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The commit which caused the regression (5ea2539d4a) looks reasonable.
However, it happens that this commit made that unification started in
the #4955 example to follow a path with problems of the form
"proj ?x == ?x" which clearly are unsolvable (both ?x have the same
instance).
We hack the corresponding very permissive occur-check function so that
it is a bit less permissive.
One day, this occur-check function would have to be rewritten in a
more stricter way.
----------------------------------------------------------------------
Extra comments:
I could list several functions for occur check of evars.
Four of them are too strict in the sense that they do not take into
account occurrences of evars which may disappear by reduction, nor
evars which have instances made in such a way that the occur-check is
solvable (as in "fst ?x[y:=(0,0)] = ?x[y:=0]"). These are:
- Termops.occur_evar for clenv, evar_refiner, tactic unification
- syntactic check without any normalization, even on defined evars
- Evarutil.occur_evar_upto for refine and the V82 compatibility mode
- syntactic check without any normalization but inlining of defined evars
- Evarsolve.occur_evar_upto_types for evar_define
- syntactic check without any normalization but inlining of defined evars
- occur-check in the type of evars met
- optimization for not visiting several time the same evar
- Evarsolve.noccur_evar for pattern unification and for inversion of
substitution (evar/evar or evar/term problems)
- syntactic check without any normalization but inlining of defined evars
- occur-check in the type of evars met in arguments of projections
- occur-check in the type of variables met in arguments of projections
- optimization for not visiting several time the same evar
- optimization for not visiting several time the type of the same variable
- note: to go this way, it seems to me that it should check also in
all types which are a cut-formula in the expression
One is much too lax:
- Evarconv.occur_rigidly
- no recursive check except on the types of "forall" and sometimes
in the arguments of an application
- note: there is obviously a large room for refinements without
loosing solutions
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The fix solves the original bug report but it only turns the Not_found
into a normal error in the alternative example by Guillaume. See
test-suite file for comments on how to eventually improve the
situation and find a solution in Guillaume's example too.
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Revert "Inference of return clause: giving uniformly priority to "small inversion"."
This reverts commit 980b434552d73cb990860f8d659b64686f6dbc87.
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The move to systematically trying small inversion first bumps
sometimes as feared to the weakness of unification (see #5107).
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Revert "Posssible abstractions over goal variables when inferring match return clause."
This reverts commit 0658ba7b908dad946200f872f44260d0e4893a94.
Revert "Trying an abstracting dependencies heuristic for the match return clause even when no type constraint is given."
This reverts commit 292f365185b7acdee79f3ff7b158551c2764c548.
Revert "Trying a no-inversion no-dependency heuristic for match return clause."
This reverts commit 2422aeb2b59229891508f35890653a9737988c00.
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We simply catch the RetypeError raised by the retyping function and translate
it into a user error, so that it is captured by the tactic monad instead of
reaching toplevel.
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Evarconv was made precociously dependent on user-declared reduction
behaviors. Only cbn should rely on that.
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This change exposed bug #4763
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Do not force all remaining conversions problems to be solved after the
_first_ solution of an evar, but only at the end of assignment of terms
to evars in w_merge. This was hell to track down, thanks for the help of
Maxime. contribs pass and HoTT too.
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Also getting rid of a global side-effect.
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Was PR#263: Fast lookup in named contexts
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This avoids leakage of universes. Also makes
Program Lemma/Fact work again, it tries to solve the
remaining evars using the obligation tactic.
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This assertion checked that two arguments in the same position were equal,
but in fact, since one might have already been reduced, they are only
convertible (which is too costly to check in an assertion).
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The no-inversion and maximal abstraction over dependencies now
supports abstraction over goal variables rather than only on "rel"
variables. In particular, it now works consistently using
"intro H; refine (match H with ... end)" or
"refine (fun H => match H with ... end)".
By doing so, we ensure that all three strategies are tried in all
situations where a return clause has to be inferred, even in the
context of a "refine".
See antepenultimate commit for discussion.
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even when no type constraint is given.
This no-inversion and maximal abstraction over dependencies in (rel)
variables heuristic was used only when a type constraint was given.
By doing so, we ensure that all three strategies "inversion with
dependencies as evars", "no-inversion and maximal abstraction over
dependencies in (rel) variables", "no-inversion and no abstraction
over dependencies" are tried in all situations where a return clause
has to be inferred.
See penultimate commit for discussion.
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The no-inversion no-dependency heuristic was used only in the absence
of type constraint. We may now use it also in the presence of a type
constraint.
See previous commit for discussion.
