# semi-iso: Weakened partial isomorphisms, reversible computations.

Semi-isomorphisms are partial isomorphisms with weakened iso laws. They are a basic
building block of reversible computations. And they work with Iso and Prism from `lens`

!

The module Control.Lens.SemiIso defines semi-isomorphisms and provides some
basic semi-isos and combinators. A `SemiIso' a b`

can be applied in both directions
to get a `a -> Either String b`

and `b -> Either String a`

. SemiIsos can be composed
with Isos and Prisms (to get another SemiIso). Isos and Prisms can be directly
used as SemiIsos.

Semi-isomorphisms obey weaker laws then isomorphisms. We require only

apply f >=> unapply f >=> apply f = apply f unapply f >=> apply f >=> unapply f = unapply f

instead of

apply f >=> unapply f = f unapply f >=> apply f = f

Modules Control.SIArrow and Control.Category.Structures define an `Arrow`

-like class
hierarchy. Unfortunately Control.Arrow cannot be used, as it is too restrictive (the
dreaded `arr`

).
SIArrow abstracts categories of reversible computations (with reversible side effects). In
the case of parsing and pretty-printing using the "syntax" library if we have an arrow
`SIArrow cat => cat a b`

then we can:

Evaluate it from left to right, turning a value of type

`a`

into a value of type`b`

, with the side effect of consuming a sequence. (Parsing)Evaluate it from right to left, turning a value of type

`b`

into a value of type`a`

, with the side effect of generating a sequence. (Pretty-printing)

In the particular case of parsing/pretty-printing the type `a`

will be usually `()`

, e.g.
we just produce a value during parsing and just consume a value during pretty-printing.
To support this style we define a functor and applicative structure on `cat () b`

, for example
`/*/`

(equivalent of `<*>`

) has type `(/*/) :: SIArrow cat => cat () a -> cat () b -> cat () (a, b)`

.

When more power then applicative is needed - for example when the syntax depends on the parsed value - we turn back to arrow composition.

Module Control.Category.Reader defines a Reader category transformer. It is like a monad transformer, but for categories. The next version will include some more transformers and mtl-style classes.

Versions | 0.1.0.0, 0.2.0.0, 0.3.0.0, 0.4.0.0, 0.4.1.0, 0.5.0.0, 1.0.0.0 |
---|---|

Dependencies | base (==4.*), lens, profunctors, semigroupoids, transformers, tuple-morph [details] |

License | MIT |

Copyright | Paweł Nowak 2014 |

Author | Paweł Nowak |

Maintainer | Paweł Nowak <pawel834@gmail.com> |

Category | Control, Data |

Source repo | head: git clone git@github.com:Pawel834/semi-iso.git |

Uploaded | by pawel834 at Fri Dec 12 23:30:20 UTC 2014 |

Distributions | NixOS:1.0.0.0 |

Downloads | 2252 total (29 in the last 30 days) |

Rating | (no votes yet) [estimated by rule of succession] |

Your Rating | |

Status | Docs uploaded by user [build log] All reported builds failed as of 2014-12-12 [all 1 reports] |

## Downloads

- semi-iso-1.0.0.0.tar.gz [browse] (Cabal source package)
- Package description (as included in the package)