| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
IsomorphismClass
Contents
Description
Lawful solution to the conversion problem.
Conversion problem
Have you ever looked for a toString function? How often do you
import Data.Text.Lazy only to call its fromStrict? How
about importing Data.ByteString.Builder only to call its
toLazyByteString and then importing
Data.ByteString.Lazy only to call its toStrict?
Those all are instances of one pattern. They are conversions between representations of the same information. Codebases that don't attempt to abstract over this pattern tend to be sprawling with this type of boilerplate. It's noise to the codereader, it's a burden to the implementor and the maintainer.
Why another conversion library?
Many libraries exist that approach the conversion problem. However most of them provide lawless typeclasses leaving it up to the author of the instance to define what makes a proper conversion. This results in inconsistencies across instances, their behaviour not being evident to the user and no way to check whether an instance is correct.
This library tackles this problem with a lawful typeclass, making it evident what any of its instances do and it provides a property-test for you to validate your instances.
The laws
The key insight of this library is that if you add a requirement for the conversion to be lossless and to have a mirror conversion in the opposite direction, there usually appears to be only one way of defining it. That makes it very clear what the conversion does to the user and how to define it to the author of the conversion. It also gives a clear criteria for validating whether the instances are correct, which can be encoded in property-tests.
That insight itself stems from an observation that almost all of the practical conversions in Haskell share a property: you can restore the original data from its converted form. E.g., you can get a text from a text-builder and you can create a text-builder from a text, you can convert a bytestring into a list of bytes and vice-versa, bytestring to/from bytearray, strict bytestring to/from lazy, list to/from sequence, sequence to/from vector, set of ints to/from int-set. In other words, it's always a two-way street with them and there's a lot of instances of this pattern.
UX
A few other accidental findings like encoding this property with recursive
typeclass constraints and fine-tuning for the use of
the TypeApplications extension resulted in a terse and clear API.
Essentially the whole API is just two functions: to and from. Both
perform a conversion between two types. The only difference between them
is in what the first type application parameter specifies. E.g.:
toText = to @Text
fromBuilder = from @Builder
The types are self-evident:
> :t to @Text to @Text :: IsomorphicTo Text b => b -> Text
> :t from @Builder from @Builder :: IsomorphicTo Builder b => Builder -> b
In other words to and from let you explicitly specify either the source
or the target type of a conversion when you need to help the type
inferencer or the reader.
Examples
combineEncodings ::ShortByteString->ByteArray->ByteString-> [Word8] combineEncodings a b c =from@Builder$toa <>tob <>toc
renderNameAndHeight ::Text->Int->TextrenderNameAndHeight name height =from@StrictTextBuilder$ "Height of " <>toname <> " is " <>fromString(show height)
Synopsis
- class IsomorphicTo b a => IsomorphicTo a b where
- to :: b -> a
- from :: IsomorphicTo a b => a -> b
- isomorphicToIso :: (IsomorphicTo a b, Profunctor p, Functor f) => p b (f b) -> p a (f a)
- isomorphicToProperties :: (IsomorphicTo a b, Eq a, Eq b, Arbitrary a, Show a, Arbitrary b, Show b) => Proxy a -> Proxy b -> [(String, Property)]
Typeclasses
class IsomorphicTo b a => IsomorphicTo a b where Source #
Bidirectional conversion between two types with no loss of information.
The bidirectionality is encoded via a recursive dependency with arguments flipped.
You can read the signature IsomorphicTo a b as "B is isomorphic to A".
Laws
B is isomorphic to A if and only if there exists a conversion from B
to A (to) and a conversion from A to B (from) such that:
from.to=idto.from=id
Testing
For testing whether your instances conform to these laws use isomorphicToProperties.
Instance Definition
For each pair of isomorphic types (A and B) the compiler will require
you to define two instances, namely: IsomorphicTo A B and IsomorphicTo B A.
Instances
from :: IsomorphicTo a b => a -> b Source #
to in reverse direction.
Particularly useful in combination with the TypeApplications extension,
where it allows to specify the input type, e.g.:
fromText :: IsomorphicTo Text b => Text -> b fromText = from @Text
The first type application of the to function on the other hand specifies
the output data type.
Optics
isomorphicToIso :: (IsomorphicTo a b, Profunctor p, Functor f) => p b (f b) -> p a (f a) Source #
Van-Laarhoven-style Isomorphism, compatible with the "lens" library.
Testing
isomorphicToProperties :: (IsomorphicTo a b, Eq a, Eq b, Arbitrary a, Show a, Arbitrary b, Show b) => Proxy a -> Proxy b -> [(String, Property)] Source #
Properties testing whether an instance satisfies the laws of IsomorphicTo.
The instance is identified via the proxy types that you provide.
E.g., here's how you can integrate it into an Hspec test-suite:
spec = do
describe "IsomorphicTo laws" do
traverse_
(uncurry prop)
(isomorphicToProperties @Int32 @Word32 Proxy Proxy)