feat(library/tactic): add 'assert' tactic, closes #349

This commit is contained in:
Leonardo de Moura 2014-11-29 21:34:26 -08:00
parent 1a7dd56f0f
commit c08f4672e4
7 changed files with 93 additions and 2 deletions

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@ -83,6 +83,9 @@ notation `clears` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)`
opaque definition revert_lst (ids : expr_list) : tactic := builtin
notation `reverts` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := revert_lst l
opaque definition assert_hypothesis (id : expr) (e : expr) : tactic := builtin
notation `assert` `(` id `:` ty `)` := assert_hypothesis id ty
infixl `;`:15 := and_then
notation `[` h:10 `|`:10 r:(foldl:10 `|` (e r, or_else r e) h) `]` := r

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@ -124,7 +124,7 @@
(,(rx (not (any "\.")) word-start
(or "\\b.*_tac" "Cond" "or_else" "then" "try" "when" "assumption" "eassumption" "rapply" "apply" "fapply" "rename" "intro" "intros"
"generalize" "generalizes" "clear" "clears" "revert" "reverts" "back" "beta" "done" "exact" "repeat"
"whnf" "rotate" "rotate_left" "rotate_right" "inversion" "cases")
"whnf" "rotate" "rotate_left" "rotate_right" "inversion" "cases" "assert")
word-end)
. 'font-lock-constant-face)
;; Types

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@ -2,6 +2,7 @@ add_library(tactic goal.cpp proof_state.cpp tactic.cpp elaborate.cpp
apply_tactic.cpp intros_tactic.cpp rename_tactic.cpp trace_tactic.cpp
exact_tactic.cpp unfold_tactic.cpp generalize_tactic.cpp
inversion_tactic.cpp whnf_tactic.cpp revert_tactic.cpp
clear_tactic.cpp expr_to_tactic.cpp util.cpp init_module.cpp)
assert_tactic.cpp clear_tactic.cpp expr_to_tactic.cpp util.cpp
init_module.cpp)
target_link_libraries(tactic ${LEAN_LIBS})

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@ -0,0 +1,58 @@
/*
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "kernel/abstract.h"
#include "library/tactic/tactic.h"
#include "library/tactic/elaborate.h"
#include "library/tactic/expr_to_tactic.h"
namespace lean {
tactic assert_tactic(elaborate_fn const & elab, name const & id, expr const & e) {
return tactic01([=](environment const & env, io_state const & ios, proof_state const & s) {
proof_state new_s = s;
goals const & gs = new_s.get_goals();
if (!gs)
return none_proof_state();
bool report_unassigned = true;
if (auto new_e = elaborate_with_respect_to(env, ios, elab, new_s, e, none_expr(), report_unassigned)) {
goals const & gs = new_s.get_goals();
goal const & g = head(gs);
if (g.find_hyp(id)) {
// goal already has a hypothesis named id
return none_proof_state();
}
name_generator ngen = new_s.get_ngen();
expr new_meta1 = g.mk_meta(ngen.next(), *new_e);
goal new_goal1(new_meta1, *new_e);
expr new_local = mk_local(ngen.next(), id, *new_e, binder_info());
buffer<expr> hyps;
g.get_hyps(hyps);
hyps.push_back(new_local);
expr new_mvar2 = mk_metavar(ngen.next(), Pi(hyps, g.get_type()));
hyps.pop_back();
expr new_meta2_core = mk_app(new_mvar2, hyps);
expr new_meta2 = mk_app(new_meta2_core, new_local);
goal new_goal2(new_meta2, g.get_type());
expr val = g.abstract(mk_app(new_meta2_core, new_meta1));
substitution new_subst = new_s.get_subst();
new_subst.assign(g.get_name(), val);
return some_proof_state(proof_state(new_s, cons(new_goal1, cons(new_goal2, tail(gs))), new_subst, ngen));
}
return none_proof_state();
});
}
void initialize_assert_tactic() {
register_tac(name{"tactic", "assert_hypothesis"},
[](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
name id = tactic_expr_to_id(app_arg(app_fn(e)), "invalid 'assert' tactic, argument must be an identifier");
check_tactic_expr(app_arg(e), "invalid 'assert' tactic, argument must be an expression");
return assert_tactic(fn, id, get_tactic_expr_expr(app_arg(e)));
});
}
void finalize_assert_tactic() {
}
}

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@ -0,0 +1,14 @@
/*
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#pragma once
#include "library/tactic/tactic.h"
namespace lean {
tactic assert_tactic(elaborate_fn const & elab, name const & id, expr const & e);
void initialize_assert_tactic();
void finalize_assert_tactic();
}

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@ -18,6 +18,7 @@ Author: Leonardo de Moura
#include "library/tactic/clear_tactic.h"
#include "library/tactic/revert_tactic.h"
#include "library/tactic/inversion_tactic.h"
#include "library/tactic/assert_tactic.h"
namespace lean {
void initialize_tactic_module() {
@ -35,9 +36,11 @@ void initialize_tactic_module() {
initialize_clear_tactic();
initialize_revert_tactic();
initialize_inversion_tactic();
initialize_assert_tactic();
}
void finalize_tactic_module() {
finalize_assert_tactic();
finalize_inversion_tactic();
finalize_revert_tactic();
finalize_clear_tactic();

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@ -0,0 +1,12 @@
import logic
variables {A : Type} {a a' : A}
definition to_eq (H : a == a') : a = a' :=
begin
assert (H₁ : ∀ (Ht : A = A), eq.rec_on Ht a = a),
intro Ht,
exact (eq.refl (eq.rec_on Ht a)),
show a = a', from
heq.rec_on H H₁ (eq.refl A)
end