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[Cao Qinxiang <caoqinxiang AT gmail.com>]

This is an interesting question. I try the following script.

Variable a: nat.

Variable b: nat.

Ltac foo1 := try reflexivity; try split.

Ltac foo2 := try reflexivity.

Goal exists c, (c = a /\ c = a + b) /\ c = b.

eexists.

split; (foo1; foo2).

Abort.

Goal exists c, (c = a /\ c = a + b) /\ c = b.

eexists.

(split; foo1); foo2.

Abort.

I thought the outcome should be different. But it turns out to be the same. Anyone can explain that?

Best,

Qinxiang Cao

Shanghai Jiao Tong University, John Hopcroft Center

Room 1110-2, SJTUSE Building

800 Dongchuan Road, Shanghai, China, 200240

On Wed, Jan 23, 2019 at 6:19 PM Théo Zimmermann <theo.zimmi AT gmail.com> wrote:

Le mer. 23 janv. 2019 à 10:33, Jeremy Dawson <Jeremy.Dawson AT anu.edu.au> a écrit :

Hi,

thanks for all the answers to my previous questions, some of which I'm
still working through.

In https://coq.inria.fr/refman/proof-engine/ltac.html
under Semantics then under Sequence it says
Sequence is associative.

I would take that to mean that
(tac1 ; tac2) ; tac3
is the same as
tac1 ; (tac2 ; tac3)

But is this so?  What if the tactics do some instantiating of
existential variables, then the order of attacking subgoals would matter?

The order would be the same in both cases.

Also, for the same reason, it would be useful to know, for
tac1 ; tac2
which order tac2 is applied to the subgoals resulting from tac1

This can depend on tactic, but in practice it would be in the listed order of the goals for virtually all tactics.

Cheers,

Jeremy