Haskell pattern matching on vectors

Question

Is it possible to use list style pattern matching on vectors?

ie

import qualified Data.Vector as V

f :: V.Vector a -> a
f (x:xs) = x 

gives an error

Answer 1

-XViewPatterns can let you do this:

{-# LANGUAGE ViewPatterns #-}
module VecViewPats where

import Data.Vector (Vector)
import qualified Data.Vector as V

uncons :: Vector a -> Maybe (a, Vector a)
uncons v = if V.null v
  then Nothing
  else Just (V.unsafeHead v, V.unsafeTail v)

vsum :: Num a => Vector a -> a
vsum (uncons -> Just (a,av)) = a + vsum av
vsum (uncons -> Nothing) = 0

Or -XLambdaCase

import Control.Category ((>>>))
-- ...
vsum :: Num a => Vector a -> a
vsum = uncons >>> \case
  Just (a,av) -> a + vsum av
  Nothing     -> 0

But honestly, that's seems like a bit of a code smell as you're using one data structure (Vector) as another ([]) which suggests that maybe your choice of data structure is off.

If you really just want to treat it like a list for the purposes of some algorithm, why not use toList?

Answer 2

@Cactus has pointed out -XPatternSynonym (introduced in 7.8) combined with -XViewPattern can be used to pattern match on vectors. I am here to extend his comment a bit further.

pattern Empty <- (V.null -> True) 

The above defines a pattern synonym Empty for the empty vector. The Empty pattern matches against an empty vector using view pattern (V.null -> True). However, it cannot be used as an expression elsewhere, i.e. a uni-directional synonym, since the system doesn't really know what Empty is as a Vector (we only know that null v is True but there could be other vectors giving True as well).

To remedy this, a where clause can be added specifying that Empty actually is a empty vector, i.e. a bi-directional synonym, as well as a type signature:

pattern Empty :: Vector a
pattern Empty <- (V.null -> True) where Empty = V.empty 

This pattern synonym can be used to define uncons without an if expression:

uncons :: Vector a -> Maybe (a, Vector a)
uncons Empty = Nothing
uncons v     = Just (unsafeHead v, unsafeTail v)

We use uncons to define uni-directional synonym. Note I don't make it bi-directional since cons is costly for vector:

pattern (:<|)  :: a -> Vector a -> Vector a
pattern x :<| xs <- (uncons -> Just (x, xs))

Anyway, we are finally able to pattern match on vectors just like lists:

vsum :: Num a => Vector a -> a 
vsum Empty = 0
vsum (x :<| xs) = x + vsum xs

A complete code is here.

Answer 3

Vectors aren't intended for that kind of pattern matching--they were created to give Haskell O(1) lists, or lists that can be accessed from any point efficiently.

The closest thing to what you wrote would be something like this:

f v = V.head v

Or, if recursion is what you are looking for, the tail function will get the rest of the list.

But if you are trying to do something that moves along a list like that, there are Vector equivalents of functions such as foldl, find, map, and the like. It depends on what you intend to do.