Pruning GADT case alternatives with uninhabitable coercion parameters

[Simon Peyton Jones]

I’m on a train, so can’t look at your code.  But I urge you (or whoever) to split the task into two:

·        Traverse the Core tree, gathering given constraints, deleting unreachable branches

·        The Contradiction Checker (CCK)

CCK is independently useful; for example George et al may use it when traversing HsSyn to report overlapping patterns.

The API of CCK might look something like this:

               contradictionCheck :: FamInstEnvs -> [PredType] -> [PredType] -> Bool


·        FamInstEnvs tells it what type-family-instances exist

·        The first [PredType] are the enclosing givens

·        The second [PredType] are the givens of a new pattern match

·        Result is True if the new pattern match is inaccessible

One might also consider a more incremental API, something like
               data ContradictionChecker
               newCCK :: FamInstEnvs -> ContradictionChecker
               check :: ContradictionChecker -> [PredType] -> Maybe ContradictionChecker

Returns Nothing for a contradiction, (Just cc) if the branch is reachable, where you should use cc for the body of the branch.

I like the latter API.  For example a ContrdictionChecker might carry a renaming of type variables, to account for shadowing.

Simon

From: conal.elliott at gmail.com [mailto:conal.elliott at gmail.com] On Behalf Of Conal Elliott
Sent: 25 June 2014 00:11
To: Simon Peyton Jones
Cc: Dimitrios Vytiniotis; ghc-devs at haskell.org; Nikolaos S. Papaspyrou (nickie at softlab.ntua.gr); George Karachalias
Subject: Re: Pruning GADT case alternatives with uninhabitable coercion parameters

I'm glad for the interest and help. I can make an initial go of it. My current simple plan is to traverse expressions, collecting type equalities from bound coercion variables as I descend, combining them progressively with successive type unifications. The traversal is thus parametrized by a TvSubst and yields a Maybe TvSubst. The coercion variables will come from lambdas, let bindings and case alternatives. If an added equality is not unifiable given the current TvSubst, we've reached a contradiction. If the contradiction arises for one of the variables in a case alternative, then remove that alternative.

How does this strategy sound?

Some issues:

*   Nominal vs representational type equalities.
*   Will I want to normalize the types (with normaliseType) before unifying?
*   How can I unify while carrying along a type substitution environment? The Unify module exports tcUnifyTy, which takes no such environment, but not unify, which does.
-- Conal

On Tue, Jun 24, 2014 at 4:43 AM, Simon Peyton Jones <simonpj at microsoft.com<mailto:simonpj at microsoft.com>> wrote:
we need to do a bit more work to re-connect to source pattern locations and nested patterns? I can’t assess very well yet if this is a real problem though

That is a very good point.

Nevertheless, given

•         the typechecked HsSyn (i.e. still in source form, but with type inference fully completed

•         the independent contradiction-detector described below (which is independent of whether the contradiction problems it is given come from HsSyn or Core)
it would be easy to give source-localised error messages

Simon

From: Dimitrios Vytiniotis
Sent: 24 June 2014 11:58
To: Simon Peyton Jones; Conal Elliott; ghc-devs at haskell.org<mailto:ghc-devs at haskell.org>
Cc: Nikolaos S. Papaspyrou (nickie at softlab.ntua.gr<mailto:nickie at softlab.ntua.gr>); George Karachalias

Subject: RE: Pruning GADT case alternatives with uninhabitable coercion parameters


Yes it would be better in the sense that we don’t really want to be dealing with unification variables and evidence when we simply use the constraint solver to detect inconsistencies in possibly missing patterns, but the concern has been that if we are already desugared and in core maybe we need to do a bit more work to re-connect to source pattern locations and nested patterns? I can’t assess very well yet if this is a real problem though …

In general I agree that a simple constraint solver for Core might be an independently useful tool for this kind of optimization. (I think George had thought about this too).

Thanks!
d-



From: Simon Peyton Jones
Sent: Tuesday, June 24, 2014 11:41 AM
To: Conal Elliott; ghc-devs at haskell.org<mailto:ghc-devs at haskell.org>
Cc: Dimitrios Vytiniotis; Nikolaos S. Papaspyrou (nickie at softlab.ntua.gr<mailto:nickie at softlab.ntua.gr>); George Karachalias; Simon Peyton Jones
Subject: RE: Pruning GADT case alternatives with uninhabitable coercion parameters

Conal

This also relates to detecting redundant or overlapped patterns in source programs. I know that Dimitrios is looking at this with Tom, Nikolas, George who I’m cc’ing him.

I think their current approach may be to integrate the overlap checking with the constraint solver in the type checker.  But that isn’t going to work for optimising Core.

An alternative approach would be to implement a specialised constraint solver.  It could be MUCH simpler than the one in the inference engine, because (a) there are no unification variables to worry about, (b) there is no need to gather evidence.  More or less it’s task could be to answer the question
            Is    C |- D    definitely a contradiction?
where C are the “given” constraints (from enclosing pattern matches) and D are the “wanted” constraints (from the current pattern match that may be unreachable).

I don’t think it would be hard to implement such a function.  I’d be happy to help advise if someone wants to take it on.

Dimitrios: If we had such a function, then maybe it’d be better to use it for the pattern-matching overlap detection too?

Simon

From: ghc-devs [mailto:ghc-devs-bounces at haskell.org] On Behalf Of Conal Elliott
Sent: 20 June 2014 18:59
To: ghc-devs at haskell.org<mailto:ghc-devs at haskell.org>
Subject: Pruning GADT case alternatives with uninhabitable coercion parameters

I'm looking for tips on pruning away impossible branches in `case` expressions on GADTs, due to uninhabited coercion parameter types.

Here's a simple example (rendered by HERMIT) from a type-specializion of the Foldable instance a GADT for perfect leaf trees in which the tree depth is part of the type:

> case ds of wild (Sum Int)
>   L (~# :: S (S Z) ~N Z) a1 -> f a1
>   B n1 (~# :: S (S Z) ~N S n1) uv -> ...

Note the kind of the coercion parameter to the leaf constructor (`L`): `S (S Z) ~N Z`, i.e., 2 == 0. I think we can safely remove this branch as impossible.

The reasoning gets subtler, however.
After inlining and simplifying in the second (`B`) alternative, the following turns up:

>     case ds0 of wild0 (Sum Int)
>       L (~# :: n1 ~N Z) a1 -> f0 a1
>       B n2 (~# :: n1 ~N S n2) uv0 -> ...

Now I want to remove the first `L` alternative with `n1 ~ Z`, given that the kind `S (S Z) ~N S n1` is inhabited (since we're in the first `B` alternative), so that `n1 ~ S Z`. With more inlining, more such equalities pile up. Soon we get to an impossible `B` alternative, whose removal would then eliminate the rest of the recursive unfolding.

My questions:

*   Does this sort of transformation already live in GHC somewhere, and if so, where?
*   Are there gotchas / sources of unsoundness in the transformation I'm suggesting?
*   Is anyone else already working on this sort of transformation?
-- Conal


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