Control.SIArrow

Categories of reversible computations.

Arrow.

class (Products cat, Coproducts cat, CatPlus cat) => SIArrow cat where

A category equipped with an embedding siarr from SemiIso into cat and some additional structure.

SIArrow abstracts categories of reversible computations (with reversible side effects).

The category cat should contain SemiIso as a sort of "subcategory of pure computations".

Minimal complete definition

(siarr | sipure), sibind

Methods

siarr :: ASemiIso' a b -> cat a b

Allows you to lift a SemiIso into cat. The resulting arrow should be in some sense minimal or "pure", similiar to pure, return and arr from Control.Category.

sipure :: ASemiIso' b a -> cat a b

Reversed version of siarr.

Use this where you would use pure.

sibind :: ASemiIso a (cat a b) (cat a b) b -> cat a b

Allows a computation to depend on a its input value.

I am not sure if this is the right way to get that ArrowApply or Monad like power. It seems quite easy to break the parser/pretty-printer inverse guarantee using this. On the other hand we have to be careful only when constructing the SemiIso using 'iso'/'semiIso' - and with an invalid SemiIso we could break everything anyway using siarr.

sisome :: cat () b -> cat () [b]

sisome v repeats v as long as possible, but no less then once.

simany :: cat () b -> cat () [b]

simany v repeats v as long as possible.

Instances

SIArrow ReifiedSemiIso'

MonadPlus m => SIArrow (Kleisli m)

SIArrow cat => SIArrow (Dual cat)

SIArrow cat => SIArrow (ReaderCT env cat)

(^>>) :: SIArrow cat => ASemiIso' a b -> cat b c -> cat a c infixr 1

Composes a SemiIso with an arrow.

(>>^) :: SIArrow cat => cat a b -> ASemiIso' b c -> cat a c infixr 1

Composes an arrow with a SemiIso.

(^<<) :: SIArrow cat => ASemiIso' b c -> cat a b -> cat a c infixr 1

Composes a SemiIso with an arrow, backwards.

(<<^) :: SIArrow cat => cat b c -> ASemiIso' a b -> cat a c infixr 1

Composes an arrow with a SemiIso, backwards.

(#>>) :: SIArrow cat => ASemiIso' b a -> cat b c -> cat a c infixr 1

Composes a reversed SemiIso with an arrow.

(>>#) :: SIArrow cat => cat a b -> ASemiIso' c b -> cat a c infixr 1

Composes an arrow with a reversed SemiIso.

(#<<) :: SIArrow cat => ASemiIso' c b -> cat a b -> cat a c infixr 1

Composes a reversed SemiIso with an arrow, backwards.

(<<#) :: SIArrow cat => cat b c -> ASemiIso' b a -> cat a c infixr 1

Composes an arrow with a reversed SemiIso, backwards.

Functor and applicative.

(/$/) :: SIArrow cat => ASemiIso' b' b -> cat a b -> cat a b' infixl 4

Postcomposes an arrow with a reversed SemiIso. The analogue of <$> and synonym for '#<<'.

(/$~) :: (SIArrow cat, HFoldable b', HFoldable b, HUnfoldable b', HUnfoldable b, Rep b' ~ Rep b) => ASemiIso' a b' -> cat c b -> cat c a infixl 4

Convenient fmap.

ai /$~ f = ai . morphed /$/ f

This operator handles all the hairy stuff with uncurried application: it reassociates the argument tuple and removes unnecessary (or adds necessary) units to match the function type. You don't have to use /* and */ with this operator.

(/*/) :: SIArrow cat => cat () b -> cat () c -> cat () (b, c) infixl 5

The product of two arrows with duplicate units removed. Side effect are sequenced from left to right.

The uncurried analogue of <*>.

(/*) :: SIArrow cat => cat () a -> cat () () -> cat () a infixl 5

The product of two arrows, where the second one has no input and no output (but can have side effects), with duplicate units removed. Side effect are sequenced from left to right.

The uncurried analogue of <*.

(*/) :: SIArrow cat => cat () () -> cat () a -> cat () a infixl 5

The product of two arrows, where the first one has no input and no output (but can have side effects), with duplicate units removed. Side effect are sequenced from left to right.

The uncurried analogue of *>.

Signaling errors.

sifail :: SIArrow cat => String -> cat a b

An arrow that fails with an error message.

(/?/) :: SIArrow cat => cat a b -> String -> cat a b infixl 3

Provides an error message in the case of failure.

Combinators.

sisequence :: SIArrow cat => [cat () a] -> cat () [a]

Equivalent of sequence.

sisequence_ :: SIArrow cat => [cat () ()] -> cat () ()

Equivalent of sequence_, restricted to units.

sireplicate :: SIArrow cat => Int -> cat () a -> cat () [a]

Equivalent of replicateM.

sireplicate_ :: SIArrow cat => Int -> cat () () -> cat () ()

Equivalent of replicateM_, restricted to units.