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
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
apply f >=> unapply f = f unapply f >=> apply f = f
Modules Control.SIArrow and Control.Category.Structures define an
hierarchy. Unfortunately Control.Arrow cannot be used, as it is too restrictive (the
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
ainto 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
binto 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
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 [faq]||0.1.0.0, 0.2.0.0, 0.3.0.0, 0.4.0.0, 0.4.1.0, 0.5.0.0, 22.214.171.124|
|Dependencies||base (==4.*), lens, profunctors, semigroupoids, transformers, tuple-morph [details]|
|Copyright||Paweł Nowak 2014|
|Maintainer||Paweł Nowak <email@example.com>|
|Source repo||head: git clone firstname.lastname@example.org:Pawel834/semi-iso.git|
|Uploaded||by pawel834 at 2014-12-12T23:30:20Z|
|Downloads||4004 total (4 in the last 30 days)|
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