defined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata (<$>) (c :: a -> b) (d :: Exp a) (e :: b)

Instances1Eval

type Eval (f <$> e) = f (Eval e)Defined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata (<*>) (c :: Exp (a -> b)) (d :: Exp a) (e :: b)

Instances1Eval

type Eval (f <*> e) = Eval f (Eval e)Defined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata Flip (d :: a -> b -> Exp c) (e :: b) (f :: a) (g :: c)

Instances1Eval

type Eval (Flip f y x) = Eval (f x y)Defined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata ConstFn (c :: a) (d :: b) (e :: a)

Instances1Eval

type Eval (ConstFn a2 _b) = a2Defined in first-class-families-0.8.2.0 · Fcf.Combinators

datadata ($) (c :: a -> Exp b) (d :: a) (e :: b)

Source#

Note that this denotes the identity function, so ($) f can usually be replaced with f.

Instances1Eval

type Eval (f $ a3) = Eval (f a3)Defined in first-class-families-0.8.2.0 · Fcf.Combinators

Operations on common types

Pairs

datadata Uncurry (d :: a -> b -> Exp c) (e :: (a, b)) (f :: c)

Instances1Eval

type Eval (Uncurry f '(x, y)) = Eval (f x y)Defined in first-class-families-0.8.2.0 · Fcf.Data.Common

datadata Fst (c :: (a, b)) (d :: a)

Instances1Eval

type Eval (Fst '(a2, _b)) = a2Defined in first-class-families-0.8.2.0 · Fcf.Data.Common

datadata Snd (c :: (a, b)) (d :: b)

Instances1Eval

type Eval (Snd '(_a, b)) = bDefined in first-class-families-0.8.2.0 · Fcf.Data.Common

datadata (***) (a :: b -> Exp c) (d :: b' -> Exp c') (e :: (b, b')) (f :: (c, c'))

Source#

Specialization of Bimap for pairs.

Instances1Eval

type Eval ((***) f f' '(b2, b'2)) = '(Eval (f b2), Eval (f' b'2))Defined in first-class-families-0.8.2.0 · Fcf.Data.Common

Either

datadata UnEither (d :: a -> Exp c) (e :: b -> Exp c) (f :: Either a b) (g :: c)

Instances2Eval

type Eval (UnEither f g ('Left x)) = Eval (f x)Defined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (UnEither f g ('Right y)) = Eval (g y)Defined in first-class-families-0.8.2.0 · Fcf.Data.Common

datadata IsLeft (c :: Either a b) (d :: Bool)

Instances2Eval

type Eval (IsLeft ('Left _a)) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsLeft ('Right _a)) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Common

datadata IsRight (c :: Either a b) (d :: Bool)

Instances2Eval

type Eval (IsRight ('Left _a)) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsRight ('Right _a)) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Common

Maybe

datadata UnMaybe (c :: Exp b) (d :: a -> Exp b) (e :: Maybe a) (f :: b)

Instances2Eval

type Eval (UnMaybe y f 'Nothing) = Eval yDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (UnMaybe y f ('Just x)) = Eval (f x)Defined in first-class-families-0.8.2.0 · Fcf.Data.Common

datadata FromMaybe (a :: k) (b :: Maybe k) (c :: k)

Instances2Eval

type Eval (FromMaybe _a ('Just b)) = bDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (FromMaybe a2 'Nothing) = a2Defined in first-class-families-0.8.2.0 · Fcf.Data.Common

datadata IsNothing (b :: Maybe a) (c :: Bool)

Instances2Eval

type Eval (IsNothing 'Nothing) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsNothing ('Just _a)) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Common

datadata IsJust (b :: Maybe a) (c :: Bool)

Instances2Eval

type Eval (IsJust 'Nothing) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Common
type Eval (IsJust ('Just _a)) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Common

Lists

datadata (++) (b :: [a]) (c :: [a]) (d :: [a])

Source#

List catenation.

