feat(library/tactic): add 'subtvars' tactic

This commit is contained in:
Leonardo de Moura 2015-05-25 15:44:22 -07:00
parent ab58e538a4
commit d0987eb3ac
7 changed files with 120 additions and 1 deletions

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@ -116,6 +116,7 @@ definition right : tactic := builtin
definition injection (e : expr) (ids : opt_identifier_list) : tactic := builtin
definition subst (ids : identifier_list) : tactic := builtin
definition substvars : tactic := builtin
definition reflexivity : tactic := builtin
definition symmetry : tactic := builtin

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@ -116,6 +116,7 @@ definition right : tactic := builtin
definition injection (e : expr) (ids : opt_identifier_list) : tactic := builtin
definition subst (ids : identifier_list) : tactic := builtin
definition substvars : tactic := builtin
definition reflexivity : tactic := builtin
definition symmetry : tactic := builtin

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@ -139,7 +139,8 @@
"generalize" "generalizes" "clear" "clears" "revert" "reverts" "back" "beta" "done" "exact" "rexact"
"refine" "repeat" "whnf" "rotate" "rotate_left" "rotate_right" "inversion" "cases" "rewrite" "esimp"
"unfold" "change" "check_expr" "contradiction" "exfalso" "split" "existsi" "constructor" "left" "right"
"injection" "congruence" "reflexivity" "symmetry" "transitivity" "state" "induction" "induction_using"))
"injection" "congruence" "reflexivity" "symmetry" "transitivity" "state" "induction" "induction_using"
"substvars"))
word-end)
(1 'font-lock-constant-face))
;; Types

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@ -181,6 +181,44 @@ tactic mk_subst_tactic(list<name> const & ids) {
return tactic(fn);
}
tactic mk_subst_vars_tactic(bool first, unsigned start) {
auto fn = [=](environment const & env, io_state const & ios, proof_state const & s) {
goals const & gs = s.get_goals();
if (empty(gs)) {
if (first)
return proof_state_seq();
else
return proof_state_seq(s);
}
goal const & g = head(gs);
auto apply_rewrite = [&](expr const & H, bool symm, unsigned i) {
tactic tac = orelse(then(mk_subst_tactic_core(mlocal_name(H), symm), mk_subst_vars_tactic(false, 0)),
mk_subst_vars_tactic(false, i+1));
return tac(env, ios, s);
};
buffer<expr> hyps;
g.get_hyps(hyps);
for (unsigned i = start; i < hyps.size(); i++) {
expr const & h = hyps[i];
expr lhs, rhs;
if (is_eq(mlocal_type(h), lhs, rhs)) {
if (is_local(rhs)) {
return apply_rewrite(h, true, i);
} else if (is_local(lhs)) {
return apply_rewrite(h, false, i);
}
}
}
if (first)
return proof_state_seq();
else
return proof_state_seq(s);
};
return tactic(fn);
}
void initialize_subst_tactic() {
register_tac(name{"tactic", "subst"},
[](type_checker &, elaborate_fn const & elab, expr const & e, pos_info_provider const *) {
@ -188,6 +226,10 @@ void initialize_subst_tactic() {
get_tactic_id_list_elements(app_arg(e), ns, "invalid 'subst' tactic, list of identifiers expected");
return then(mk_subst_tactic(to_list(ns)), try_tactic(refl_tactic(elab)));
});
register_tac(name{"tactic", "substvars"},
[](type_checker &, elaborate_fn const & elab, expr const &, pos_info_provider const *) {
return then(mk_subst_vars_tactic(true, 0), try_tactic(refl_tactic(elab)));
});
}
void finalize_subst_tactic() {
}

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@ -0,0 +1,52 @@
open nat
example (A B : Type) (a : A) (b : B) (h₁ : A = B) (h₂ : eq.rec_on h₁ a = b) : b = eq.rec_on h₁ a :=
begin
substvars
end
example (A B : Type) (a : A) (b : B) (h₁ : A = B) (h₂ : eq.rec_on h₁ a = b) : b = eq.rec_on h₁ a :=
begin
substvars
end
example (a b c : nat) (a0 : a = 0) (b1 : b = 1 + a) (ab : a = b) : empty :=
begin
substvars,
contradiction
end
example (a : nat) : a = 0 → a = 1 → empty :=
begin
intro a0 a1,
substvars,
contradiction
end
example (a b c : nat) : a = 0 → b = 1 + a → a = b → empty :=
begin
intro a0 b1 ab,
substvars,
state,
contradiction
end
example (a b c : nat) : a = 0 → b = 1 + a → a = b → empty :=
begin
intro a0 b1 ab,
substvars,
contradiction
end
example (a b c : nat) : a = 0 → 1 + a = b → a = b → empty :=
begin
intro a0 b1 ab,
substvars,
contradiction
end
example (a b c : nat) : a = 0 → 1 + a = b → a = b → empty :=
begin
intros,
substvars,
contradiction
end

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@ -0,0 +1,14 @@
inductive list (A : Type) :=
| nil : list A
| cons : A → list A → list A
open nat prod
example (A B : Type) (d c : nat) (h₀ : c = 0) (a : A) (b : list B) (h₁ : A = list B) (h₂ : eq.rec_on h₁ a = @list.nil B) (h₃ : d = c) (h₄ : d + 1 = d + 2)
: b = eq.rec_on h₁ a × c = 1:=
begin
substvars,
state,
injection h₄,
contradiction
end

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@ -0,0 +1,8 @@
substvars2.hlean:11:2: proof state
A B : Type,
a : A,
b : list B,
h₁ : A = list B,
h₂ : eq.rec_on h₁ a = list.nil B,
h₄ : 0 + 1 = 0 + 2
⊢ b = eq.rec_on h₁ a × 0 = 1