All Questions
25
questions
1
vote
1
answer
32
views
Feeding rewrites and other hints into an omnibus tactic
How do I feed rewrites that I've marked as safe into a custom tactic?
I'm trying to write shorter Coq proofs with more of the easy stuff hidden. To that end, in the script below I proved that ...
- 3,095
0
votes
1
answer
60
views
Coq equivalent of Lean's `nth_rewrite`
Does Coq have an equivalent of Lean's nth_rewrite? rewrite ... at ... appears to specialize at its first unification site ...
- 3,095
2
votes
1
answer
43
views
Coq cannot `simple apply reflexivity` in custom tactic
The fast reflexivity tactic shown below is very interesting. It exposes some of the unification machinery by disabling it.
I'm planning on going back and using it in the first part of Software ...
- 3,095
3
votes
1
answer
66
views
What's the idiomatic way to instantiate a tuple of evars in Ltac2?
Suppose that I have a local definition of a type ty in the context, and ty can be any nested tuple, e.g.:
...
- 33
0
votes
1
answer
61
views
Ltac, How to intro a fresh variable which may already have a good estiblished name given by a universal quantifier?
Context
I am currently self studying Coq following the Software Foundations book series which I am finding very approachable.
I have finally gotten round to ...
- 133
2
votes
1
answer
100
views
What does `induction ... in ...` do in Coq?
I'm self-studying the Semantics course, and met the following proof script in the warmup directory:
...
- 123
0
votes
1
answer
39
views
Tactic to Propify a bool expression
Let's say I have bool expressions <bexp> consisting of true, false, variables, ...
- 1,502
3
votes
2
answers
74
views
Creating a tactic for 'destructing' a list by last element?
Sometimes, I have a context in which I have some l : list X, and I want to prove the goal by proving that (1) If l = [], the ...
- 1,502
2
votes
1
answer
99
views
Proving that equality is decidable on an ``Inductive Set``
I've managed to prove that equality within a type is indeed decidable.
...
- 191
3
votes
1
answer
200
views
Selecting both a hypothesis and Goal while applying a tactic
I have a hypothesis H and some function foo. I want to simplify foo in both H and the ...
- 1,502
0
votes
1
answer
119
views
Specializing forall quantifiers in Coq
I have an inductively defined type of expressions:
...
4
votes
0
answers
65
views
Using CoqHammer from Ltac2
As it seems most likely to me, due to the special way arguments are evaluated in CoqHammer tactics (I tried to read the source code in OCaml but unfortunately I didn't understand much of it), it is ...
1
vote
1
answer
128
views
Rewriting inside quantified propositions in Coq?
Is there a simple way to use rewrites inside quantified Props? As an example, consider the following:
...
- 1,502
2
votes
1
answer
154
views
Debug autorewrite in Coq
I often meet proofs using autorewrite which Coq takes a while to process for some reason. (Setoid rewriting)
I then manually figure out which rewrite rules were ...
- 224
3
votes
3
answers
213
views
In Coq, is there a simpler tactic for introducing a disjunction and immediately destructing it?
Very often, I find myself writing some tactics like these:
assert (delta = 1 \/ delta <> 1) as Hd by lia.
destruct Hd.
...(proceed to work with two cases)...
...
- 1,502
3
votes
1
answer
156
views
Applying custom tactic in hypothesis
To avoid tedious repetition I have a tactic that looks something like this:
Ltac unfolds := try unfold foo;
try unfold bar;
try unfold baz;
apply some_lemma.
...
- 170
3
votes
2
answers
232
views
Coq: can `tauto` be used to prove classical tautologies?
When I experiment, I get inconsistent results.
Running the following code (with a proof included to double-check that it's provable)
...
3
votes
0
answers
93
views
Where is the discriminate tactic defined in Coq?
One can read the Coq documentation about discriminate tactic here.
Were is this tactic actually defined?
6
votes
1
answer
405
views
How to evaluate proof terms through opaque definitions?
Is there is a way to force computation over opaque terms, for the purposes of debugging/meta-analysis of proof scripts.
I understand why Coq doesn’t do this by default, and guess it would probably ...
5
votes
0
answers
164
views
Prove equality in a record type
I am trying to prove something about monoids an categories. This results in the following (partial) proof:
...
- 265
5
votes
1
answer
313
views
Cannot discriminate `0 = 1`
I am just practicing a bit with coq, doing some UniMath exercises and am trying to prove (0 = 1) -> empty. However, for some reason, I seem unable to reason ...
- 265
11
votes
2
answers
415
views
Proving uniqueness of an instance of an indexed inductive type
Consider the simple indexed inductive type
Inductive Single : nat -> Set :=
| single_O : Single O
| single_S {n} : Single n -> Single (S n).
Intuitively, I ...
- 213
4
votes
1
answer
175
views
Why does this trivial proof fail with structuring tacticals?
Given this:
Inductive color := Black | White.
Inductive point_state :=
| Occupied of color
| Empty
.
this works:
...
- 143
1
vote
1
answer
371
views
Form of intros in Coq specifically for `forall` and explicitly for `->`
Are there tactics in Coq that are more limited versions (subtactics?) of intros?
I'm curious if there are any specifically for ...
- 3,095
8
votes
2
answers
228
views
How to prove `forall m n : nat, m == n -> m = n`?
I am learning Coq with ssreflect. Just to understand things, I've proved forall a b : bool, a == b -> a = b but I can't figure out how to prove ...
- 317