lean2/src/library/tactic/generalize_tactic.cpp

/*
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 "library/constants.h"
#include "kernel/abstract.h"
#include "kernel/instantiate.h"
#include "kernel/kernel_exception.h"
#include "library/reducible.h"
#include "library/util.h"
#include "library/tactic/elaborate.h"
#include "library/tactic/expr_to_tactic.h"

namespace lean {
expr mk_generalize_tactic_expr(expr const & e, name const & id) {
    return mk_app(mk_constant(get_tactic_generalize_tac_name()),
                  e, mk_constant(id));
}

optional<proof_state> generalize_core(environment const & env, io_state const & ios, elaborate_fn const & elab,
                                      expr const & e, name const & x, proof_state const & s, name const & tac_name,
                                      bool intro) {
    proof_state new_s = s;
    if (auto new_e = elaborate_with_respect_to(env, ios, elab, new_s, e)) {
        name_generator ngen = new_s.get_ngen();
        substitution subst  = new_s.get_subst();
        goals const & gs    = new_s.get_goals();
        goal const & g      = head(gs);
        auto tc     = mk_type_checker(env, ngen.mk_child());
        auto e_t_cs = tc->infer(*new_e);
        if (e_t_cs.second) {
            throw_tactic_exception_if_enabled(s, sstream() << "invalid '" << tac_name << "' tactic, unification constraints "
                                              "have been generated when inferring type");
            return none_proof_state(); // constraints were generated
        }
        expr e_t    = e_t_cs.first;
        expr t      = subst.instantiate(g.get_type());
        name n;
        if (is_constant(e))
            n = const_name(e);
        else if (is_local(e))
            n = local_pp_name(e);
        else
            n = x;
        expr new_t, new_m, new_val;
        if (intro) {
            buffer<expr> hyps;
            g.get_hyps(hyps);
            expr new_h = mk_local(ngen.next(), get_unused_name(x, hyps), e_t, binder_info());
            new_t   = instantiate(abstract(t, *new_e), new_h);
            new_m   = mk_metavar(ngen.next(), Pi(hyps, Pi(new_h, new_t)));
            new_m   = mk_app(new_m, hyps);
            new_val = mk_app(new_m, *new_e);
            new_m   = mk_app(new_m, new_h);
        } else {
            new_t   = mk_pi(n, e_t, abstract(t, *new_e));
            new_m   = g.mk_meta(ngen.next(), new_t);
            new_val = mk_app(new_m, *new_e);
        }
        try {
            check_term(*tc, g.abstract(new_t));
        } catch (kernel_exception const & ex) {
            std::shared_ptr<kernel_exception> ex_ptr(static_cast<kernel_exception*>(ex.clone()));
            throw_tactic_exception_if_enabled(s, [=](formatter const & fmt) {
                    format r = format("invalid '") + format(tac_name) + format("' tactic, type error");
                    r       += line();
                    r       += ex_ptr->pp(fmt);
                    return r;
                });
            return none_proof_state();
        }
        assign(subst, g, new_val);
        goal new_g(new_m, new_t);
        return some(proof_state(new_s, goals(new_g, tail(gs)), subst, ngen));
    }
    return none_proof_state();
}

optional<proof_state> generalize(environment const & env, io_state const & ios, elaborate_fn const & elab,
                                 expr const & e, name const & x, proof_state const & s) {
    return generalize_core(env, ios, elab, e, x, s, "generalize", false);
}

tactic generalize_tactic(elaborate_fn const & elab, expr const & e, name const & x) {
    return tactic01([=](environment const & env, io_state const & ios, proof_state const & s) {
            return generalize(env, ios, elab, e, x, s);
        });
}

void initialize_generalize_tactic() {
    register_tac(get_tactic_generalize_tac_name(),
                 [](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
                     check_tactic_expr(app_arg(app_fn(e)), "invalid 'generalize' tactic, invalid argument");
                     name id = tactic_expr_to_id(app_arg(e), "invalid 'generalize' tactic, argument must be an identifier");
                     return generalize_tactic(fn, get_tactic_expr_expr(app_arg(app_fn(e))), id);
                 });

    register_tac(get_tactic_generalizes_name(),
                 [](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
                     buffer<expr> args;
                     get_tactic_expr_list_elements(app_arg(e), args, "invalid 'generalizes' tactic, list of expressions expected");
                     if (args.empty())
                         return id_tactic();
                     tactic r = generalize_tactic(fn, args.back(), "x");
                     args.pop_back();
                     while (!args.empty()) {
                         r = then(generalize_tactic(fn, args.back(), "x"), r);
                         args.pop_back();
                     }
                     return r;
                 });
}

void finalize_generalize_tactic() {
}
}