543 lines
19 KiB
C++
543 lines
19 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 "kernel/find_fn.h"
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#include "kernel/instantiate.h"
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#include "kernel/abstract.h"
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#include "kernel/type_checker.h"
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#include "kernel/inductive/inductive.h"
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#include "library/locals.h"
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#include "library/util.h"
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#include "library/constants.h"
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namespace lean {
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bool is_def_app(environment const & env, expr const & e) {
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if (!is_app(e))
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return false;
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expr const & f = get_app_fn(e);
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if (!is_constant(f))
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return false;
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auto decl = env.find(const_name(f));
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return decl && decl->is_definition() && !decl->is_opaque();
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}
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optional<expr> unfold_app(environment const & env, expr const & e) {
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if (!is_app(e))
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return none_expr();
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expr const & f = get_app_fn(e);
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if (!is_constant(f))
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return none_expr();
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auto decl = env.find(const_name(f));
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if (!decl || !decl->is_definition() || decl->is_opaque())
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return none_expr();
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expr d = instantiate_value_univ_params(*decl, const_levels(f));
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buffer<expr> args;
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get_app_rev_args(e, args);
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return some_expr(apply_beta(d, args.size(), args.data()));
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}
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optional<level> dec_level(level const & l) {
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switch (kind(l)) {
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case level_kind::Zero: case level_kind::Param: case level_kind::Global: case level_kind::Meta:
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return none_level();
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case level_kind::Succ:
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return some_level(succ_of(l));
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case level_kind::Max:
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if (auto lhs = dec_level(max_lhs(l))) {
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if (auto rhs = dec_level(max_rhs(l))) {
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return some_level(mk_max(*lhs, *rhs));
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}}
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return none_level();
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case level_kind::IMax:
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// Remark: the following mk_max is not a typo. The following
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// assertion justifies it.
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if (auto lhs = dec_level(imax_lhs(l))) {
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if (auto rhs = dec_level(imax_rhs(l))) {
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return some_level(mk_max(*lhs, *rhs));
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}}
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return none_level();
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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/** \brief Return true if environment has a constructor named \c c that returns
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an element of the inductive datatype named \c I, and \c c must have \c nparams parameters.
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*/
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bool has_constructor(environment const & env, name const & c, name const & I, unsigned nparams) {
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auto d = env.find(c);
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if (!d || d->is_definition())
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return false;
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expr type = d->get_type();
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unsigned i = 0;
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while (is_pi(type)) {
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i++;
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type = binding_body(type);
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}
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if (i != nparams)
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return false;
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type = get_app_fn(type);
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return is_constant(type) && const_name(type) == I;
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}
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bool has_unit_decls(environment const & env) {
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return has_constructor(env, get_unit_star_name(), get_unit_name(), 0);
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}
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bool has_eq_decls(environment const & env) {
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return has_constructor(env, get_eq_refl_name(), get_eq_name(), 2);
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}
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bool has_heq_decls(environment const & env) {
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return has_constructor(env, get_heq_refl_name(), get_heq_name(), 2);
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}
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bool has_prod_decls(environment const & env) {
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return has_constructor(env, get_prod_mk_name(), get_prod_name(), 4);
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}
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bool has_lift_decls(environment const & env) {
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return has_constructor(env, get_lift_up_name(), get_lift_name(), 2);
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}
