Data.SemiIsoFunctor

Defines a functor from the category of semi-isomoprihsms to Hask.

The most interesting property of that class is that it can be instantiated by both covariant (like Parser) and contravariant (like Printer) functors. Therefore it can be used as a common interface to unify parsing and pretty printing.

Operator names are up to bikeshedding :)

Documentation

class SemiIsoFunctor f where

A functor from the category of semi-isomorphisms to Hask.

It is both covariant and contravariant in its single arugment.

The contravariant map is used by default to provide compatibility with Prisms (otherwise you would have to reverse them in most cases).

Instances should satisfy laws:

simap id      = id
simap (f . g) = simap g . simap f
simap         = simapCo . fromSemi
simapCo       = simap   . fromSemi

Minimal complete definition

simap | simapCo

Methods

simap :: ASemiIso' a b -> f b -> f a

The contravariant map.

simapCo :: ASemiIso' a b -> f a -> f b

The covariant map.

(/$/) :: SemiIsoFunctor f => ASemiIso' a b -> f b -> f a infixl 4

A infix operator for simap.

class SemiIsoFunctor f => SemiIsoApply f where

Equivalent of Applicative for SemiIsoFunctor.

However, this class implements uncurried application, unlike Applicative which gives you curried application.

Instances should satisfy laws:

TODO (they should be fine)

Minimal complete definition

sipure, (/*/)

Methods

sipure :: ASemiIso' a () -> f a

(/*/) :: f a -> f b -> f (a, b) infixl 5

(/*) :: f a -> f () -> f a infixl 5

(*/) :: f () -> f b -> f b infixl 5

class SemiIsoApply f => SemiIsoAlternative f where

Equivalent of Alternative for SemiIsoFunctor.

f a should form a monoid with identity siempty and binary operation /|/.

Minimal complete definition

siempty, (/|/)

Methods

siempty :: f a

(/|/) :: f a -> f a -> f a infixl 3

sisome :: f a -> f [a]

simany :: f a -> f [a]

sisequence :: SemiIsoApply f => [f a] -> f [a]

Equivalent of sequence.

Note that it is not possible to write sequence_, because you cannot void a SemiIsoFunctor.

sireplicate :: SemiIsoApply f => Int -> f a -> f [a]

Equivalent of replicateM.