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the concl
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Talking about the difference between ident and pattern. Giving
examples.
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Concretely, we bypass the following limitation: The notation
"{ ' pat | P }" broke the parsing of expressions of the form
"{ forall x, P } + { Q }". Indeed the latter works thanks to a
tolerance of Camlp5 in parsing "forall x, P" at level 200 while the
rule asks to actually parse the interior of "{ ... }" at level 99 (the
reason for 99 is to be below the rule for "M : T" which is at level
100, so that "{ x : A | P }" does not see "x : A" as a cast). Adding
an extra "'"; pat = pattern in parallel to c = constr LEVEL "99" broke
the tolerance for constr at level 200.
We fix this by adding an ad hoc rule for "{ binder_constr }" in the
native grammar (g_constr.ml4).
Actually, this is inconsistent with having a rule for "{ constr at level 99 }"
in Notations.v. We should have both rules in Notations.v or both rules
hard-wired in the native grammar. But I still don't know what is the best
decision to take, so leaving as it at the current time.
Advantages of hard-wiring both rules in g_constr.ml4: a bit simpler in
metasyntax.ml (no need to ensure that the rule exist). Disadvantages:
if one wants a different initial state without the business needing
the "{ }" for sumbool, sumor, sig, sigT, one still have the rules
there.
Advantages of having them in Notations.v: more modular, we can change
the initial state. Disadvantages: one would need a new kind of
modifier, something like "x at level 99 || binder_constr", with all
the difficulty to find a nice, intuitive, name for "binder_constr",
and the difficulty of understanding if there is a generality to this
"||" disjunction operator, and whether it should be documented or not.
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For compatibility, the default is to parse as ident and not as pattern.
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Concretely, we provide "constr as ident", "constr as strict pattern"
and "constr as pattern".
This tells to parse a binder as a constr, restricting to only ident or
to only a strict pattern, or to a pattern which can also be an ident.
The "strict pattern" modifier allows to restrict the use of patterns
in printing rules. This allows e.g. to select the appropriate rule for
printing between {x|P} and {'pat|P}.
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- Avoid dummy use of unit
- Do not decide as early as parsing the default level for pattern
- Prepare to further extensions
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Renaming it register_grammars_by_name.
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We generalize the possibility to refer to a notation not only by its
"_ U _" form but also using its "a 'U' b".
(Wish from EJGA)
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We reason up to order, and accept to match a final catch-all clauses
with any other clause.
This allows for instance to parse and print a notation of the form
"if t is S n then p else q".
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This now works not only for parsing of fun/forall (as in 8.6), but
also for arbitraty notations with binders and for printing.
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Example which is now reprinted as parsed:
fun '((x,y) as z) => (y,x)=z
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To deal with existing notations starting with a "let" (see notation
"for" in output/Notation2.v) we adopt the pragmatic approach of
glueing only inner let by default.
Ideally, it might be nicer to detect if there is an overlap of
notation, and not to glue only in case of overlap. We could also
decide that a notation starting with a "let" should always be
protected by some constant, say "id", so as to avoid possible
collisions, but this would require changes user side.
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For historical reasons (this was one of the first examples of
notations with binders), there was a special treatment for notations
whose right-hand side had the form "forall x, P" or "fun x => P". Not
only this is not necessary, but this prevents notations binding to
expressions such as "forall x, x>0 -> P" to be used in printing.
We let the general case absorb this particular case.
We add the integration of "let x:=c in ..." in the middle of a
notation with recursive binders as part of the binder list, reprinting
it "(x:=c)" (this was formerly the case only for the above particular
case).
Note that integrating "let" in sequence of binders is stil not the
case for the regular "forall"/"fun". Should we?
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This allows in particular to define notations with 'pat style binders.
E.g.:
A non-trivial change in this commit is storing binders and patterns
separately from terms.
This is not strictly necessary but has some advantages.
However, it is relatively common to have binders also used as terms,
or binders parsed as terms. Thus, it is already relatively common to
embed binders into terms (see e.g. notation for ETA in output test
Notations3.v) or to coerce terms to idents (see e.g. the notation for
{x|P} where x is parsed as a constr).
So, it is as simple to always store idents (and eventually patterns)
as terms.
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For instance, the following is now possible:
Check {(x,y)|x+y=0}.
Some questions remains. Maybe, by consistency, the notation should be
"{'(x,y)|x+y=0}"...
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Reordering the maps for binders and terms while uninterpreting a
notation the same way it will be at the time of interpreting a
notation.
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Factorizing the place where the different form of extended binders
(i.e. possibly including the 'pat form) are matched.
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(binders shall be substitutable by arbitrary cases patterns).
Giving a proper status to the functions unifying different instance of
the same notation variable (up to alpha-renaming).
