[Haskell-cafe] Non-linear patterns.

[Simon Thompson]

Repeated variables in patterns were allowed in Miranda, a predecessor of Haskell. In a lazy context there are interesting questions about how pattern matches fail, and in particular the point at which equality tests take place in matching a complex pattern. This paper

<https://dl.acm.org/doi/pdf/10.1007/BF01887213>
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BF01887213<https://dl.acm.org/doi/pdf/10.1007/BF01887213>
PDF Document · 1.5 MB<https://dl.acm.org/doi/pdf/10.1007/BF01887213>

section 6.2 explains how these two definitions differ in meaning

g [x,x] = 37
g z = 42

h [x,y] = 37 , x=y
h z = 42

Simon

On 6 May 2025, at 10:01, Serguey Zefirov <sergueyz at gmail.com> wrote:

There are artifacts of old Haskell standards that are a matching against integer value (2 + 2 = 5) and a matching against arithmetic expression (f (n+1) = f n).

Both are interesting in requiring a class over type to match.

f 10 = 11 has type f :: (Eq a1, Num a1, Num a2) => a1 -> a2

f (n+1) = f n has type f :: Integral t1 => t1 -> t2

In that vein it is possible to add non-linear patterns by adding an equality constraint on the non-linear matches.

E.g., f x x = x would have type f :: Eq a => a -> a -> a

For example:

data Logic = True | False | Not Logic | Or Logic Logic | And Logic Logic deriving Eq

simplify (And x x) = simplify x
simplify (Or x x) = simplify x
simplify (Not (Not x)) = simplify x
simplify x = x

Patterns like that are common in simplification/optimization rules. Also, by making them legal, it would be possible to use them in Template Haskell to make better embedded languages.

On the implementation side, it can be implemented much like the (n+k) pattern. I also think that pattern matching completeness checker should not change.

What would you say?
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Simon Thompson | Professor of Logic and Computation
School of Computing | University of Kent | Canterbury, CT2 7NF, UK
s.j.thompson at kent.ac.uk | M +44 7986 085754 | W www.cs.kent.ac.uk/~sjt

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