Safe Haskell	Safe
Language	Haskell2010

Options.Harg.Het.Proofs

Description

This module provides type-level functions that need proofs to work properly.

Synopsis

type family (xs :: [k]) ++ (ts :: [k]) = (res :: [k]) where ...
class Proof xs y zs where
- proof :: (xs ++ (y ': zs)) :~~: ((xs ++ '[y]) ++ zs)
hgcastWith :: forall (a :: k) (b :: k') (r :: Type). (a :~~: b) -> (a ~~ b => r) -> r

Documentation

type family (xs :: [k]) ++ (ts :: [k]) = (res :: [k]) where ... Source #

Append two type-level lists

> :kind! '[Int, Bool] ++ '[Char, Maybe Int]
'[Int, Bool, Char, Maybe Int]

Equations

'[] ++ ys = ys
(x ': xs) ++ ys = x ': (xs ++ ys)

class Proof xs y zs where Source #

Proof that appending two lists is the same as appending the first element of the second list to the first one, and then appending the rest.

Methods

proof :: (xs ++ (y ': zs)) :~~: ((xs ++ '[y]) ++ zs) Source #

Instances details

Proof ('[] :: [k]) (y :: k) (zs :: [k]) Source #
Instance details Defined in Options.Harg.Het.Proofs Methods proof :: ('[] ++ (y ': zs)) :~~: (('[] ++ '[y]) ++ zs) Source #
Proof ('[] :: [k]) (y :: k) ('[] :: [k]) Source #
Instance details Defined in Options.Harg.Het.Proofs Methods proof :: ('[] ++ (y ': '[])) :~~: (('[] ++ '[y]) ++ '[]) Source #
ProofNil (xs ++ '[y]) => Proof (x ': xs :: [k]) (y :: k) ('[] :: [k]) Source #
Instance details Defined in Options.Harg.Het.Proofs Methods proof :: ((x ': xs) ++ (y ': '[])) :~~: (((x ': xs) ++ '[y]) ++ '[]) Source #
Proof xs y (z ': zs) => Proof (x ': xs :: [a]) (y :: a) (z ': zs :: [a]) Source #	Induction on the tail of the list
Instance details Defined in Options.Harg.Het.Proofs Methods proof :: ((x ': xs) ++ (y ': (z ': zs))) :~~: (((x ': xs) ++ '[y]) ++ (z ': zs)) Source #

hgcastWith :: forall (a :: k) (b :: k') (r :: Type). (a :~~: b) -> (a ~~ b => r) -> r Source #

Same as gcastWith but for heterogeneous propositional equality