Example

Example2 expressions

>>> data Example where Ex :: a -> Example  -- Hide the type of examples to avoid brittleness in different GHC versions>>> :kind! Ex (Eval ([1, 2] ++ [3, 4]) :: [Natural])Ex (Eval ([1, 2] ++ [3, 4]) :: [Natural]) :: Example= Ex [1, 2, 3, 4]

Instances1Eval

type Eval (xs ++ ys) = xs <> ysDefined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Head (b :: [a]) (c :: Maybe a)

Instances2Eval

type Eval (Head '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Head (a2 ': _as)) = 'Just a2Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Last (b :: [a]) (c :: Maybe a)

Instances3Eval

type Eval (Last '[a2]) = 'Just a2Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Last '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Last (a2 ': b ': as)) = Eval (Last (b ': as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Tail (b :: [a]) (c :: Maybe [a])

Instances2Eval

type Eval (Tail '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Tail (_a ': as)) = 'Just asDefined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Cons (b :: a) (c :: [a]) (d :: [a])

Source#

Append an element to a list.

Example

Example2 expressions

>>> :kind! Eval (Cons 1 [2, 3])Eval (Cons 1 [2, 3]) :: [Natural]= [1, 2, 3]>>> :kind! Eval (Cons Int [Char, Maybe Double])Eval (Cons Int [Char, Maybe Double]) :: [*]= [Int, Char, Maybe Double]

Instances1Eval

type Eval (Cons a2 as) = a2 ': asDefined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Snoc (b :: [a]) (c :: a) (d :: [a])

Source#

Append an element to the end of a list.

Example

Example1 expression

>>> :kind! Eval (Snoc [1,2,3] 4)Eval (Snoc [1,2,3] 4) :: [Natural]= [1, 2, 3, 4]

Instances1Eval

type Eval (Snoc lst a) = Eval (lst ++ '[a])Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Cons2 (c :: (a, b)) (d :: ([a], [b])) (e :: ([a], [b]))

Source#

Append elements to two lists. Used in the definition of Unzip.

Instances1Eval

type Eval (Cons2 '(a3, b) '(as, bs)) = '(a3 ': as, b ': bs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Init (b :: [a]) (c :: Maybe [a])

Instances3Eval

type Eval (Init '[a2]) = 'Just '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Init '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Init (a2 ': b ': as)) = Eval (Map (Cons a2) =<< Init (b ': as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Uncons (b :: [a]) (c :: Maybe (a, [a]))

Instances2Eval

type Eval (Uncons '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Uncons (a ': xs)) = 'Just '(a, xs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Unsnoc (b :: [a]) (c :: Maybe ([a], a))

Source#

Decompose a list into init and last

Example

Example1 expression

>>> :kind! Eval (Unsnoc '[])Eval (Unsnoc '[]) :: Maybe ([a], a)= Nothing

Example1 expression

>>> :kind! Eval (Unsnoc '[1])Eval (Unsnoc '[1]) :: Maybe ([Natural], Natural)= Just '( '[], 1)

Example1 expression

>>> :kind! Eval (Unsnoc '[1,2,3])Eval (Unsnoc '[1,2,3]) :: Maybe ([Natural], Natural)= Just '([1, 2], 3)

Instances3Eval

type Eval (Unsnoc '[x]) = 'Just '('[], x)Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Unsnoc '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Unsnoc (x ': y ': ys)) = Eval (Map (PrependF x) =<< Unsnoc (y ': ys))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Singleton (b :: a) (c :: [a])

Instances1Eval

type Eval (Singleton x) = '[x]Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Null (b :: [a]) (c :: Bool)

Instances2Eval

type Eval (Null '[]) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Null (a2 ': as)) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Length (b :: [a]) (c :: Nat)

Instances2Eval

type Eval (Length '[]) = 0Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Length (a2 ': as)) = 1 + Eval (Length as)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Reverse (b :: [a]) (c :: [a])

Source#

Reverse a list.

Example

Example1 expression

>>> :kind! Eval (Reverse [1,2,3,4,5])Eval (Reverse [1,2,3,4,5]) :: [Natural]= [5, 4, 3, 2, 1]

Instances1Eval

type Eval (Reverse l) = Eval (Rev l '[])Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Intersperse (b :: a) (c :: [a]) (d :: [a])

Source#

Intersperse a separator between elements of a list.

Example

Example1 expression

>>> :kind! Eval (Intersperse 0 [1,2,3,4])Eval (Intersperse 0 [1,2,3,4]) :: [Natural]= [1, 0, 2, 0, 3, 0, 4]

Instances2Eval

type Eval (Intersperse _1 '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Intersperse sep (x ': xs)) = x ': Eval (PrependToAll sep xs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Intercalate (b :: [a]) (c :: [[a]]) (d :: [a])

Source#

Join a list of words separated by some word.

