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in69665dd2480d364162933972de7ffa955eccab4d. There are still situations
when "as" is not given where equations coming from injection are not
yet removed, making invalid the computation of dependencies, what
prevents an hypothesis to be cleared and replaced.
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Schemes] option.
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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instances of "foo allows to bar" could have been replaced by "foo bars"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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Isolating a core tactic in replace, shareable to cutrewrite.
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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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subgoals and the role of the "by tac" clause swapped.
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no spacing in English before ":".
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Now that [idtac] can print a single message for several goals, printing the number of goals is readable.
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explicitly or implicitly to the variables in the as and in clauses +
formatting.
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multi-goal semantics of tactics.
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See bug #1041
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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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backtracks, print time spent in each of successive calls.
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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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