Weakened partial isomorphisms, reversible computations.
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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
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
Control.Category.Structures define an
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.
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