242 lines
9.8 KiB
C++
242 lines
9.8 KiB
C++
/*
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Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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*/
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#include <string>
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#include <utility>
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#include <algorithm>
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#include <vector>
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#include "util/optional.h"
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#include "util/name.h"
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#include "util/rb_map.h"
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#include "util/buffer.h"
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#include "util/interrupt.h"
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#include "kernel/environment.h"
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#include "library/equivalence_manager.h"
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#include "library/module.h"
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#include "library/constants.h"
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#include "library/choice.h"
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#include "library/placeholder.h"
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#include "library/explicit.h"
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#include "library/scoped_ext.h"
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#include "library/annotation.h"
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#include "library/typed_expr.h"
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#include "library/sorry.h"
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#include "library/tactic/expr_to_tactic.h"
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#include "frontends/lean/parser.h"
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#include "frontends/lean/util.h"
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#include "frontends/lean/tokens.h"
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#include "frontends/lean/begin_end_ext.h"
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namespace lean {
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optional<std::tuple<name, unsigned, unsigned>> get_calc_refl_info(environment const & env, name const & op) {
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return get_refl_extra_info(env, op);
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}
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optional<std::tuple<name, unsigned, unsigned>> get_calc_subst_info(environment const & env, name const & op) {
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return get_subst_extra_info(env, op);
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}
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optional<std::tuple<name, unsigned, unsigned>> get_calc_symm_info(environment const & env, name const & op) {
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return get_symm_extra_info(env, op);
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}
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static name * g_calc_name = nullptr;
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static expr mk_calc_annotation_core(expr const & e) { return mk_annotation(*g_calc_name, e); }
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static expr mk_calc_annotation(expr const & pr) {
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if (is_by(pr) || is_begin_end_annotation(pr) || is_sorry(pr)) {
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return pr;
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} else {
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return mk_calc_annotation_core(pr);
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}
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}
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bool is_calc_annotation(expr const & e) { return is_annotation(e, *g_calc_name); }
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typedef std::tuple<name, expr, expr> calc_pred;
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typedef pair<calc_pred, expr> calc_step;
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inline name const & pred_op(calc_pred const & p) { return std::get<0>(p); }
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inline expr const & pred_lhs(calc_pred const & p) { return std::get<1>(p); }
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inline expr const & pred_rhs(calc_pred const & p) { return std::get<2>(p); }
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inline calc_pred const & step_pred(calc_step const & s) { return s.first; }
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inline expr const & step_proof(calc_step const & s) { return s.second; }
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static void decode_expr_core(expr const & e, buffer<calc_pred> & preds) {
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buffer<expr> args;
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expr const & fn = get_app_args(e, args);
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if (!is_constant(fn))
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return;
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unsigned nargs = args.size();
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if (nargs < 2)
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return;
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preds.emplace_back(const_name(fn), args[nargs-2], args[nargs-1]);
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}
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// Check whether e is of the form (f ...) where f is a constant. If it is return f.
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static void decode_expr(expr const & e, buffer<calc_pred> & preds, pos_info const & pos) {
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preds.clear();
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if (is_choice(e)) {
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for (unsigned i = 0; i < get_num_choices(e); i++)
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decode_expr_core(get_choice(e, i), preds);
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} else {
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decode_expr_core(e, preds);
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}
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if (preds.empty())
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throw parser_error("invalid 'calc' expression, expression must be a function application 'f a_1 ... a_k' "
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"where f is a constant, and k >= 2", pos);
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}
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// Create (op _ _ ... _)
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static expr mk_op_fn(parser & p, name const & op, unsigned num_placeholders, pos_info const & pos) {
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expr r = p.save_pos(mk_explicit(mk_constant(op)), pos);
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while (num_placeholders > 0) {
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num_placeholders--;
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r = p.mk_app(r, p.save_pos(mk_expr_placeholder(), pos), pos);
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}
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return r;
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}
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static void parse_calc_proof(parser & p, buffer<calc_pred> const & preds, std::vector<calc_step> & steps) {
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steps.clear();
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auto pos = p.pos();
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p.check_token_next(get_colon_tk(), "invalid 'calc' expression, ':' expected");
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if (p.curr_is_token(get_lcurly_tk())) {
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p.next();
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environment const & env = p.env();
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expr pr = p.parse_expr();
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p.check_token_next(get_rcurly_tk(), "invalid 'calc' expression, '}' expected");
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for (auto const & pred : preds) {
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if (auto refl_it = get_refl_extra_info(env, pred_op(pred))) {
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if (auto subst_it = get_subst_extra_info(env, pred_op(pred))) {
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expr refl = mk_op_fn(p, std::get<0>(*refl_it), std::get<1>(*refl_it)-1, pos);
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expr refl_pr = p.mk_app(refl, pred_lhs(pred), pos);
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expr subst = mk_op_fn(p, std::get<0>(*subst_it), std::get<1>(*subst_it)-2, pos);
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expr subst_pr = p.mk_app({subst, pr, refl_pr}, pos);
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steps.emplace_back(pred, subst_pr);
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}
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}
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}
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if (steps.empty())
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throw parser_error("invalid 'calc' expression, reflexivity and/or substitution rule is not defined for operator", pos);
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} else {
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expr pr = p.parse_expr();
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for (auto const & pred : preds)
