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This means that you can declare a morphism signature that has an argument
(or its output type) that is just eq.
E.g.:
Add Morphism incl with signature incl --> eq ++> impl.
is a correct signature for a morphism property of type
forall A, list A -> list A -> Prop
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* error message improved
* bug fixed: it was not checked whether the carrier of a relation of class
Leibniz matched the expected type
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there exists an i such that (c x1 ... xi) is a morphism. Previously
only the case c was tried.
* [ bug fixed ]: the term that must be replaced must not occur in c
(i.e. in (c x1 ... xi))
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not correctly de-lifted.
* [EXPERIMENTAL]: the Add Relation and Add Morphism commands now accept also
quantified relations and quantified morphisms. [ Add Setoid doesn't do that
yet. ] However, in case of quantified relations the matching between
an argument type and the (quantified) carrier expected for it is quite weak
and is complete only not modulus conversion.
* Many bugs have probably been introduced by the experimental feature.
However, the bugs should manifest only in the case of quantified relations.
In particular Leibniz has a strange status and its management should be
revised.
* Open problem: should the data type for relations and morphisms be changed
to explicitly show the quantifications?
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This is particular useful in case of modules (when it often happens to
have two setoids that can be composed only up to convertibility of their
input/output types).
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of the morphism. Previously the name was automatically generated, but it
was impossible to generate the same name in a module type and in a module.
2. behaviour of the relation/morphism tables w.r.t. module types and functors
fixed.
3. relations/setoids/morphisms can now happear in a module type. Add Morphism
in a module type declares an axiom instead of starting a new proof.
Add Morphism/Add Relation/Add Setoid in a module now generate objects
that match those generated by the same commands in a module type.
4. error messages improved/fixed.
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to generate the name of the morphism. Previously the name was automatically
generated, but this behaviour was not compatible with module typing: it
was not possible to generate the same identifier in the module type and in
the module.
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setoid_replace ... with ... in ... [using relation ...]
[generate side conditions ...]
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Leibniz equality and no side conditions are imposed by the user simply
calls the rewrite tactic. This was already done for setoid_replace/replace.
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Thus it does not work for setoid relations and it can replace setoid_replace
when the user wants to specify what the relation should be.
To solve the problem this commit enables the syntax
setoid_replace E1 with E2 using relation R ...
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now replaces E1 with E2 either generating the goal E1 R E2
or the goal E2 R E1 (as expected).
Note: the relation R is guessed when more than one is applicable.
This is not very nice, since it can guess the wrong one.
Since making the tactic compute R requires much code refactoring, I
would suggest the user to always use cutrewrite in place of setoid_rewrite.
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* msg_warning no longer used (since it pretty prints the messages on the
stderr and coqide does not show them). Is this a Coq bug???
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1) if the proposed morphism named has already been used
2) if the proposed signature matches the function type
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"setoid_rewrite dir term generate side conditions constr_list"
to specify a list of side conditions that must be a subset of the generated
new goals. Used to disambiguate in case of multiple set of generated
side conditions.
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This is now checked.
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2. cleaner behaviour: occurrences of the pattern in the type of a variable
bound by a dependent product are no longer
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only. Now the head of the relation is used to.
2) much nicer pretty-printing of the multiple set of side conditions that
the tactic can now produce
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longer two set of goals such that the first is a subset of the second.
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Add Morphism constr @ arugments_list @ output as name
replaced with the nicer (stable?) notation
Add Morphism constr with signature signature as name
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[ Note: untested, since the source of uncompleteness fixed is extremely
unlikely to happen and it never happens in my test cases. ]
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multiple solutions).
Since several solutions are observationally equal (i.e. they open the same
new set of goals), they are identified by the tactic. In case of multiple
non observationally equal solutions, the list of them is presented to the
user and the first one is randomically chosen. The user should be given
a possibility to choose.
Still todo: making the quoting function completely complete.
Note: the wf_unifty_to_subterm is now called twice. The first time is not
modulus delta conversion (the reasonable choice). The second time is modulus
delta conversion and the call is made iff the first call failed.
This is required by Ring that exploits the delta conversion ;-(
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that it generates are well-typed Coq terms. A limited form of backtracking is
used to avoid non well-typed choices.
The function is not complete yet (since the backtracking algorithm is
incomplete). This will be fixed shortly.
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disparus dès la version 1.11 de proofs/tacinterp.ml
- Prise en compte du contexte de filtrage sous-terme du but dans
'match goal with' quand des hypothèses aussi sont filtrées ce qui
avait disparu dans la version 1.56 de proofs/tacinterp.ml
- Restauration du filtrage sous-terme dans 'match c with' qui avait
disparu dans la version 1.27 de tactics/tacinterp.ml
- Nettoyage
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"Add Morphism m @ arg1 ... argn @ out as ident"
where argi = constr arrow
and arrow = "-->" | "++>" | "==>" (for contravariant, covariant and
bi-variant morphisms).
The syntax should be improved by getting rid of the "@" and maybe choosing
better symbols to represent the arrows.
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* Code clean-up.
* Preparation for the last implementation phase.
The last implementation phase will consist in the algorithm that, performing
backtracking, chooses the right combination of morphisms in the syntactic
representation of the goal.
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arguments. However, it still does not know about rewrite directions.
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2. partial setoids (a.k.a. areflexive relations) are now properly supported
3. the first two arguments of proj2 in the proof term have been simplified
to be just the mutual coimplication of the old and the new goal.
4. code simplification
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the morphism.
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* the data type for relations has been extended to cover all the cases
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In particular it can deal with partial setoids (also called typoids).
The latter feature was request by Marco Maggesi.
This commit is just a porting of the ML part of the tactic to the new
Coq part. It does not allow to exploit the new potentialities, yet.
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asymmetric relations thanks to the introduction of morphisms that are
covariant or contravariant in their arguments.
* The ML part of the tactic is updated only for backward compatibility: it
is still not possible to benefit from the asymmetric relations and relative
morphisms.
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introduces a few backward incompatibilities:
1. setoid_replace used to try to close the new goal using full_trivial.
The new implementation does not try to close the goal.
To fix the script it is sufficient to add a "; [ idtac | trivial ]."
after every application of setoid_replace that used to generate just
one goal.
2. (setoid_replace c1 c2) used to replace either c1 with c2 or c2 with c1
(if c1 did not occur in the goal). The new implementation only replaces
c1 with c2.
To fix the script it is sufficient to replace
(setoid_replace c1 with c2) with
(setoid_replace c1 with c2) || (setoid_replace c2 with c1)
in those cases where it is unknown what should be substituted with what.
3. the goal generated by the "Add Morphism" command has the hypothesis
permutated w.r.t. the old implementation. I.e. the old implementation
used to generate: forall x1 x2, forall x3 x4, x1=x2 -> x3=x4 -> ...
whereas the new implementation generates
forall x1 x2, x1=x2 -> forall x3 x4, x3 = x4 -> ...
Fixing the script is usually trivial.
4. the "Add Morphism P" command used to generate a non-standard goal in the
case of P being a predicate (i.e. a function whose codomain is Prop).
In that case the goal ended with an implication (instead of ending with
a coimplication). The new implementation generates a standard goal that
ends with a coimplication.
To fix the script you can add the following line at the very beginning:
cut <<old_goal>>; intro Hold; split; apply Hold;
assumption || (symmetry;assumption).
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