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bool is_recursive_datatype(environment const & env, name const & n) {
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optional<inductive::inductive_decls> decls = inductive::is_inductive_decl(env, n);
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if (!decls)
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return false;
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for (inductive::inductive_decl const & decl : std::get<2>(*decls)) {
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for (inductive::intro_rule const & intro : inductive::inductive_decl_intros(decl)) {
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expr type = inductive::intro_rule_type(intro);
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while (is_pi(type)) {
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if (find(binding_domain(type), [&](expr const & e, unsigned) {
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return is_constant(e) && const_name(e) == n; })) {
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return true;
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}
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type = binding_body(type);
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}
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}
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}
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return false;
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}
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bool is_reflexive_datatype(type_checker & tc, name const & n) {
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environment const & env = tc.env();
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name_generator ngen = tc.mk_ngen();
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optional<inductive::inductive_decls> decls = inductive::is_inductive_decl(env, n);
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if (!decls)
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return false;
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for (inductive::inductive_decl const & decl : std::get<2>(*decls)) {
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for (inductive::intro_rule const & intro : inductive::inductive_decl_intros(decl)) {
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expr type = inductive::intro_rule_type(intro);
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while (is_pi(type)) {
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expr arg = tc.whnf(binding_domain(type)).first;
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if (is_pi(arg) && find(arg, [&](expr const & e, unsigned) { return is_constant(e) && const_name(e) == n; })) {
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return true;
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}
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expr local = mk_local(ngen.next(), binding_domain(type));
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type = instantiate(binding_body(type), local);
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}
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}
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}
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return false;
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}
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level get_datatype_level(expr ind_type) {
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while (is_pi(ind_type))
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ind_type = binding_body(ind_type);
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return sort_level(ind_type);
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}
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bool is_inductive_predicate(environment const & env, name const & n) {
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if (!env.impredicative())
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return false; // environment does not have Prop
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if (!inductive::is_inductive_decl(env, n))
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return false; // n is not inductive datatype
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return is_zero(get_datatype_level(env.get(n).get_type()));
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}
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void get_intro_rule_names(environment const & env, name const & n, buffer<name> & result) {
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if (auto decls = inductive::is_inductive_decl(env, n)) {
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for (inductive::inductive_decl const & decl : std::get<2>(*decls)) {
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if (inductive::inductive_decl_name(decl) == n) {
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for (inductive::intro_rule const & ir : inductive::inductive_decl_intros(decl))
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result.push_back(inductive::intro_rule_name(ir));
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return;
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}
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}
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}
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}
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optional<name> is_constructor_app(environment const & env, expr const & e) {
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expr const & fn = get_app_fn(e);
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if (is_constant(fn))
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if (auto I = inductive::is_intro_rule(env, const_name(fn)))
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return optional<name>(const_name(fn));
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return optional<name>();
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}
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optional<name> is_constructor_app_ext(environment const & env, expr const & e) {
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if (auto r = is_constructor_app(env, e))
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return r;
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expr const & f = get_app_fn(e);
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if (!is_constant(f))
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return optional<name>();
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auto decl = env.find(const_name(f));
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if (!decl || !decl->is_definition() || decl->is_opaque())
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return optional<name>();
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expr const * it = &decl->get_value();
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while (is_lambda(*it))
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it = &binding_body(*it);
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return is_constructor_app_ext(env, *it);
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}
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expr instantiate_univ_param (expr const & e, name const & p, level const & l) {
