idris2-profunctors/Data/Tensor.idr

62 lines
1.3 KiB
Idris

module Data.Tensor
%default total
public export
interface Bifunctor ten => Associative ten where
assoc : a `ten` (b `ten` c) <=> (a `ten` b) `ten` c
public export
interface Bifunctor ten => Symmetric ten where
swap : a `ten` b -> b `ten` a
swap = symmetric.leftToRight
symmetric : a `ten` b <=> b `ten` a
symmetric = MkEquivalence swap swap
public export
interface Associative ten => Tensor ten i | ten where
unitl : i `ten` a <=> a
unitr : a `ten` i <=> a
export
Associative Pair where
assoc = MkEquivalence (\(x,(y,z)) => ((x,y),z)) (\((x,y),z) => (x,(y,z)))
export
Symmetric Pair where
swap = Builtin.swap
export
Tensor Pair () where
unitl = MkEquivalence snd ((),)
unitr = MkEquivalence fst (,())
export
Associative Either where
assoc = MkEquivalence f b
where
f : forall a,b,c. Either a (Either b c) -> Either (Either a b) c
f (Left x) = Left (Left x)
f (Right (Left x)) = Left (Right x)
f (Right (Right x)) = Right x
b : forall a,b,c. Either (Either a b) c -> Either a (Either b c)
b (Left (Left x)) = Left x
b (Left (Right x)) = Right (Left x)
b (Right x) = Right (Right x)
export
Symmetric Either where
swap = either Right Left
export
Tensor Either Void where
unitl = MkEquivalence (either absurd id) Right
unitr = MkEquivalence (either id absurd) Left