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As noted by Jason Gross on coq-club (Aug 18, 2016), the "small
inversion" heuristic is not used consistently depending on whether the
variables in the type constraint are Rel or Var.
This commit simply gives uniformly preference to the inversion of the
predicate along the indices of the type over other heuristics.
The next three commits will improve further a uniform use of the
different heuristics.
----------------------------------------------------------------------
Here are some extra comments on how to go further with the inference
of the return predicate:
The "small inversion" heuristic build_inversion_problem (1) is
characterized by two features:
- small inversion properly speaking (a), i.e. that is for a match on
t:I params p1(u11..u1p1) ... pn(un1..unpn) with pi exposing the
constructor structure of the indices of the type of t, a return
clause of the form "fun x1..xn (y:I params x1..xn) => match x1..xn y with
| p1(z11..z1p1) ... pn(zn1..znpn) => ?T@{z11..znpn}
| _ => IDProp
end" is used,
- the dependent subterms in the external type constraint U are replaced
by existential variables (b) which can be filled either by projecting
(i.e. installing a dependency) or imitating (i.e. no dependency);
this is obtained by solving the constraint ?T@{u11..unpn} == U by
setting ?T@{z11..znpn} := U'(...?wij@{zij:=uij}...) where U has been
written under the form U'(...uij...) highlighting all occurrences of
each of the uij occurring in U; otherwise said the problem is reduced to
the question of instantiating each wij, deciding whether wij@{zij} := zij
(projection) or wij@{zij} := uij (imitation) [There may be different
way to expose the uij in U, e.g. in the presence of overlapping, or of
evars in U; this is left undetermined].
The two other heuristics used are:
- prepare_predicate_from_arsign_tycon (2): takes the external type
constraint U and decides that each subterm of the form xi or y for a
match on "y:I params x1 ... xn" is dependent; otherwise said, it
corresponds to the degenerated form of (1) where
- no constructor structure is exposed (i.e. each pi is trivial)
- only uij that are Rel are replaced by an evar ?wij and this evar is
directly instantiated by projection (hence creating a dependency),
- simple use of of an evar in case no type constraint is given (3):
this evar is not dependent on the indices nor on the term to match.
Heuristic (1) is not strictly more powerful than other heuristics
because of (at least) two weaknesses.
- The first weakness is due to feature (b), i.e. to letting
unification decide whether these evars have to create a dependency
(projection) or not (imitation).
In particular, the heuristic (2) gives priority to systematic
abstraction over the dependencies (i.e. giving priority to
projection over imitation) and it can then be better as the
following example (from RelationClasses.v) shows:
Fixpoint arrows (l : Tlist) (r : Type) : Type :=
match l with
| Tnil => r
| A :: l' => A -> arrows l' r
end.
Fixpoint predicate_all (l : Tlist) : arrows l Prop -> Prop :=
match l with
| Tnil => fun f => f
| A :: tl => fun f => forall x : A, predicate_all tl (f x)
end.
Using (1) fails. It proposes the predicate
"fun l' => arrows ?l[l':=l'] Prop" so that typing the first branch
leads to unify "arrows ?l[l:=Tnil] Prop == Prop", a problem about
which evarconv unification is not able (yet!) to see what are the
two possible solutions. Using (2) works. It instead directly
suggests that the predicate is "fun l => arrows l Prop" is used, so
that unification is not needed.
Even if in practice the (2) is good (and hence could be added to
(1)), it is not universally better. Consider e.g.
y:bool,H1:P y,H2:P y,f:forall y, P y -> Q y |-
match y as z return Q y with
| true => f y H1
| false => f y H2
end : Q y
There is no way to type it with clause "as z return Q z" even if
trying to generalize H1 and H2 so that they get type P z.
- A second weakness is due to the interaction between small inversion
and constructors having a type whose indices havex a less refined
constructor structure than in the term to match, as in:
Inductive I : nat -> Set :=
| C1 : forall n : nat, listn n -> I n
| C2 : forall n : nat, I n -> I n.
Check (fun x : I 0 => match x with
| C1 n l => 0
| C2 n c => 0
end).
where the inverted predicate is "in I n return match n with 0 => ?T | _ => IDProp end"
but neither C1 nor C2 have fine enough types so that n becomes
constructed. There is a generic solution to that kind of situation which
is to compile the above into
Check (fun x : I 0 => match x with
| C1 n l => match n with 0 => 0 | _ -> id end
| C2 n c => match n with 0 => 0 | _ -> id end
end).
but this is not implemented yet.
In the absence of this refinement, heuristic (3) can here work
better.
