Data.Function.Reverse

This module provides the reverseArgs function which flips the arguments of a function of arbitrary arity. The return value of the flipped function can not be fully polymorphic as this could imply it is a function.

Example:

myFlip :: (a -> b -> c -> d -> [e]) -> d -> c -> b -> a -> [e]
myFlip = reverseArgs

However, if you supply a proof (of the form IsFun a ~ 'False) that a is not a function, you can also return a polymorphic type.

Example:

myFlip :: IsFun e ~ 'False => (a -> b -> c -> d -> e) -> d -> c -> b -> a -> e
myFlip = reverseArgs

Reversing arguments

reverseArgs :: (ReverseArgs (BoxResult a), Coercible a (BoxResult a), Coercible (ReversedArgs a) (BoxResult (ReversedArgs a)), ReversedArgs (BoxResult a) ~ BoxResult (ReversedArgs a)) => a -> ReversedArgs a

Reverse the arguments of a function. Does work with polymorphic return values if you supply a proof that the result is not a function.

Utilities

type family IsFun f

Determine whether the argument is a function.

Equations

IsFun (a -> b) = True

IsFun a = False

Internal types and functions

Applying the last argument

type family ApplyLast a z

Apply the last argument of a function to it.

Equations

ApplyLast (a -> b) z = If (IsFun b) (a -> ApplyLast b z) (MatchLastArg a b z)

type family MatchLastArg a b z

Match the last argument away.

Equations

MatchLastArg z b z = b

class ApplyingLast f z | f -> z where

Like ApplyLast, but on the value level.

Methods

applyLast :: f -> z -> ApplyLast f z

Apply a function f to its last argument z.

Instances

((~) * (ApplyLast (a -> b -> c) z) (a -> ApplyLast (b -> c) z), ApplyingLast (b -> c) z) => ApplyingLast (a -> b -> c) z

((~) Bool (IsFun b) False, (~) * a c) => ApplyingLast (a -> b) c

Reversing arguments

type ReversedArgs a = If (IsFun a) (ReverseOneArg a) a

Reverse the arguments of a function.

type family ReverseOneArg a

Reverse one of the arguments of a function and recurse for the rest.

Equations

ReverseOneArg (a -> b) = InsertAtEnd a (ReversedArgs b)

type InsertAtEnd a f = If (IsFun f) (InsertAtEndStep a f) (a -> f)

Insert an argument at the end.

type family InsertAtEndStep a f

Shift one to the left and insert something at the end.

Equations

InsertAtEndStep a (x -> y) = x -> InsertAtEnd a y

class ReverseArgs a where

Methods

reverseArgs' :: a -> ReversedArgs a

Reverse the arguments of some function. Does not work with functions with fully polymorphic return values, use reverseArgs instead.

Instances

(~) * (ReversedArgs a) a => ReverseArgs a

(ApplyingLast (a -> b) z, (~) * (ReversedArgs (a -> b)) (z -> r), (~) * (ReversedArgs (ApplyLast (a -> b) z)) r, ReverseArgs (ApplyLast (a -> b) z)) => ReverseArgs (a -> b)

Boxing results

type BoxResult a = If (IsFun a) (BoxArrow a) (Identity a)

Box the result in the Identity monad.

type family BoxArrow a

Box the result of a function in the Identity monad.

Equations

BoxArrow (a -> b) = a -> BoxResult b

boxResult :: Coercible a (BoxResult a) => a -> BoxResult a

Box the result in the Identity monad.

unboxResult :: Coercible a (BoxResult a) => BoxResult a -> a

Unbox the result, which is in the Identity monad.