Example

Example1 expression

>>> :kind! Eval (Intercalate '[", "] [ '["Lorem"], '["ipsum"], '["dolor"] ])Eval (Intercalate '[", "] [ '["Lorem"], '["ipsum"], '["dolor"] ]) :: [TL.Symbol]= ["Lorem", ", ", "ipsum", ", ", "dolor"]

Instances1Eval

type Eval (Intercalate xs xss) = Eval (Concat =<< Intersperse xs xss)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Foldr (c :: a -> b -> Exp b) (d :: b) (e :: t a) (f :: b)

Source#

Right fold.

Example

Example1 expression

>>> :kind! Eval (Foldr (+) 0 [1, 2, 3, 4])Eval (Foldr (+) 0 [1, 2, 3, 4]) :: Natural= 10

Instances6Eval

type Eval (Foldr f y 'Nothing) = yDefined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Foldr f y '[]) = yDefined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Foldr f y ('Left _a)) = yDefined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Foldr f y ('Right x)) = Eval (f x y)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Foldr f y ('Just x)) = Eval (f x y)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable
type Eval (Foldr f y (x ': xs)) = Eval (f x (Eval (Foldr f y xs)))Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable

datadata UnList (c :: b) (d :: a -> b -> Exp b) (e :: [a]) (f :: b)

Source#

This is Foldr with its argument flipped.

Instances1Eval

type Eval (UnList y f xs) = Eval (Foldr f y xs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Concat (a :: t m) (b :: m)

Source#

Concatenate a collection of elements from a monoid.

Example

For example, fold a list of lists.

Concat :: [[a]] -> Exp [a]

Example2 expressions

>>> :kind! Eval (Concat ([[1,2], [3,4], [5,6]]))Eval (Concat ([[1,2], [3,4], [5,6]])) :: [Natural]= [1, 2, 3, 4, 5, 6]>>> :kind! Eval (Concat ([[Int, Maybe Int], [Maybe String, Either Double Int]]))Eval (Concat ([[Int, Maybe Int], [Maybe String, Either Double Int]])) :: [*]= [Int, Maybe Int, Maybe [Char], Either Double Int]

Instances1Eval

type Eval (Concat xs) = Eval (FoldMap Pure xs)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable

datadata ConcatMap (c :: a -> Exp [b]) (d :: t a) (e :: [b])

Source#

Map a function and concatenate the results.

This is FoldMap specialized to the list monoid.

Instances1Eval

type Eval (ConcatMap f xs) = Eval (FoldMap f xs)Defined in first-class-families-0.8.2.0 · Fcf.Class.Foldable

datadata Unfoldr (c :: b -> Exp (Maybe (a, b))) (d :: b) (e :: [a])

Source#

Unfold a generator into a list.

Example

Example2 expressions

>>> data ToThree :: Nat -> Exp (Maybe (Nat, Nat))>>> :{type instance Eval (ToThree b) =  If (4 TL.<=? b)    Nothing    (Just '(b, b TL.+ 1)):}

Example1 expression

>>> :kind! Eval (Unfoldr ToThree 0)Eval (Unfoldr ToThree 0) :: [Natural]= [0, 1, 2, 3]

Example

Example1 expression

>>> :kind! Eval (Replicate 4 '("ok", 2))Eval (Replicate 4 '("ok", 2)) :: [(TL.Symbol, Natural)]= ['("ok", 2), '("ok", 2), '("ok", 2), '("ok", 2)]

Instances1Eval

type Eval (Replicate n a2) = Eval (Unfoldr (NumIter a2) n)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Take (b :: Nat) (c :: [a]) (d :: [a])

Source#

Take a prefix of fixed length.

Example

Example1 expression

>>> :kind! Eval (Take 2 [1,2,3,4,5])Eval (Take 2 [1,2,3,4,5]) :: [Natural]= [1, 2]

Instances1Eval

type Eval (Take n as) = Take_ n asDefined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Drop (b :: Nat) (c :: [a]) (d :: [a])

Source#

Drop a prefix of fixed length, evaluate to the remaining suffix.

Example

Example1 expression

>>> :kind! Eval (Drop 2 [1,2,3,4,5])Eval (Drop 2 [1,2,3,4,5]) :: [Natural]= [3, 4, 5]

Instances1Eval

type Eval (Drop n as) = Drop_ n asDefined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata SplitAt (b :: Nat) (c :: [a]) (d :: ([a], [a]))

Source#

Return a tuple where first element is xs prefix of length n and second element is the remainder of the list.