Note: The a priori change of semantics in "bind_binding_as_term_env"
which now apply renaming from "unify_id" (as it did in
"bind_bindinglist_as_term_env") should not have an effect since, as
the former comment said, this corresponds to a "Anonymous" case which
should not occur, since the term would have to be bound upwards.
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Moving earlier functions which will be needed earlier.
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(binders shall be substitutable by arbitrary cases patterns).
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Seizing this opportunity to generalize the possibility for different
associativity into simply reversing the order or not. Also dropping
some dead code.
Example of recursive notation now working:
Notation "[ a , .. , b |- A ]" := (cons b .. (cons a nil) .., A).
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This allows for instance to support recursive notations of the form:
Notation "! x .. y # A #" :=
(((forall x, x=x),(forall x, x=0)), .. (((forall y, y=y),(forall y, y=0)), A) ..)
(at level 200, x binder).
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This makes treatment of recursive binders closer to the one of
recursive terms. It is unclear whether there are interesting notations
liable to use this, but this shall make easier mixing recursive
binders and recursive terms as in next commits.
Example of (artificial) notation that this commit supports:
Notation "! x .. y # A #" :=
(.. (A,(forall x, True)) ..,(forall y, True))
(at level 200, x binder).
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- The "terminator" of a recursive notation is now interpreted in the
environment in which it occurs rather than the environment at the
beginning of the recursive patterns.
Note that due to a tolerance in checking unbound variables of
notations, a variable unbound in the environment was still working
ok as long as no user-given variable was shadowing a private
variable of the notation - see the "exists_mixed" example in
test-suite.
Conversely, in a notation such as:
Notation "!! x .. y # A #" :=
((forall x, True), .. ((forall y, True), A) ..)
(at level 200, x binder).
Check !! a b # a=b #.
The unbound "a" was detected only at pretyping and not as expected
at internalizing time, due to "a=b" interpreted in context
containing a and b.
- Similarly, each binder is now interpreted in the environment in
which it occurs rather than as if the sequence of binders was
dependent from the left to the right (such a dependency was ok for
"forall" or "exists" but not in general).
For instance, in:
Notation "!! x .. y # A #" :=
((forall x, True), .. ((forall y, True), A) ..)
(at level 200, x binder).
Check !! (a:nat) (b:a=a) # True #.
The illegal dependency of the type of b in a was detected only at
pretyping time.
- If a let-in occurs in the sequence of binders of a notation with a
recursive pattern, it is now inserted in between the occurrences of
the iterator rather than glued with the forall/fun of the iterator.
For instance, in:
Notation "'exists_true' x .. y , P" :=
(exists x, True /\ .. (exists y, True /\ P) ..)
(at level 200, x binder).
Check exists_true '(x,y) (u:=0), x=y.
We now get
exists '(x, y), True /\ (let u := 0 in True /\ x = y)
while we had before the let-in breaking the repeated pattern:
exists '(x, y), (let u := 0 in True /\ x = y)
This is more compositional, and, in particular, the printer algorithm
now recognizes the pattern which is otherwise broken.
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productions.
This type describes the grammar non-terminal. It typically contains
ETConstrList (now renamed ETProdConstrList) but not ETBinder. It is
the type for metasyntax.ml and egramcoq.ml to communicate together.
The type constr_prod_entry_key with ETConstr, ETBinder, is now used
only in metasyntax.ml. This allows to get rid of some "assert false"
in uselessly matching over ETConstrList in metasyntax.ml and of some
"assert false" in uselessly matching over ETBinder in egramcoq.ml.
Also exporting less of extend.mli in API.
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- renaming lvar into ntnvars when relevant, for consistency
- renaming sometimes genv into env (intern_env) so as to remain
consistent with other parts of the code
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This works for contexts in Definition and co, but not yet for "fun" and co.
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The motivations are:
- To reflect the concrete syntax more closely.
- To factorize the different places where "contexts" are internalized:
before this patch, there is a different treatment of `Definition f
'(x,y) := x+y` and `Definition f := fun '(x,y) => x+y`, and a hack
to interpret `Definition f `pat := c : t`. With the patch, the fix
to avoid seeing a variable named `pat` works for both `fun 'x =>
...` and `Definition f 'x := ...`.
The drawbacks are:
- Counterpart to reflecting the concrete syntax more closerly, there
are more redundancies in the syntax. For instance, the case `CLetIn
(na,b,t,c)` can appears also in the form `CProdN (CLocalDef
(na,b,t)::rest,d)` and `CLambdaN (CLocalDef (na,b,t)::rest,d)`.
- Changes in the API, hence adaptation of plugins referring to `constr_expr` needed.
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Was apparently forgotten in a67bd7f9.
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Maxime Dénès
Hugo Herbelin