Pattern Synonyms

Most language entities in Haskell can be named so that they can be abbreviated instead of written out in full. This proposal provides the same power for patterns. See the implementation page for implementation details.

Tickets should include PatternSynonyms in their Keywords to appear in these summary lists.

Open Tickets:

Pattern synonym used in an expression context could have different constraints to pattern used in a pattern context
Associated pattern synonyms
Exhaustiveness checks for pattern synonyms
Allow expressions in patterns
Some as-patterns could be accepted in pattern synonyms
Partial type signatures should work in pattern synonym signatures
Should be more liberal parsing pattern synonyms with view patterns
Interaction between ORF and record pattern synonyms needs to be resolved.
Allow visible type application in patterns
Pattern synonym name is mangled when patterns are non-exhaustive
Allow pattern synonyms to be bundled with type classes?
Ambiguous types in pattern synonym not determined by functional dependencies
Allow one type signature for multiple pattern synonyms
Haddock documentation for pattern synonyms printed with explicit forall quantifiers
Importing doubly exported pattern synonym and associated pattern synonym panics
Allow record wildcards with pattern synonyms which are defined in GHCi
RFC, allow local bindings in pattern synonyms
Can't infer constraint of pattern synonyms
GHC leaks GHC.Prim.~# into type
Order of constraints forced (in pattern synonyms, type classes in comments)

Closed Tickets:

Pattern synonyms
Record syntax for pattern synonyms
Pattern synonym type signatures
Pattern synonyms crash GHCi
Make pattern synonyms work with Template Haskell
PatternSynonyms error gives wrong source locations
Pattern synonyms and GADTs
Pattern synonyms interact badly with data kinds
Internal error when using equality constraint in pattern synonyms
Pattern synonyms across modules broken in Haddock
Haddock panics when exporting a module with pattern synonyms
Panic on a pattern synonym in a class
Pattern synonyms and unboxed values
Pattern synonym matcher is unnecessarily strict on unboxed continuations
Poor error message for unbound variable in pattern synonym
PatternSynonyms + ScopedTypeVariables triggers an internal error
Pattern synonym does not work in top-level pattern bind
Fixity declarations for pattern synonyms not persisted
Support pattern synonyms in GHCi
Pattern synonyms with no signatures should yield warnings
Pattern synonyms don't work with GADTs
Required constraints are not inferred for pattern synonyms involving GADTs
Pattern synonym type signature documentation out of date
RecordWildcards and PatternSynonyms cause impossible bug
PatternSynonyms confuse exhaustiveness check
GHC panic when creating a monomorphised pattern synonym for GADT
matchGroupArity panic with PatternSynonyms
PatternSynonyms should be imported/exported as part of the wildcard notation
Infix pattern synonyms fail to parse (regression)
Bad error message for incorrect pattern synonym signature
Incorrect ASSERT for buildPatSyn
Pattern synonym causes Iface error.
Panic with incorrect pattern synonym signature
Incorrect reported pattern synonym signature
Program doesn't preserve semantics after pattern synonym inlining.
Unable to provide type signature for pattern synonym
Interaction between ORF and record pattern synonyms needs to be resolved.
Improve optimisation of pattern synonym matching
PatternSynonms and DisambiguateRecordFields causes panic
GHC craches on this combination of ViewPatterns and PatternSynonyms
Scoped type variables in pattern synonyms
[Regression] Only one clause allowed in (explicitly bidirectional) pattern synonyms
Something is amiss with quantification in pattern synonym type signatures
Record field order in a bidirectional pattern synonym match is order dependent
Make pattern synonym export type mismatch a warning
Incorrect pattern synonym types in error messages
Core lint errors
ghc doesn't agree with its own inferred pattern type
Core lint error on record syntax update/pattern synonym
Record fields not defined with pattern synonym in ghci
GHC panics on pattern synonym ‘kindPrimRep’
Allow duplicate record fields in pattern synonyms
Regression: Pattern synonyms make GHCi 8.0.1 crash
Function type synonym fails in pattern synonym
Matching on pattern synonym succeeds compiled with ghc, fails with ghci

Motivating example

Here is a simple representation of types

    data Type = App String [Type]

Using this representations the arrow type looks like App "->" [t1, t2]. Here are functions that collect all argument types of nested arrows and recognize the Int type:

   collectArgs :: Type -> [Type]
   collectArgs (App "->" [t1, t2]) = t1 : collectArgs t2
   collectArgs _ = []

   isInt (App "Int" []) = True
   isInt _ = False

Matching on App directly is both hard to read and error prone to write.