Example

Example1 expression

>>> :kind! Eval (SplitAt 3 '[1,2,3,4,5])Eval (SplitAt 3 '[1,2,3,4,5]) :: ([Natural], [Natural])= '([1, 2, 3], [4, 5])

Instances1Eval

type Eval (SplitAt n xs) = '(Eval (Take n xs), Eval (Drop n xs))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata TakeWhile (b :: a -> Exp Bool) (c :: [a]) (d :: [a])

Source#

Take the longest prefix of elements satisfying a predicate.

Example

Example1 expression

>>> :kind! Eval (TakeWhile ((>=) 3) [1, 2, 3, 4, 5])Eval (TakeWhile ((>=) 3) [1, 2, 3, 4, 5]) :: [Natural]= [1, 2, 3]

Instances2Eval

type Eval (TakeWhile p '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (TakeWhile p (x ': xs)) = Eval (If (Eval (p x)) ('(:) x <$> TakeWhile p xs) (Pure '[]))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata DropWhile (b :: a -> Exp Bool) (c :: [a]) (d :: [a])

Source#

Drop the longest prefix of elements satisfying a predicate, evaluate to the remaining suffix.

Example

:kind! Eval (DropWhile ((>=) 3) [1, 2, 3, 4, 5]) Eval (DropWhile ((>=) 3) [1, 2, 3, 4, 5]) :: [Natural] = [4, 5]

Instances2Eval

type Eval (DropWhile p '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (DropWhile p (x ': xs)) = Eval (If (Eval (p x)) (DropWhile p xs) (Pure (x ': xs)))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Span (b :: a -> Exp Bool) (c :: [a]) (d :: ([a], [a]))

Source#

Span, applied to a predicate p and a list xs, returns a tuple: the first component is the longest prefix (possibly empty) of xs whose elements satisfy p; the second component is the remainder of the list.

See also TakeWhile, DropWhile, and Break.

Example

Example1 expression

>>> :kind! Eval (Span (Flip (<) 3) [1,2,3,4,1,2])Eval (Span (Flip (<) 3) [1,2,3,4,1,2]) :: ([Natural], [Natural])= '([1, 2], [3, 4, 1, 2])

Example1 expression

>>> :kind! Eval (Span (Flip (<) 9) [1,2,3])Eval (Span (Flip (<) 9) [1,2,3]) :: ([Natural], [Natural])= '([1, 2, 3], '[])

Example1 expression

>>> :kind! Eval (Span (Flip (<) 0) [1,2,3])Eval (Span (Flip (<) 0) [1,2,3]) :: ([Natural], [Natural])= '( '[], [1, 2, 3])

Instances1Eval

type Eval (Span p lst) = '(Eval (TakeWhile p lst), Eval (DropWhile p lst))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Break (b :: a -> Exp Bool) (c :: [a]) (d :: ([a], [a]))

Source#

Break, applied to a predicate p and a list xs, returns a tuple: the first component is the longest prefix (possibly empty) of xs whose elements do not satisfy p; the second component is the remainder of the list.

Example

Example1 expression

>>> :kind! Eval (Break (Flip (>) 3) [1,2,3,4,1,2])Eval (Break (Flip (>) 3) [1,2,3,4,1,2]) :: ([Natural], [Natural])= '([1, 2, 3], [4, 1, 2])

Example1 expression

>>> :kind! Eval (Break (Flip (<) 9) [1,2,3])Eval (Break (Flip (<) 9) [1,2,3]) :: ([Natural], [Natural])= '( '[], [1, 2, 3])

Example1 expression

>>> :kind! Eval (Break (Flip (>) 9) [1,2,3])Eval (Break (Flip (>) 9) [1,2,3]) :: ([Natural], [Natural])= '([1, 2, 3], '[])

Instances1Eval

type Eval (Break p lst) = Eval (Span (Not <=< p) lst)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Tails (b :: [a]) (c :: [[a]])

Source#

List of suffixes of a list.