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return instantiate_univ_params(e, to_list(p), to_list(l));
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}
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expr to_telescope(bool pi, name_generator & ngen, expr e, buffer<expr> & telescope,
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optional<binder_info> const & binfo) {
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while ((pi && is_pi(e)) || (!pi && is_lambda(e))) {
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expr local;
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if (binfo)
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local = mk_local(ngen.next(), binding_name(e), binding_domain(e), *binfo);
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else
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local = mk_local(ngen.next(), binding_name(e), binding_domain(e), binding_info(e));
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telescope.push_back(local);
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e = instantiate(binding_body(e), local);
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}
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return e;
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}
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expr to_telescope(name_generator & ngen, expr const & type, buffer<expr> & telescope, optional<binder_info> const & binfo) {
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return to_telescope(true, ngen, type, telescope, binfo);
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}
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expr fun_to_telescope(name_generator & ngen, expr const & e, buffer<expr> & telescope,
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optional<binder_info> const & binfo) {
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return to_telescope(false, ngen, e, telescope, binfo);
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}
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expr to_telescope(type_checker & tc, expr type, buffer<expr> & telescope, optional<binder_info> const & binfo,
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constraint_seq & cs) {
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type = tc.whnf(type, cs);
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while (is_pi(type)) {
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expr local;
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if (binfo)
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local = mk_local(tc.mk_fresh_name(), binding_name(type), binding_domain(type), *binfo);
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else
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local = mk_local(tc.mk_fresh_name(), binding_name(type), binding_domain(type), binding_info(type));
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telescope.push_back(local);
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type = tc.whnf(instantiate(binding_body(type), local), cs);
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}
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return type;
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}
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expr to_telescope(type_checker & tc, expr type, buffer<expr> & telescope, optional<binder_info> const & binfo) {
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constraint_seq cs;
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return to_telescope(tc, type, telescope, binfo, cs);
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}
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static expr * g_true = nullptr;
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static expr * g_true_intro = nullptr;
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static expr * g_and = nullptr;
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static expr * g_and_intro = nullptr;
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static expr * g_and_elim_left = nullptr;
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static expr * g_and_elim_right = nullptr;
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void initialize_library_util() {
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g_true = new expr(mk_constant(get_true_name()));
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g_true_intro = new expr(mk_constant(get_true_intro_name()));
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g_and = new expr(mk_constant(get_and_name()));
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g_and_intro = new expr(mk_constant(get_and_intro_name()));
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g_and_elim_left = new expr(mk_constant(get_and_elim_left_name()));
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g_and_elim_right = new expr(mk_constant(get_and_elim_right_name()));
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}
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void finalize_library_util() {
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delete g_true;
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delete g_true_intro;
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delete g_and;
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delete g_and_intro;
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delete g_and_elim_left;
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delete g_and_elim_right;
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}
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expr mk_true() {
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return *g_true;
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}
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expr mk_true_intro() {
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return *g_true_intro;
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}
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expr mk_and(expr const & a, expr const & b) {
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return mk_app(*g_and, a, b);
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}
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expr mk_and_intro(type_checker & tc, expr const & Ha, expr const & Hb) {
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return mk_app(*g_and_intro, tc.infer(Ha).first, tc.infer(Hb).first, Ha, Hb);
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}
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expr mk_and_elim_left(type_checker & tc, expr const & H) {
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expr a_and_b = tc.whnf(tc.infer(H).first).first;
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return mk_app(*g_and_elim_left, app_arg(app_fn(a_and_b)), app_arg(a_and_b), H);
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}
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expr mk_and_elim_right(type_checker & tc, expr const & H) {
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expr a_and_b = tc.whnf(tc.infer(H).first).first;
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return mk_app(*g_and_elim_right, app_arg(app_fn(a_and_b)), app_arg(a_and_b), H);
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}