The proposal is to introduce a way to give patterns names:

   pattern Arrow t1 t2 = App "->" [t1, t2]
   pattern Int = App "Int" []

And now we can write

   collectArgs :: Type -> [Type]
   collectArgs (Arrow t1 t2) = t1 : collectArgs t2
   collectArgs _ = []

   isInt Int = True
   isInt _ = False

Here is a second example from pigworker on Reddit. Your basic sums-of-products functors can be built from this kit.

newtype K a        x  = K a
newtype I          x  = I x
newtype (:+:) f g  x  = Sum (Either (f x) (g x))
newtype (:*:) f g  x  = Prod (f x, g x)

and then you can make recursive datatypes via

newtype Fix f = In (f (Fix f))


type Tree = Fix (K () :+: (I :*: I))

and you can get useful generic operations cheaply because the functors in the kit are all Traversable, admit a partial zip operation, etc.

You can define friendly constructors for use in expressions

leaf :: Tree
leaf = In (Sum (Left (K ())))
node :: Tree -> Tree -> Tree
node l r = In (Sum (Right (Prod (I l, I r))))

but any Tree-specific pattern matching code you write will be wide and obscure. Turning these definitions into pattern synonyms means you can have both readable type-specific programs and handy generics without marshalling your data between views.

Uni-directional (pattern-only) synonyms

The simplest form of pattern synonyms is the one from the examples above. The grammar rule is:

pattern conid varid1 ... varidn <- pat

pattern varid1 consym varid2 <- pat

  • Each of the variables on the left hand side must occur exactly once on the right hand side
  • Pattern synonyms are not allowed to be recursive. Cf. type synonyms.

There have been several proposals for the syntax of defining pattern-only synonyms:

  • pattern conid varid1 ... varidn ~ pat
  • pattern conid varid1 ... varidn := pat
  • pattern conid varid1 ... varidn -> pat
  • pattern conid varid1 ... varidn <- pat

Pattern synonyms can be exported and imported by prefixing the conid with the keyword pattern:

   module Foo (pattern Arrow) where ...

This is required because pattern synonyms are in the namespace of constructors, so it's perfectly valid to have

   data P = C
   pattern P = 42

You may also give a type signature for a pattern, but as with most other type signatures in Haskell it is optional:

pattern conid :: type


   pattern Arrow :: Type -> Type -> Type
   pattern Arrow t1 t2 <- App "->" [t1, t2]

Together with ViewPatterns we can now create patterns that look like regular patterns to match on existing (perhaps abstract) types in new ways:

import qualified Data.Sequence as Seq

pattern Empty <- (Seq.viewl -> Seq.EmptyL)
pattern x :< xs <- (Seq.viewl -> x Seq.:< xs)
pattern xs :> x <- (Seq.viewr -> xs Seq.:> x)

Simply-bidirectional pattern synonyms

In cases where pat is in the intersection of the grammars for patterns and expressions (i.e. is valid both as an expression and a pattern), the pattern synonym can be made bidirectional, and can be used in expression contexts as well. Bidirectional pattern synonyms have the following syntax:

pattern conid varid1 ... varidn = pat

pattern varid1 consym varid2 = pat

For example, the following two pattern synonym definitions are rejected, because they are not bidirectional (but they would be valid as pattern-only synonyms)

   pattern ThirdElem x = _:_:x:_
   pattern Snd y = (x, y)

since the right-hand side is not a closed expression of {x} and {y} respectively.

In contrast, the pattern synonyms for Arrow and Int above are bidirectional, so you can e.g. write:

   arrows :: [Type] -> Type -> Type
   arrows = flip $ foldr Arrow

Explicitly-bidirectional pattern synonyms

What if you want to use Succ in an expression:

    pattern Succ n <- n1 | let n = n1 -1, n >= 0

It's clearly impossible since its expansion is a pattern that has no meaning as an expression. Nevertheless, if we want to make what looks like a constructor for a type we will often want to use it in both patterns and expressions. This is the rationale for the most complicated synonyms, the bidirectional ones. They provide two expansions, one for patterns and one for expressions.

pattern conid varid1 ... varidn <- pat where cfunlhs rhs

where cfunlhs is like funlhs, except that the functions symbol is a conid instead of a varid.


   pattern Succ n <- n1 | let n = n1-1, n >= 0 where
      Succ n = n + 1

TODO: Rewrite this example to not use ViewPatternsAlternative

The first part as is before and describes the expansion of the synonym in patterns. The second part describes the expansion in expressions.

   fac 0 = 0
   fac (Succ n) = Succ n * fac n 

Associated pattern synonyms

Just like data types and type synonyms can be part of a class declaration, it would be possible to have pattern synonyms as well.


   class ListLike l where
      pattern Nil :: l a
      pattern Cons :: a -> l a -> a
      isNil :: l a -> Bool
      isNil Nil = True
      isNil (Cons _ _) = False
      append :: l a -> l a -> l a

   instance ListLike [] where
      pattern Nil = []
      pattern Cons x xs = x:xs
      append = (++)

   headOf :: (ListLike l) => l a -> Maybe a
   headOf Nil = Nothing
   headOf (Cons x _) = Just x

One could go one step further and leave out the pattern keyword to obtain associated constructors, which are required to be bidirectional. The capitalized identifier would indicate that a pattern synonym is being defined. For complicated cases one could resort to the where syntax (shown above).