Example

Example1 expression

>>> :kind! Eval (Tails [0,1,2,3])Eval (Tails [0,1,2,3]) :: [[Natural]]= [[0, 1, 2, 3], [1, 2, 3], [2, 3], '[3]]

Instances2Eval

type Eval (Tails '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Tails (a2 ': as)) = (a2 ': as) ': Eval (Tails as)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata IsPrefixOf (b :: [a]) (c :: [a]) (d :: Bool)

Source#

Return True when the first list is a prefix of the second.

Example

Example1 expression

>>> :kind! Eval ([0,1,2] `IsPrefixOf` [0,1,2,3,4,5])Eval ([0,1,2] `IsPrefixOf` [0,1,2,3,4,5]) :: Bool= True

Example1 expression

>>> :kind! Eval ([0,1,2] `IsPrefixOf` [0,1,3,2,4,5])Eval ([0,1,2] `IsPrefixOf` [0,1,3,2,4,5]) :: Bool= False

Example1 expression

>>> :kind! Eval ('[] `IsPrefixOf` [0,1,3,2,4,5])Eval ('[] `IsPrefixOf` [0,1,3,2,4,5]) :: Bool= True

Example1 expression

>>> :kind! Eval ([0,1,3,2,4,5] `IsPrefixOf` '[])Eval ([0,1,3,2,4,5] `IsPrefixOf` '[]) :: Bool= False

Instances1Eval

type Eval (IsPrefixOf xs ys) = IsPrefixOf_ xs ysDefined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata IsSuffixOf (b :: [a]) (c :: [a]) (d :: Bool)

Source#

Return True when the first list is a suffix of the second.

Example

Example1 expression

>>> :kind! Eval (IsSuffixOf [3,4,5] [0,1,2,3,4,5])Eval (IsSuffixOf [3,4,5] [0,1,2,3,4,5]) :: Bool= True

Example1 expression

>>> :kind! Eval (IsSuffixOf [3,4,5] [0,1,3,2,4,5])Eval (IsSuffixOf [3,4,5] [0,1,3,2,4,5]) :: Bool= False

Example1 expression

>>> :kind! Eval (IsSuffixOf '[] [0,1,3,2,4,5])Eval (IsSuffixOf '[] [0,1,3,2,4,5]) :: Bool= True

Example1 expression

>>> :kind! Eval (IsSuffixOf [0,1,3,2,4,5] '[])Eval (IsSuffixOf [0,1,3,2,4,5] '[]) :: Bool= False

Instances1Eval

type Eval (IsSuffixOf xs ys) = Eval (IsPrefixOf (Reverse @@ xs) (Reverse @@ ys))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata IsInfixOf (b :: [a]) (c :: [a]) (d :: Bool)

Source#

Return True when the first list is contained within the second.

Example

Example1 expression

>>> :kind! Eval (IsInfixOf [2,3,4] [0,1,2,3,4,5,6])Eval (IsInfixOf [2,3,4] [0,1,2,3,4,5,6]) :: Bool= True

Example1 expression

>>> :kind! Eval (IsInfixOf [2,4,4] [0,1,2,3,4,5,6])Eval (IsInfixOf [2,4,4] [0,1,2,3,4,5,6]) :: Bool= False

Instances1Eval

type Eval (IsInfixOf xs ys) = Eval (Any (IsPrefixOf xs) =<< Tails ys)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Elem (b :: a) (c :: [a]) (d :: Bool)

Source#

Return True if an element is in a list.

Example

Example2 expressions

>>> :kind! Eval (Elem 1 [1,2,3])Eval (Elem 1 [1,2,3]) :: Bool= True>>> :kind! Eval (Elem 1 [2,3])Eval (Elem 1 [2,3]) :: Bool= False

Instances1Eval

type Eval (Elem a2 as) = Eval (IsJust =<< FindIndex (TyEq a2) as)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Lookup (a :: k) (c :: [(k, b)]) (d :: Maybe b)

Source#

Find an element associated with a key in an association list.

Instances1Eval

type Eval (Lookup a as) = Eval (Map Snd (Eval (Find (TyEq a <=< Fst) as)))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Find (b :: a -> Exp Bool) (c :: [a]) (d :: Maybe a)

Source#

Find Just the first element satisfying a predicate, or evaluate to Nothing if no element satisfies the predicate.