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expr mk_unit(level const & l) {
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return mk_constant(get_unit_name(), {l});
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}
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expr mk_unit_mk(level const & l) {
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return mk_constant(get_unit_star_name(), {l});
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}
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expr mk_prod(type_checker & tc, expr const & A, expr const & B) {
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level l1 = sort_level(tc.ensure_type(A).first);
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level l2 = sort_level(tc.ensure_type(B).first);
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return mk_app(mk_constant(get_prod_name(), {l1, l2}), A, B);
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}
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expr mk_pair(type_checker & tc, expr const & a, expr const & b) {
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expr A = tc.infer(a).first;
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expr B = tc.infer(b).first;
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level l1 = sort_level(tc.ensure_type(A).first);
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level l2 = sort_level(tc.ensure_type(B).first);
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return mk_app(mk_constant(get_prod_mk_name(), {l1, l2}), A, B, a, b);
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}
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expr mk_pr1(type_checker & tc, expr const & p) {
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expr AxB = tc.whnf(tc.infer(p).first).first;
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expr const & A = app_arg(app_fn(AxB));
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expr const & B = app_arg(AxB);
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return mk_app(mk_constant(get_prod_pr1_name(), const_levels(get_app_fn(AxB))), A, B, p);
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}
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expr mk_pr2(type_checker & tc, expr const & p) {
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expr AxB = tc.whnf(tc.infer(p).first).first;
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expr const & A = app_arg(app_fn(AxB));
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expr const & B = app_arg(AxB);
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return mk_app(mk_constant(get_prod_pr2_name(), const_levels(get_app_fn(AxB))), A, B, p);
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}
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expr mk_unit(level const & l, bool prop) { return prop ? mk_true() : mk_unit(l); }
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expr mk_unit_mk(level const & l, bool prop) { return prop ? mk_true_intro() : mk_unit_mk(l); }
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expr mk_prod(type_checker & tc, expr const & a, expr const & b, bool prop) { return prop ? mk_and(a, b) : mk_prod(tc, a, b); }
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expr mk_pair(type_checker & tc, expr const & a, expr const & b, bool prop) {
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return prop ? mk_and_intro(tc, a, b) : mk_pair(tc, a, b);
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}
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expr mk_pr1(type_checker & tc, expr const & p, bool prop) { return prop ? mk_and_elim_left(tc, p) : mk_pr1(tc, p); }
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expr mk_pr2(type_checker & tc, expr const & p, bool prop) { return prop ? mk_and_elim_right(tc, p) : mk_pr2(tc, p); }
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bool is_iff(expr const & e) {
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expr const & fn = get_app_fn(e);
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return is_constant(fn) && const_name(fn) == get_iff_name();
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}
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expr mk_iff(expr const & lhs, expr const & rhs) {
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return mk_app(mk_constant(get_iff_name()), lhs, rhs);
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}
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expr mk_iff_refl(expr const & a) {
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return mk_app(mk_constant(get_iff_refl_name()), a);
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}
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expr mk_eq(type_checker & tc, expr const & lhs, expr const & rhs) {
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expr A = tc.whnf(tc.infer(lhs).first).first;
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level lvl = sort_level(tc.ensure_type(A).first);
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return mk_app(mk_constant(get_eq_name(), {lvl}), A, lhs, rhs);
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}
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expr mk_refl(type_checker & tc, expr const & a) {
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expr A = tc.whnf(tc.infer(a).first).first;
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level lvl = sort_level(tc.ensure_type(A).first);
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return mk_app(mk_constant(get_eq_refl_name(), {lvl}), A, a);
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}
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expr mk_symm(type_checker & tc, expr const & H) {
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expr p = tc.whnf(tc.infer(H).first).first;
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lean_assert(is_eq(p));
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expr lhs = app_arg(app_fn(p));
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expr rhs = app_arg(p);
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expr A = tc.infer(lhs).first;
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level lvl = sort_level(tc.ensure_type(A).first);
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return mk_app(mk_constant(get_eq_symm_name(), {lvl}), A, lhs, rhs, H);
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}
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expr mk_heq(type_checker & tc, expr const & lhs, expr const & rhs) {
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expr A = tc.whnf(tc.infer(lhs).first).first;
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expr B = tc.whnf(tc.infer(rhs).first).first;
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level lvl = sort_level(tc.ensure_type(A).first);
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return mk_app(mk_constant(get_heq_name(), {lvl}), A, lhs, B, rhs);
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}
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bool is_eq_rec(expr const & e) {
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expr const & fn = get_app_fn(e);
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return is_constant(fn) && const_name(fn) == get_eq_rec_name();
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}