TODO: Syntax for associated pattern synonym declarations to discern between pattern-only and bidirectional pattern synonyms

Static semantics

A unidirectional pattern synonym declaration has the form

pattern P var1 var2 ... varN <- pat

The formal pattern synonym arguments var1, var2, ..., varN are brought into scope by the pattern pat on the right-hand side. The declaration brings the name P as a pattern synonym into the module-level scope.

The pattern synonym P is assigned a pattern type of the form

pattern P :: CProv => CReq => t1 -> t2 -> ... -> tN -> t 

where t1, ..., tN are the types of the parameters var1, ..., varN, t is the simple type (with no context) of the thing getting matched, and CReq and CProv are type contexts.

CReq can be omitted if it is empty. If CProv is empty, but CReq is not, () is used. The following example shows cases:

data Showable where
    MkShowable :: (Show a) => a -> Showable

-- Required context is empty
pattern Sh :: (Show a) => a -> Showable
pattern Sh x <- MkShowable x

-- Provided context is empty, but required context is not
pattern One :: () => (Num a, Eq a) => a
pattern One <- 1

A pattern synonym can be used in a pattern if the instatiated (monomorphic) type satisfies the constraints of CReq. In this case, it extends the context available in the right-hand side of the match with CProv, just like how an existentially-typed data constructor can extend the context.

As with function and variable types, the pattern type signature can be inferred, or it can be explicitly written out on the program.

Here's a more complex example. Let's look at the following definition:

{-# LANGUAGE PatternSynonyms, GADTs, ViewPatterns #-}
module ShouldCompile where

data T a where
	MkT :: (Eq b) => a -> b -> T a

f :: (Show a) => a -> Bool

pattern P x <- MkT (f -> True) x

Here, the inferred type of P is

pattern P :: (Eq b) => (Show a) => b -> T a

A bidirectional pattern synonym declaration has the form

pattern P var1 var2 ... varN = pat

where both of the following are well-typed declarations:

pattern P1 var1 var2 ... varN <- pat

P2 = \var1 var2 ... varN -> pat

In this case, the pattern type of P is simply the pattern type of P1, and its expression type is the type of P2. The name P is brought into the module-level scope both as a pattern synonym and as an expression.

Dynamic semantics

A pattern synonym occurance in a pattern is evaluated by first matching against the pattern synonym itself, and then on the argument patterns. For example, given the following definitions:

pattern P x y <- [x, y]

f (P True True) = True
f _             = False

g [True, True] = True
g _            = False

the behaviour of f is the same as

f [x, y] | True <- x, True <- y = True
f _                             = False

Because of this, the eagerness of f and g differ:

*Main> f (False:undefined)
*** Exception: Prelude.undefined
*Main> g (False:undefined)

This is because we generate the matching function at the definition site.

Typed pattern synonyms

So far patterns only had syntactic meaning. In comparison Ωmega has typed pattern synonyms, so they become first class values. For bidirectional pattern synonyms this seems to be the case

data Nat = Z | S Nat deriving Show
pattern Ess p = S p

And it works:

*Main> map S [Z, Z, S Z]
[S Z,S Z,S (S Z)]
*Main> map Ess [Z, Z, S Z]
[S Z,S Z,S (S Z)]

Branching pattern-only synonyms

N.B. this is a speculative suggestion!

Sometimes you want to match against several summands of an ADT simultaneously. E.g. in a data type of potentially unbounded natural numbers:

data Nat = Zero | Succ Nat
type UNat = Maybe Nat -- Nothing meaning unbounded

Conceptually Nothing means infinite, so it makes sense to interpret it as a successor of something. We wish it to have a predecessor just like Just (Succ Zero)!

I suggest branching pattern synonyms for this purpose:

pattern S pred <- pred@Nothing | pred@(Just a <- Just (Succ a))
pattern Z = Just Zero

Here pred@(Just a <- Just (Succ a)) means that the pattern invocation S pred matches against Just (Succ a) and - if successful - binds Just a to pred.

This means we can syntactically address unbound naturals just like bounded ones:

greetTimes :: UNat -> String -> IO ()
greetTimes Z _ = return ()
greetTimes (S rest) message = putStrLn message >> greetTimes rest message

As a nice collateral win this proposal handles pattern Name name <- Person name workplace | Dog name vet too.

Record Pattern Synonyms

See PatternSynonyms/RecordPatternSynonyms

Associating synonyms with types

See PatternSynonyms/AssociatingSynonyms

Last modified 4 weeks ago Last modified on Apr 29, 2016 8:05:11 PM