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Reversible printing/parsing

This is a library for encoding serialization format descriptions that can be used as both printers and parsers for that format, without duplicating the code.

The library is implemented in an uber-abstract way that supports printing/parsing arbitrary data structures, both as input and output. Two targets are included in the box - (1) parsing from/printing to text strings, and (2) parsing from/printing to browser URLs, with support for path segments and querystring parameters. The latter target was the primary inspiration for developing the library, and the former target is, at the moment, a toy one, more of a proof-of-concept.

The implementation is loosely based on a 2010 paper by Rendel and Ostermann.

Standing example

This is a working example that uses the library for printing/parsing browser URLs (aka "routes"). To see how all the pieces fit together, read on.

data Route
    = Home
    | Profile String
    | Foo Int String

routesDef :: forall syntax. Syntax syntax => syntax PathInfo Route
routesDef =
          (Ctor::Ctor "Home") <|:|> empty
    <|||> (Ctor::Ctor "Profile") <|:|> literal "profile" *|> value
    <|||> (Ctor::Ctor "Foo") <|:|> literal "foo" *|> query "id" <|*|> value

printRoute routesDef Home == "/"
printRoute routesDef (Profile "john") == "/profile/john"
printRoute routesDef (Foo 42 "bar") == "/foo/bar?id=42"


What is called "syntax" here is either a "printer" or a "parser". We have to give them one collective name, so that we can refer to them both by it, which is necessary for expressing the encoding format without repeating it twice. In other words, we have to call both printer and parser something, and that word is "syntax". In the code this is expressed by having both printer and parser implement the Syntax type class.

As can be seen from the signature of routesDef above, a thing that is a "syntax" (i.e. printer or parser) has two parameters:

  • The first parameter (PathInfo in the example) is the "target" of the syntax - i.e. input of the parser and output of the printer.
  • The second parameter (Route in the example) is the data type whose encoding we're describing - i.e. output of the parser and input of the printer.

Thus, a syntax a b can be seen as an isomorphism (of sorts) between a and b.


The smallest building blocks of a syntax are primitive printing/parsing operations. In the example above three such operations are visible:

  • literal means "there should be a path segment with exactly this value here".
  • value means "this path segment matches the next route constructor parameter".
  • query means "this route constructor parameter matches querystring parameter with the given key".

These primitives are provided in Data.Intertwine.Route, but it is also possible to define your own.

Combining primitives

Unlike regular parser combinators (think Parsec), syntax elements combine right-to-left via the <|*|> operator, which is right-associative. When two syntax elements of types a and b combine, they produce a syntax element of type (a, b) (using Haskell tuple notation here, because it's not as cumbersome):

x :: syntax PathInfo a
y :: syntax PathInfo b
x <|*|> y :: syntax PathInfo (a, b)

This can go on to produce nested tuples:

z :: syntax PathInfo c
z <|*|> x <|*|> y :: syntax PathInfo (c, (a, b))

Injecting/applying constructors

Once a sufficiently nested tuple of values is assembled, it can be "applied" to a constructor of the ADT that we're encoding. This is done via the operator <|:|> and the special type Ctor. The result of such operation would be another syntax that describes the type of the constructor:

data Foo
    = Bar c a b
    | Baz p q

r :: syntax PathInfo Foo
r = (Ctor::Ctor "Bar") <|:|> z <|*|> x <|*|> y

Here the term "apply constructor", again, means both directions: when parsing, we need to "inject" the accumulated tuple of values into the constructor to produce a value, and when printing, we need to produce such tuple from the value by "deconstructing" the constructor. This means that we can't just apply the constructor as a function, the way we would with regular parsers. Instead, we need to create a thing that can convert both directions - tuple to ADT or ADT to tuple. Sort of a "partial isomorphism".


The thing that can convert from ADT to tuple and back again - is kind of like an isomorphism, but not exactly. The difference is that it can fail. When parsing, it can obviously fail when the input is unexpected, but when printing, it can also fail for a less obvious reason: as noted above, such "partial isomorphism" represents only one constructor of a potentially multi-constructor ADT, and therefore, it would fail when given an ADT value constructed by a different constructor.

In the code such "partial isomorphisms" are represented by the Iso type, which is just a pair of functions:

newtype Iso a b = Iso { apply :: a -> Maybe b, inverse :: b -> Maybe b }

If we were to encode such isomorphism by hand, it would look something like this (using the above definition of Foo):

iso_bar :: Iso Foo (c, (a, b))
iso_bar = Iso {
    apply: \foo -> case foo of
        Bar c a b -> Just (c, (a, b))
        _ -> Nothing
    inverse: \(c, (a, b)) ->
        Just (Bar c a b)

And then we can inject/apply this Iso to the tuple-typed syntax with the <|$|> operator:

r :: syntax PathInfo Foo
r = iso_bar <|$|> z <|*|> x <|*|> y

Autogenerating Iso

But of course, encoding such isomorphisms for every constructor isn't a lot of fun. Not to mention that it kills the whole idea of not repeating the code twice :-)

So, in order to help with that, the library provides a way to do that automatically, based on Generic:

iso_bar = iso (SProxy :: SProxy "Bar")

Armed with this automation, we can construct our syntax description like this:

r :: syntax PathInfo Foo
r = iso (SProxy :: SProxy "Bar") <|$|> z <|*|> x <|*|> y

Slightly shorter syntax

To make the whole thing slightly more readable, we can shorten the notation iso (SProxy :: SProxy "Bar") slightly: we can get rid of the iso call by itroducing a new type Ctor (which is just like SProxy) and a new operator <|:|>, which would combine the effects of iso and <|$|>, producing a notation that reads more intuitively:

r :: syntax PathInfo Foo
r = (Ctor::Ctor "Bar") <|:|> z <|*|> x <|*|> y

Combining syntaxes as alernatives

The final piece of the puzzle is combining several alternative syntaxes with the operator <|||>. This part works pretty much the same as combining parsers in Parsec:

u :: syntax PathInfo a
v :: syntax PathInfo a
u <|||> v :: syntax PathInfo a

And so, combining all of the above, we get the final result:

x :: syntax PathInfo a
y :: syntax PathInfo b
z :: syntax PathInfo c
p :: syntax PathInfo p
q :: syntax PathInfo q

-- x <|*|> y :: syntax PathInfo (a, b)
-- z <|*|> x <|*|> y :: syntax PathInfo (c, (a, b))

data Foo
    = Bar c a b
    | Baz p q

r :: syntax PathInfo Foo
r =
          (Ctor::Ctor "Bar") <|:|> z <|*|> x <|*|> y
    <|||> (Ctor::Ctor "Bar") <|:|> p <|*|> q

Actually using the syntax

Once we have the syntax definition, we can use printRoute and parseRoute to print or parse:

r :: syntax PathInfo Foo

i = printRoute r (Bar c a b)
j = parseRoute r i
-- j == Bar c a b