Example

Example1 expression

>>> :kind! Eval (Find (TyEq 0) [1,2,3])Eval (Find (TyEq 0) [1,2,3]) :: Maybe Natural= Nothing

Example1 expression

>>> :kind! Eval (Find (TyEq 0) [1,2,3,0])Eval (Find (TyEq 0) [1,2,3,0]) :: Maybe Natural= Just 0

Instances2Eval

type Eval (Find _p '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Find p (a2 ': as)) = Eval (If (Eval (p a2)) (Pure ('Just a2)) (Find p as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Filter (b :: a -> Exp Bool) (c :: [a]) (d :: [a])

Source#

Keep all elements that satisfy a predicate, remove all that don't.

Example

Example1 expression

>>> :kind! Eval (Filter ((>) 3) [1,2,3,0])Eval (Filter ((>) 3) [1,2,3,0]) :: [Natural]= [1, 2, 0]

Instances2Eval

type Eval (Filter _p '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (Filter p (a2 ': as)) = Eval (If (Eval (p a2)) ('(:) a2 <$> Filter p as) (Filter p as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Partition (b :: a -> Exp Bool) (c :: [a]) (d :: ([a], [a]))

Source#

Split a list into one where all elements satisfy a predicate, and a second where no elements satisfy it.

Example

Example1 expression

>>> :kind! Eval (Partition ((>=) 35) [20, 30, 40, 50])Eval (Partition ((>=) 35) [20, 30, 40, 50]) :: ([Natural],                                                [Natural])= '([20, 30], [40, 50])

Instances1Eval

type Eval (Partition p lst) = Eval (Foldr (PartHelp p) '('[], '[]) lst)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata FindIndex (b :: a -> Exp Bool) (c :: [a]) (d :: Maybe Nat)

Source#

Find the index of an element satisfying the predicate.

Example

Example1 expression

>>> :kind! Eval (FindIndex ((<=) 3) [1,2,3,1,2,3])Eval (FindIndex ((<=) 3) [1,2,3,1,2,3]) :: Maybe Natural= Just 2

Example1 expression

>>> :kind! Eval (FindIndex ((>) 0) [1,2,3,1,2,3])Eval (FindIndex ((>) 0) [1,2,3,1,2,3]) :: Maybe Natural= Nothing

Instances2Eval

type Eval (FindIndex _p '[]) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (FindIndex p (a2 ': as)) = Eval (If (Eval (p a2)) (Pure ('Just 0)) (Map ((+) 1) =<< FindIndex p as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata SetIndex (b :: Nat) (c :: a) (d :: [a]) (e :: [a])

Source#

Modify an element at a given index.

The list is unchanged if the index is out of bounds.

Example

Example1 expression

>>> :kind! Eval (SetIndex 2 7 [1,2,3])Eval (SetIndex 2 7 [1,2,3]) :: [Natural]= [1, 2, 7]

Instances1Eval

type Eval (SetIndex n a' as) = SetIndexImpl n a' asDefined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata ZipWith (d :: a -> b -> Exp c) (e :: [a]) (f :: [b]) (g :: [c])

Source#

Combine elements of two lists pairwise.

Example

Example1 expression

>>> :kind! Eval (ZipWith (+) [1,2,3] [1,1,1])Eval (ZipWith (+) [1,2,3] [1,1,1]) :: [Natural]= [2, 3, 4]

Instances3Eval

type Eval (ZipWith _f '[] _bs) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (ZipWith _f _as '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Data.List
type Eval (ZipWith f (a2 ': as) (b2 ': bs)) = Eval (f a2 b2) ': Eval (ZipWith f as bs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Zip (c :: [a]) (d :: [b]) (e :: [(a, b)])

Instances1Eval

type Eval (Zip as bs) = Eval (ZipWith (Pure2 '((,))) as bs)Defined in first-class-families-0.8.2.0 · Fcf.Data.List

datadata Unzip (c :: Exp [(a, b)]) (d :: ([a], [b]))

Instances1Eval

type Eval (Unzip as) = Eval (Foldr Cons2 '('[], '[]) (Eval as))Defined in first-class-families-0.8.2.0 · Fcf.Data.List

Bool

datadata UnBool (b :: Exp a) (c :: Exp a) (d :: Bool) (e :: a)

Source#

N.B.: The order of the two branches is the opposite of "if": UnBool ifFalse ifTrue bool.