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steps.emplace_back(pred, mk_calc_annotation(pr));
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}
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}
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/** \brief Collect distinct rhs's */
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static void collect_rhss(std::vector<calc_step> const & steps, buffer<expr> & rhss) {
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rhss.clear();
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for (auto const & step : steps) {
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calc_pred const & pred = step_pred(step);
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expr const & rhs = pred_rhs(pred);
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if (std::find(rhss.begin(), rhss.end(), rhs) == rhss.end())
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rhss.push_back(rhs);
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}
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lean_assert(!rhss.empty());
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}
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static unsigned get_arity_of(parser & p, name const & op) {
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return get_arity(p.env().get(op).get_type());
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}
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static void join(parser & p, std::vector<calc_step> const & steps1, std::vector<calc_step> const & steps2,
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std::vector<calc_step> & res_steps, pos_info const & pos) {
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environment const & env = p.env();
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res_steps.clear();
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for (calc_step const & s1 : steps1) {
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check_interrupted();
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calc_pred const & pred1 = step_pred(s1);
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expr const & pr1 = step_proof(s1);
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for (calc_step const & s2 : steps2) {
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calc_pred const & pred2 = step_pred(s2);
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expr const & pr2 = step_proof(s2);
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if (!is_eqp(pred_rhs(pred1), pred_lhs(pred2)))
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continue;
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auto trans_it = get_trans_extra_info(env, pred_op(pred1), pred_op(pred2));
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if (trans_it) {
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expr trans = mk_op_fn(p, std::get<0>(*trans_it), std::get<2>(*trans_it)-5, pos);
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expr trans_pr = p.mk_app({trans, pred_lhs(pred1), pred_rhs(pred1), pred_rhs(pred2), pr1, pr2}, pos);
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res_steps.emplace_back(calc_pred(std::get<1>(*trans_it), pred_lhs(pred1), pred_rhs(pred2)), trans_pr);
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} else if (pred_op(pred1) == get_eq_name()) {
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expr trans_right = mk_op_fn(p, get_trans_rel_right_name(), 1, pos);
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expr R = mk_op_fn(p, pred_op(pred2), get_arity_of(p, pred_op(pred2))-2, pos);
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expr trans_pr = p.mk_app({trans_right, pred_lhs(pred1), pred_rhs(pred1), pred_rhs(pred2), R, pr1, pr2}, pos);
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res_steps.emplace_back(calc_pred(pred_op(pred2), pred_lhs(pred1), pred_rhs(pred2)), trans_pr);
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} else if (pred_op(pred2) == get_eq_name()) {
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expr trans_left = mk_op_fn(p, get_trans_rel_left_name(), 1, pos);
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expr R = mk_op_fn(p, pred_op(pred1), get_arity_of(p, pred_op(pred1))-2, pos);
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expr trans_pr = p.mk_app({trans_left, pred_lhs(pred1), pred_rhs(pred1), pred_rhs(pred2), R, pr1, pr2}, pos);
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res_steps.emplace_back(calc_pred(pred_op(pred1), pred_lhs(pred1), pred_rhs(pred2)), trans_pr);
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}
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}
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}
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}
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static expr mk_implies(parser & p, expr const & lhs, expr const & rhs, pos_info const & pos) {
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return p.mk_app(p.mk_app(p.save_pos(mk_constant(get_implies_name()), pos), lhs, pos), rhs, pos);
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}
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expr parse_calc(parser & p) {
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buffer<calc_pred> preds, new_preds;
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buffer<expr> rhss;
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std::vector<calc_step> steps, new_steps, next_steps;
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auto pos = p.pos();
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bool is_std = is_standard(p.env());
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expr first_pred = p.parse_expr();
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if (is_std && is_arrow(first_pred))
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first_pred = mk_implies(p, binding_domain(first_pred), binding_body(first_pred), pos);
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decode_expr(first_pred, preds, pos);
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parse_calc_proof(p, preds, steps);
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bool single = true; // true if calc has only one step
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expr dummy = mk_expr_placeholder();
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while (p.curr_is_token(get_ellipsis_tk())) {
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single = false;
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pos = p.pos();
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p.next();
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expr next_pred;
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if (is_std && p.curr_is_token(get_arrow_tk())) {
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p.next();
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expr rhs = p.parse_expr();
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next_pred = mk_implies(p, dummy, rhs, pos);
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} else {
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next_pred = p.parse_led(dummy);
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}
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decode_expr(next_pred, preds, pos);
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collect_rhss(steps, rhss);
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new_steps.clear();
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for (auto const & pred : preds) {
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if (is_eqp(pred_lhs(pred), dummy)) {
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for (expr const & rhs : rhss)
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new_preds.emplace_back(pred_op(pred), rhs, pred_rhs(pred));
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}
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}
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if (new_preds.empty())
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throw parser_error("invalid 'calc' expression, invalid expression", pos);
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parse_calc_proof(p, new_preds, new_steps);
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join(p, steps, new_steps, next_steps, pos);
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if (next_steps.empty())
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throw parser_error("invalid 'calc' expression, transitivity rule is not defined for current step", pos);
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steps.swap(next_steps);
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}
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buffer<expr> choices;
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for (auto const & s : steps) {
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if (single) {
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expr new_s = p.save_pos(mk_typed_expr(first_pred, step_proof(s)), pos);
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choices.push_back(new_s);
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} else {
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choices.push_back(step_proof(s));
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}
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}
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return p.save_pos(mk_choice(choices.size(), choices.data()), pos);
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}
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void initialize_calc() {
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g_calc_name = new name("calc");
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register_annotation(*g_calc_name);
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}
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void finalize_calc() {
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delete g_calc_name;
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}
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}
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