Idris2/libs/prelude/Prelude/Basics.idr

72 lines
1.6 KiB
Idris

module Prelude.Basics
import Builtin
%default total
public export
Not : Type -> Type
Not x = x -> Void
-----------------------
-- UTILITY FUNCTIONS --
-----------------------
||| Manually assign a type to an expression.
||| @ a the type to assign
||| @ x the element to get the type
public export %inline
the : (0 a : Type) -> (1 x : a) -> a
the _ x = x
||| Identity function.
public export %inline
id : (1 x : a) -> a -- Hopefully linearity annotation won't
-- break equality proofs involving id
id x = x
||| Constant function. Ignores its second argument.
public export %inline
const : a -> b -> a
const x = \value => x
||| Function composition.
public export %inline
(.) : (b -> c) -> (a -> b) -> a -> c
(.) f g = \x => f (g x)
||| Takes in the first two arguments in reverse order.
||| @ f the function to flip
public export
flip : (f : a -> b -> c) -> b -> a -> c
flip f x y = f y x
||| Function application.
public export
apply : (a -> b) -> a -> b
apply f a = f a
public export
curry : ((a, b) -> c) -> a -> b -> c
curry f a b = f (a, b)
public export
uncurry : (a -> b -> c) -> (a, b) -> c
uncurry f (a, b) = f a b
-- $ is compiled specially to shortcut any tricky unification issues, but if
-- it did have a type this is what it would be, and it might be useful to
-- use directly sometimes (e.g. in higher order functions)
public export
($) : forall a, b . ((x : a) -> b x) -> (x : a) -> b x
($) f a = f a
-------------------
-- PROOF HELPERS --
-------------------
||| Equality is a congruence.
public export
cong : (0 f : t -> u) -> (1 p : a = b) -> f a = f b
cong f Refl = Refl