This mirrors the default order of constructors:

data Bool = False | True
----------- False < True

Instances2Eval

type Eval (UnBool fal tru 'False) = Eval falDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (UnBool fal tru 'True) = Eval truDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool

datadata (||) (a :: Bool) (b :: Bool) (c :: Bool)

Instances4Eval

type Eval ('False || b) = bDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval ('True || b) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (a || 'False) = aDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (a || 'True) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool

datadata (&&) (a :: Bool) (b :: Bool) (c :: Bool)

Instances4Eval

type Eval ('False && b) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval ('True && b) = bDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (a && 'False) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (a && 'True) = aDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool

datadata Not (a :: Bool) (b :: Bool)

Instances2Eval

type Eval (Not 'False) = 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool
type Eval (Not 'True) = 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Data.Bool

Case splitting

datadata Case (a :: [Match j k]) (b :: j) (c :: k)

Source#

(Limited) equivalent of \case { .. } syntax. Supports matching of exact values (-->) and final matches for any value (Any) or for passing value to subcomputation (Else). Examples:

type BoolToNat = Case
  [ 'True  --> 0
  , 'False --> 1
  ]

type NatToBool = Case
  [ 0 --> 'False
  , Any   'True
  ]

type ZeroOneOrSucc = Case
  [ 0  --> 0
  , 1  --> 1
  , Else   ((+) 1)
  ]

Instances1Eval

type Eval (Case ms a) = Case_ ms aDefined in first-class-families-0.8.2.0 · Fcf.Utils

datadata Match j k

typetype (-->) = 'Match_

Source#

Match concrete type in Case.

typetype Is = 'Is_

Source#

Match on predicate being successful with type in Case.

typetype Any = 'Any_

Source#

Match any type in Case. Should be used as a final branch.

Note: this identifier conflicts with Any (from Fcf.Class.Foldable) Any (from Data.Monoid), and Any (from GHC.Exts).

We recommend importing this one qualified.

typetype Else = 'Else_

Source#

Pass type being matched in Case to subcomputation. Should be used as a final branch.

Nat

datadata (+) (a :: Nat) (b :: Nat) (c :: Nat)

Instances1Eval

type Eval (a + b) = a + bDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat

datadata (-) (a :: Nat) (b :: Nat) (c :: Nat)

Instances1Eval

type Eval (a - b) = a - bDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat

datadata (*) (a :: Nat) (b :: Nat) (c :: Nat)

Instances1Eval

type Eval (a * b) = a * bDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat

datadata (^) (a :: Nat) (b :: Nat) (c :: Nat)

Instances1Eval

type Eval (a ^ b) = a ^ bDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat

datadata (<=) (a :: Nat) (b :: Nat) (c :: Bool)

Instances1Eval

type Eval (a <= b) = a <=? bDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat

datadata (>=) (a :: Nat) (b :: Nat) (c :: Bool)

Instances1Eval

type Eval (a >= b) = b <=? aDefined in first-class-families-0.8.2.0 · Fcf.Data.Nat

datadata (<) (a :: Nat) (b :: Nat) (c :: Bool)

Instances1Eval

type Eval (a < b) = Eval (Not =<< (a >= b))Defined in first-class-families-0.8.2.0 · Fcf.Data.Nat

datadata (>) (a :: Nat) (b :: Nat) (c :: Bool)

Instances1Eval

type Eval (a > b) = Eval (Not =<< (a <= b))Defined in first-class-families-0.8.2.0 · Fcf.Data.Nat

Overloaded operations

datadata Map (c :: a -> Exp b) (d :: f a) (e :: f b)

Source#

Type-level fmap for type-level functors.

Note: this name clashes with Data.Map.Lazy.Map from containers. FMap is provided as a synonym to avoid this.

Example

Example4 expressions

>>> data Example where Ex :: a -> Example  -- Hide the type of examples to avoid brittleness in different GHC versions>>> data AddMul :: Nat -> Nat -> Exp Nat>>> type instance Eval (AddMul x y) = (x TL.+ y) TL.* (x TL.+ y)>>> :kind! Ex (Eval (Map (AddMul 2) '[0, 1, 2, 3, 4]) :: [Nat])Ex (Eval (Map (AddMul 2) '[0, 1, 2, 3, 4]) :: [Nat]) :: Example= Ex [4, 9, 16, 25, 36]

Instances10Eval, …

type Eval (Map f 'Nothing) = 'NothingDefined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f '(x, a2)) = '(x, Eval (f a2))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f '(x, y, a2)) = '(x, y, Eval (f a2))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f '(x, y, z, a2)) = '(x, y, z, Eval (f a2))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f '(x, y, z, w, a2)) = '(x, y, z, w, Eval (f a2))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f '[]) = '[]Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f ('Left x)) = 'Left xDefined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f ('Right a3)) = 'Right (Eval (f a3))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f ('Just a3)) = 'Just (Eval (f a3))Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor
type Eval (Map f (a2 ': as)) = Eval (f a2) ': Eval (Map f as)Defined in first-class-families-0.8.2.0 · Fcf.Class.Functor

datadata Bimap (c :: a -> Exp a') (d :: b -> Exp b') (e :: f a b) (g :: f a' b')

Source#

Type-level bimap.