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bool is_eq(expr const & e) {
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expr const & fn = get_app_fn(e);
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return is_constant(fn) && const_name(fn) == get_eq_name();
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}
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bool is_eq_a_a(expr const & e) {
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if (!is_eq(e))
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return false;
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buffer<expr> args;
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get_app_args(e, args);
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return args.size() == 3 && args[1] == args[2];
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}
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bool is_eq_a_a(type_checker & tc, expr const & e) {
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if (!is_eq(e))
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return false;
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buffer<expr> args;
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get_app_args(e, args);
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if (args.size() != 3)
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return false;
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pair<bool, constraint_seq> d = tc.is_def_eq(args[1], args[2]);
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return d.first && !d.second;
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}
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void mk_telescopic_eq(type_checker & tc, buffer<expr> const & t, buffer<expr> const & s, buffer<expr> & eqs) {
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lean_assert(t.size() == s.size());
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lean_assert(std::all_of(s.begin(), s.end(), is_local));
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lean_assert(inductive::has_dep_elim(tc.env(), get_eq_name()));
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buffer<buffer<expr>> t_aux;
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name e_name("e");
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for (unsigned i = 0; i < t.size(); i++) {
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expr s_i = s[i];
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expr s_i_ty = mlocal_type(s_i);
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expr s_i_ty_a = abstract_locals(s_i_ty, i, s.data());
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expr t_i = t[i];
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t_aux.push_back(buffer<expr>());
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t_aux.back().push_back(t_i);
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for (unsigned j = 0; j < i; j++) {
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if (depends_on(s_i_ty, s[j])) {
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// we need to "cast"
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buffer<expr> ty_inst_args;
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for (unsigned k = 0; k <= j; k++)
|
|
ty_inst_args.push_back(s[k]);
|
|
for (unsigned k = j + 1; k < i; k++)
|
|
ty_inst_args.push_back(t_aux[k][j+1]);
|
|
lean_assert(ty_inst_args.size() == i);
|
|
expr s_i_ty = instantiate_rev(s_i_ty_a, i, ty_inst_args.data());
|
|
buffer<expr> rec_args;
|
|
rec_args.push_back(mlocal_type(s[j]));
|
|
rec_args.push_back(t_aux[j][j]);
|
|
rec_args.push_back(Fun(s[j], Fun(eqs[j], s_i_ty))); // type former ("promise")
|
|
rec_args.push_back(t_i); // minor premise
|
|
rec_args.push_back(s[j]);
|
|
rec_args.push_back(eqs[j]);
|
|
level rec_l1 = sort_level(tc.ensure_type(s_i_ty).first);
|
|
level rec_l2 = sort_level(tc.ensure_type(mlocal_type(s[j])).first);
|
|
t_i = mk_app(mk_constant(get_eq_rec_name(), {rec_l1, rec_l2}), rec_args.size(), rec_args.data());
|
|
}
|
|
t_aux.back().push_back(t_i);
|
|
}
|
|
expr eq = mk_local(tc.mk_fresh_name(), e_name.append_after(i+1), mk_eq(tc, t_i, s_i), binder_info());
|
|
eqs.push_back(eq);
|
|
}
|
|
}
|
|
|
|
void mk_telescopic_eq(type_checker & tc, buffer<expr> const & t, buffer<expr> & eqs) {
|
|
lean_assert(std::all_of(t.begin(), t.end(), is_local));
|
|
lean_assert(inductive::has_dep_elim(tc.env(), get_eq_name()));
|
|
buffer<expr> s;
|
|
for (unsigned i = 0; i < t.size(); i++) {
|
|
expr ty = mlocal_type(t[i]);
|
|
ty = abstract_locals(ty, i, t.data());
|
|
ty = instantiate_rev(ty, i, s.data());
|
|
expr local = mk_local(tc.mk_fresh_name(), local_pp_name(t[i]).append_after("'"), ty, local_info(t[i]));
|
|
s.push_back(local);
|
|
}
|
|
return mk_telescopic_eq(tc, t, s, eqs);
|
|
}
|
|
|
|
level mk_max(levels const & ls) {
|
|
if (!ls)
|
|
return mk_level_zero();
|
|
else if (!tail(ls))
|
|
return head(ls);
|
|
else
|
|
return mk_max(head(ls), mk_max(tail(ls)));
|
|
}
|
|
|
|
expr telescope_to_sigma(type_checker & tc, unsigned sz, expr const * ts, constraint_seq & cs) {
|
|
lean_assert(sz > 0);
|
|
unsigned i = sz - 1;
|
|
expr r = mlocal_type(ts[i]);
|
|
while (i > 0) {
|
|
--i;
|
|
expr const & a = ts[i];
|
|
expr const & A = mlocal_type(a);
|
|
expr const & Ba = r;
|
|
level l1 = sort_level(tc.ensure_type(A, cs));
|
|
level l2 = sort_level(tc.ensure_type(Ba, cs));
|
|
r = mk_app(mk_constant(get_sigma_name(), {l1, l2}), A, Fun(a, Ba));
|
|
}
|
|
return r;
|
|
}
|
|
|
|
expr mk_sigma_mk(type_checker & tc, unsigned sz, expr const * ts, expr const * as, constraint_seq & cs) {
|
|
lean_assert(sz > 0);
|
|
if (sz == 1)
|
|
return as[0];
|
|
buffer<expr> new_ts;
|
|
for (unsigned i = 1; i < sz; i++)
|
|
new_ts.push_back(instantiate(abstract_local(ts[i], ts[0]), as[0]));
|
|
expr arg1 = mlocal_type(ts[0]);
|
|
expr arg2_core = telescope_to_sigma(tc, sz-1, ts+1, cs);
|
|
expr arg2 = Fun(ts[0], arg2_core);
|
|
expr arg3 = as[0];
|
|
expr arg4 = mk_sigma_mk(tc, sz-1, new_ts.data(), as+1, cs);
|
|
level l1 = sort_level(tc.ensure_type(arg1, cs));
|
|
level l2 = sort_level(tc.ensure_type(arg2_core, cs));
|
|
return mk_app(mk_constant(get_sigma_mk_name(), {l1, l2}), arg1, arg2, arg3, arg4);
|
|
}
|
|
|
|
expr mk_sigma_mk(type_checker & tc, buffer<expr> const & ts, buffer<expr> const & as, constraint_seq & cs) {
|
|
lean_assert(ts.size() == as.size());
|
|
return mk_sigma_mk(tc, ts.size(), ts.data(), as.data(), cs);
|
|
}
|
|
|
|
expr infer_implicit_params(expr const & type, unsigned nparams, implicit_infer_kind k) {
|
|
switch (k) {
|
|
case implicit_infer_kind::Implicit: {
|
|
bool strict = true;
|
|
return infer_implicit(type, nparams, strict);
|
|
}
|
|
case implicit_infer_kind::RelaxedImplicit: {
|
|
bool strict = false;
|
|
return infer_implicit(type, nparams, strict);
|
|
}
|
|
case implicit_infer_kind::None:
|
|
return type;
|
|
}
|
|
lean_unreachable(); // LCOV_EXCL_LINE
|
|
}
|
|
|
|
bool has_expr_metavar_relaxed(expr const & e) {
|
|
if (!has_expr_metavar(e))
|
|
return false;
|
|
bool found = false;
|
|
for_each(e, [&](expr const & e, unsigned) {
|
|
if (found || !has_expr_metavar(e))
|
|
return false;
|
|
if (is_metavar(e)) {
|
|
found = true;
|
|
return false;
|
|
}
|
|
if (is_local(e))
|
|
return false; // do not visit type
|
|
return true;
|
|
});
|
|
return found;
|
|
}
|
|
}
|