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(but deactivated still).
Set Keyed Unification to activate the option, which changes
subterm selection to _always_ use full conversion _after_ finding a
subterm whose head/key matches the key of the term we're looking for.
This applies to rewrite and higher-order unification in
apply/elim/destruct.
Most proof scripts already abide by these semantics. For those that
don't, it's usually only a matter of using:
Declare Equivalent Keys f g.
This make keyed unification consider f and g to match as keys.
This takes care of most cases of abbreviations: typically Def foo :=
bar and rewriting with a bar-headed lhs in a goal mentioning foo works
once they're set equivalent.
For canonical structures, these hints should be automatically declared.
For non-global-reference headed terms, the key is the constructor name
(Sort, Prod...). Evars and metas are no keys.
INCOMPATIBILITIES:
In FMapFullAVL, a Function definition doesn't go through with keyed
unification on.
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Introduced in c74a70a73b3bf39394c551f1cdb224450bf77176.
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irrelevance.
Application of previous commit in Hurkens.v.
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In particular there is no retract of the type of negative propositions in a negative proposition.
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Adds a more generic and modular proof of Hurkens, where a shallow embedding of U- is given in the most general way. Subsumes all the previous proofs, opens the way to new proofs.
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experiments about computing PI
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Printing All cases (bug #3597).
- Fix Ltac matching with primitive projections (bug #3598).
- Spotted a problem with printing of constants with maximally implicit
arguments due to strange "compatibility" interpretation of Arguments [X]
as Arguments {X} but didn't fix it entirely yet (might cause incompatibilities).
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Left a README, just in case someone will discover the remnants of it
decades from now.
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For consistency with ChoiceFacts
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The generalized versions are names *_one_var. We preserve backwards
compatibility by defining the old versions in terms of the generalized
ones.
This closes the rest of Bug 3019, and closes pull request #6.
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It's possible that I should have removed more "allows", as many
instances of "foo allows to bar" could have been replaced by "foo bars"
(e.g., "[Qed] allows to check and save a complete proof term" could be
"[Qed] checks and saves a complete proof term"), but not always (e.g.,
"the optional argument allows to ignore universe polymorphism" should
not be "the optional argument ignores universe polymorphism" but "the
optional argument allows the caller to instruct Coq to ignore universe
polymorphism" or something similar).
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I'm not quite sure why, but I'm pretty sure it's not. Rather, in
"allowing for foo" and "allowing to foo", "foo" modifies the sense in
which someting is allowed, rather than it being "foo" that's allowed.
"Allowing fooing" generally works, though it can sound a bit awkward.
"Allowing one to foo" (or "Allowing {him,her,it,Coq} to foo") is always
acceptable, in-as-much as it's ok to use "one".
I haven't touched the older instances of it in the CHANGES file.
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"pat/term" for "apply term on current_hyp as pat".
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integrate to "rewrite"?) with the code of "replace".
Incidentally, "inversion" relies on dependent rewrite, with an
incompatibility introduced. Left-to-right rewriting is now done with
"eq_rec_r" while before it was done using "eq_rec" of "eq_sym". The
first one reduces to the second one but simpl is not anymore able to
reduce "eq_rec_r eq_refl". Hopefully cbn is able to do it (see
Zdigits).
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change of printing format of forall (need more thinking).
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all the tactics using the constructor keyword in one entry. This has the
side-effect to also remove the other variant of constructor from the AST.
I also needed to hack around the "tauto" tactic to make it work, by
calling directly the ML tactic through a TacExtend node. This may be
generalized to get rid of the intermingled dependencies between this
tactic and the infamous Ltac quotation mechanism.
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with possible further use of token "[]" + slight restructuration.
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hypothesis when using it in apply or rewrite (prefix ">",
undocumented), and a modifier to explicitly keep it in induction or
destruct (prefix "!", reminiscent of non-linerarity).
Also added undocumented option "Set Default Clearing Used Hypotheses"
which makes apply and rewrite default to erasing the hypothesis they
use (if ever their argument is indeed an hypothesis of the context).
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a dependent elimination principle for Prop arguments.
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variables.
Simplifies instantiation of constants/inductives, requiring less allocation and Map.find's.
Abstraction by variables is handled mostly inside the kernel but could be moved outside.
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This commit should be refactored by Pierre L. if he thinks this should
replace the previous version of fold_Equal, for now it is a different
lemma fold_Equal2. Same for the Section addded to SetoiList, it should
maybe replace the previous one.
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Standard library now compiles fully.
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Thanks to Arthur Azevedo de Amorim!
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corresponding proof in ssreflect.
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new files (WeakFan.v and WKL.v).
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Renamed Fan.v into WeakFan.v since this was a proof of Weak Fan Theorem
after all.
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- The earlier proof-of-concept file NPeano (which instantiates
the "Numbers" framework for nat) becomes now the entry point
in the Arith lib, and gets renamed PeanoNat. It still provides
an inner module "Nat" which sums up everything about type nat
(functions, predicates and properties of them).
This inner module Nat is usable as soon as you Require Import Arith,
or just Arith_base, or simply PeanoNat.
- Definitions of operations over type nat are now grouped in a new
file Init/Nat.v. This file is meant to be used without "Import",
hence providing for instance Nat.add or Nat.sqrt as soon as coqtop
starts (but no proofs about them).
- The definitions that used to be in Init/Peano.v (pred, plus, minus, mult)
are now compatibility notations (for Nat.pred, Nat.add, Nat.sub, Nat.mul
where here Nat is Init/Nat.v).
- This Coq.Init.Nat module (with only pure definitions) is Include'd
in the aforementioned Coq.Arith.PeanoNat.Nat. You might see Init.Nat
sometimes instead of just Nat (for instance when doing "Print plus").
Normally it should be ok to just ignore these "Init" since
Init.Nat is included in the full PeanoNat.Nat. I'm investigating if
it's possible to get rid of these "Init" prefixes.
- Concerning predicates, orders le and lt are still defined in Init/Peano.v,
with their notations "<=" and "<". Properties in PeanoNat.Nat directly
refer to these predicates in Peano. For instantation reasons, PeanoNat.Nat
also contains a Nat.le and Nat.lt (defined via "Definition le := Peano.le",
we cannot yet include an Inductive to implement a Parameter), but these
aliased predicates won't probably be very convenient to use.
- Technical remark: I've split the previous property functor NProp in
two parts (NBasicProp and NExtraProp), it helps a lot for building
PeanoNat.Nat incrementally. Roughly speaking, we have the following schema:
Module Nat.
Include Coq.Init.Nat. (* definition of operations : add ... sqrt ... *)
... (** proofs of specifications for basic ops such as + * - *)
Include NBasicProp. (** generic properties of these basic ops *)
... (** proofs of specifications for advanced ops (pow sqrt log2...)
that may rely on proofs for + * - *)
Include NExtraProp. (** all remaining properties *)
End Nat.
- All other files in directory Arith are now taking advantage of PeanoNat :
they are now filled with compatibility notations (when earlier lemmas
have exact counterpart in the Nat module) or lemmas with one-line proofs
based on the Nat module. All hints for database "arith" remain declared
in these old-style file (such as Plus.v, Lt.v, etc). All the old-style
files are still Require'd (or not) by Arith.v, just as before.
- Compatibility should be almost complete. For instance in the stdlib,
the only adaptations were due to .ml code referring to some Coq constant
name such as Coq.Init.Peano.pred, which doesn't live well with the
new compatibility notations.
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its universe doesn't get constrained unnecessarily (bug found in MathClasse).
Also avoid using rewrite itself in a proof in Morphisms.
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