Example

Example2 expressions

>>> data Example where Ex :: a -> Example  -- Hide the type of examples to avoid brittleness in different GHC versions>>> :kind! Ex (Eval (Bimap ((+) 1) (Flip (-) 1) '(2, 4)) :: (Natural, Natural))Ex (Eval (Bimap ((+) 1) (Flip (-) 1) '(2, 4)) :: (Natural, Natural)) :: Example= Ex '(3, 3)

Instances3Eval

type Eval (Bimap f g '(x, y)) = '(Eval (f x), Eval (g y))Defined in first-class-families-0.8.2.0 · Fcf.Class.Bifunctor
type Eval (Bimap f g ('Left x)) = 'Left (Eval (f x))Defined in first-class-families-0.8.2.0 · Fcf.Class.Bifunctor
type Eval (Bimap f g ('Right y)) = 'Right (Eval (g y))Defined in first-class-families-0.8.2.0 · Fcf.Class.Bifunctor

Miscellaneous

datadata Error (b :: Symbol) (c :: a)

Source#

Type-level error.

Instances1Eval

type Eval (Error msg) = TypeError ('Text msg)Defined in first-class-families-0.8.2.0 · Fcf.Utils

datadata Constraints (a :: [Constraint]) (b :: Constraint)

Source#

Conjunction of a list of constraints.

Instances2Eval

type Eval (Constraints '[]) = ()Defined in first-class-families-0.8.2.0 · Fcf.Utils
type Eval (Constraints (a ': as)) = (a, Eval (Constraints as))Defined in first-class-families-0.8.2.0 · Fcf.Utils

datadata TyEq (c :: a) (d :: b) (e :: Bool)

Source#

Type equality.

Details

The base library also defines a similar (Type.Equality.==); it differs from TyEq in the following ways:

TyEq is heterogeneous: its arguments may have different kinds;
TyEq is reflexive: TyEq a a always reduces to True even if a is a variable.

Instances1Eval

type Eval (TyEq a b) = TyEqImpl a bDefined in first-class-families-0.8.2.0 · Fcf.Utils

familytype family Stuck :: a

Source#

A stuck type that can be used like a type-level undefined.

classclass IsBool (b :: Bool) where

Methods

_If :: (b ~ 'True => r) -> (b ~ 'False => r) -> r

Instances2IsBool

IsBool 'FalseDefined in first-class-families-0.8.2.0 · Fcf.Utils
IsBool 'TrueDefined in first-class-families-0.8.2.0 · Fcf.Utils

familytype family If (cond :: Bool) (tru :: k) (fls :: k) :: k where

Source#

Type-level If. If True a b ==> a; If False a b ==> b

Equations

If 'True tru fls = tru
If 'False tru fls = fls

datadata Assert (a :: ErrorMessage) (b :: Exp Bool) (c :: r) (d :: r)

Source#

A compile-time assert.

Raises the provided TypeError, whenever the condition evaluates to False.

Usage example: type ExampleAssertionFailure = Eval ( Pure '["foo", "bar"] >>= Length >>= Assert ('Text Assertion) (TyEq Int Void) )

Instances1Eval

type Eval (Assert msg mcond k) = Eval (If (Eval mcond) (Pure k) (TError msg))Defined in first-class-families-0.8.2.0 · Fcf.Utils

datadata AssertNot (a :: ErrorMessage) (b :: Exp Bool) (c :: r) (d :: r)

Source#

Compile-time assert, with condition negated.

Raises the provided TypeError, whenever the condition evaluates to True.

Also see Assert.

Instances1Eval

type Eval (AssertNot err mcond k) = Eval (Assert err (Not =<< mcond) k)Defined in first-class-families-0.8.2.0 · Fcf.Utils