Pattern synonym constraints :: Ord a => () => ...

[Richard Eisenberg]

> On Oct 3, 2021, at 5:38 AM, Anthony Clayden <anthony.d.clayden at gmail.com> wrote:
> 
> >    pattern  SmartConstr :: Ord a => () => ...
> 
> Seems to mean:
> 
> * Required constraint is Ord a  -- fine, for building

Yes.

> * Provided constraint is Ord a  -- why? for matching/consuming

No. Your signature specified that there are no provided constraints: that's your ().

> 
> I'm using `SmartConstr` with some logic inside it to validate/build a well-behaved data structure. But this is an ordinary H98 datatype, not a GADT.

I believe there is no way to have provided constraints in Haskell98. You would need either GADTs or higher-rank types.

> 
> This feels a lot like one of the things that's wrong with 'stupid theta' datatype contexts.

You're onto something here. Required constraints are very much like the stupid theta datatype contexts. But, unlike the stupid thetas, required constraints are sometimes useful: they might be needed in order to, say, call a function in a view pattern.

For example:

> checkLT5AndReturn :: (Ord a, Num a) => a -> (Bool, a)
> checkLT5AndReturn x = (x < 5, x)
> 
> pattern LessThan5 :: (Ord a, Num a) => a -> a
> pattern LessThan5 x <- ( checkLT5AndReturn -> (True, x) )

My view pattern requires (Ord a, Num a), and so I must declare these as required constraints in the pattern synonym type. Because vanilla data constructors never do computation, any required constraints for data constructors are always useless.

> 
> For definiteness, the use case is a underlying non-GADT constructor for a BST
> 
> >      Node :: Tree a -> a -> Tree a -> Tree a
> >
> >    pattern SmartNode :: Ord a => () => Tree a -> a -> Tree a -> Tree a
> 
> with the usual semantics that the left Tree holds elements less than this node. Note it's the same `a` with the same `Ord a` 'all the way down' the Tree.

Does SmartNode need Ord a to match? Or just to produce a node? It seems that Ord a is used only for production, not for matching. This suggests that you want a separate smartNode function (not a pattern synonym) and to have no constraints on the pattern synonym, which can be unidirectional (that is, work only as a pattern, not as an expression).

It has been mooted to allow pattern synonyms to have two types: one when used as a pattern and a different one when used as an expression. That might work for you here: you want SmartNode to have no constraints as a pattern, but an Ord a constraint as an expression. At the time, the design with two types was considered too complicated and abandoned.

Does this help?

Richard
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