So, the current status of the claim is that for (1) to be strictly
more powerful than other current heuristics, work has to be done
- (A) at the unification level (by either being able to reduce problems of
the form "match ?x[constructor] with ... end = a-rigid-term", or, at
worst, by being able to use the heuristic favoring projecting for such
a problem), so that it is better than (2),
- (B) at the match compilation level, by enforcing that, in each branch,
the corresponding constructor is refined so has to match (or
discriminate) the constraints given by the type of the term to
match, and hence being better than (3).
Moreover, (2) and (3) are disjoint. Here is an example which (3) can
solve but not (2) (and (1) cannot because of (B)). [To be fixed in
next commit.]
Inductive I : bool -> bool -> Type := C : I true true | D x : I x x.
Check fun z P Q (y:I true z) (H1 H2:P y) (f:forall y, P y -> Q y z) =>
match y with
| C => f y H1
| D _ => f y H2
end : Q y z.
Indeed, (2) infers "as y' in I b z return Q y z" which does not work.
Here is an example which (2) can solve but not (3) (and (1) cannot
because of (B) again). [To be fixed in 2nd next commit].
Check fun z P Q (y:I true z) (H1 H2:P y) (f:forall y z, P y -> Q y z) =>
match y with
| C => f y true H1
| D b => f y b H2
end : Q y z.
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The fix is essentially a revert of f22ad60 that introduced the use of the
pretyper version of whd_all instead of the one from the kernel. The exact
cause of slowness of the pretyper version is still to be investigated, but
it is believed that it is due to a call-by-name strategy, to compare with
call-by-need in the kernel.
Note that there is still something fishy in presence of evars. Technically
vm_compute does not handle them, but if this comes to be the case, it might
be worthwile to use an evar-aware variant of whd_all.
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We untangle many dependencies on Ltac datastructures and modules from the
lower strata, resulting in a self-contained ltac/ folder. While not a plugin
yet, the change is now very easy to perform. The main API changes have been
documented in the dev/doc/changes file.
The patches are quite rough, and it may be the case that some parts of the
code can migrate back from ltac/ to a core folder. This should be decided on
a case-by-case basis, according to a more long-term consideration of what is
exactly Ltac-dependent and whatnot.
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Typing.type_of was using conversion for types of fixpoints while it
could have used unification.
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Add a boolean for refolding during reduction, and an option
that is off by default in 8.6, to turn refolding on in all reduction
functions, as in 8.5.
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This legacy function is still used by destruct, and is a hotspot in various
examples from the wild. We hijack the check from Typeclass and perform a
double check at once not to mark unresolvable evars in vain a lot.
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This is a follow-up to #244 and corrects a minor bug introduced by the
patch.
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composition operator.
Short story:
This pull-request:
(1) removes the definition of the "right-to-left" function composition operator
(2) adds the definition of the "left-to-right" function composition operator
(3) rewrites the code relying on "right-to-left" function composition to rely on "left-to-right" function composition operator instead.
Long story:
In mathematics, function composition is traditionally denoted with ∘ operator.
Ocaml standard library does not provide analogous operator under any name.
Batteries Included provides provides two alternatives:
_ % _
and
_ %> _
The first operator one corresponds to the classical ∘ operator routinely used in mathematics.
I.e.:
(f4 % f3 % f2 % f1) x ≜ (f4 ∘ f3 ∘ f2 ∘ f1) x
We can call it "right-to-left" composition because:
- the function we write as first (f4) will be called as last
- and the function write as last (f1) will be called as first.
The meaning of the second operator is this:
(f1 %> f2 %> f3 %> f4) x ≜ (f4 ∘ f3 ∘ f2 ∘ f1) x
We can call it "left-to-right" composition because:
- the function we write as first (f1) will be called first
- and the function we write as last (f4) will be called last
That is, the functions are written in the same order in which we write and read them.
I think that it makes sense to prefer the "left-to-right" variant because
it enables us to write functions in the same order in which they will be actually called
and it thus better fits our culture
(we read/write from left to right).
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composition in a more obvious way
This commit rewrites terms
(fun x -> f1 (f2 ... (fN x)...))
to
f1 % f2 % ... % fN
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"Context.Named.{to,of}_rel_decl"
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mainly concerning referring to "Context.{Rel,Named}.get_{id,value,type}" functions.
If multiple modules define a function with a same name, e.g.:
Context.{Rel,Named}.get_type
those calls were prefixed with a corresponding prefix
to make sure that it is obvious which function is being called.
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Pierre-Marie Pédrot
Hugo Herbelin
Matthieu Sozeau
Maxime Dénès
Matthieu Sozeau
Guillaume Melquiond
Paul Steckler
Emilio Jesus Gallego Arias
Matej Kosik
Matej Kosik