541 lines
22 KiB
C++
541 lines
22 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 <utility>
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#include <string>
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#include "util/rb_map.h"
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#include "util/sstream.h"
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#include "kernel/instantiate.h"
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#include "library/coercion.h"
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#include "library/module.h"
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#include "library/kernel_serializer.h"
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#include "library/kernel_bindings.h"
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#include "library/scoped_ext.h"
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namespace lean {
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enum class coercion_class_kind { User, Sort, Fun };
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/**
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\brief A coercion is a mapping between classes.
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We support three kinds of classes: User, Sort, Function.
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*/
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class coercion_class {
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coercion_class_kind m_kind;
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name m_name; // relevant only if m_kind == User
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coercion_class(coercion_class_kind k, name const & n = name()):m_kind(k), m_name(n) {}
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public:
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coercion_class():m_kind(coercion_class_kind::Sort) {}
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static coercion_class mk_user(name n) { return coercion_class(coercion_class_kind::User, n); }
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static coercion_class mk_sort() { return coercion_class(coercion_class_kind::Sort); }
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static coercion_class mk_fun() { return coercion_class(coercion_class_kind::Fun); }
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friend bool operator==(coercion_class const & c1, coercion_class const & c2) { return c1.m_kind == c2.m_kind && c1.m_name == c2.m_name; }
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friend bool operator!=(coercion_class const & c1, coercion_class const & c2) { return !(c1 == c2); }
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coercion_class_kind kind() const { return m_kind; }
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name get_name() const { return m_name; }
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};
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std::ostream & operator<<(std::ostream & out, coercion_class const & cls) {
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switch (cls.kind()) {
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case coercion_class_kind::User: out << cls.get_name(); break;
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case coercion_class_kind::Sort: out << "Sort-class"; break;
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case coercion_class_kind::Fun: out << "Function-class"; break;
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}
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return out;
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}
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struct coercion_class_cmp_fn {
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int operator()(coercion_class const & c1, coercion_class const & c2) const {
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if (c1.kind() != c2.kind())
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return c1.kind() < c2.kind() ? -1 : 1;
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else
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return quick_cmp(c1.get_name(), c2.get_name());
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}
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};
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struct coercion_info {
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expr m_fun;
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expr m_fun_type;
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level_param_names m_level_params;
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unsigned m_num_args;
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coercion_class m_to;
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coercion_info() {}
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coercion_info(expr const & f, expr const & f_type, level_param_names const & ls, unsigned num, coercion_class const & cls):
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m_fun(f), m_fun_type(f_type), m_level_params(ls), m_num_args(num), m_to(cls) {}
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};
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struct coercion_state {
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rb_map<name, list<coercion_info>, name_quick_cmp> m_coercion_info;
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// m_from and m_to contain "direct" coercions
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rb_map<name, list<coercion_class>, name_quick_cmp> m_from;
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rb_map<coercion_class, list<name>, coercion_class_cmp_fn> m_to;
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rb_tree<name, name_quick_cmp> m_coercions;
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coercion_info get_info(name const & from, coercion_class const & to) {
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auto it = m_coercion_info.find(from);
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lean_assert(it);
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for (coercion_info info : *it) {
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if (info.m_to == to)
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return info;
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}
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lean_unreachable(); // LCOV_EXCL_LINE
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}
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void update_from_to(name const & C, coercion_class const & D, io_state const & ios) {
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auto it1 = m_from.find(C);
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if (!it1)
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m_from.insert(C, list<coercion_class>(D));
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else if (std::find(it1->begin(), it1->end(), D) == it1->end())
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m_from.insert(C, list<coercion_class>(D, *it1));
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else
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ios.get_diagnostic_channel() << "replacing the coercion from '" << C << "' to '" << D << "'\n";
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auto it2 = m_to.find(D);
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if (!it2)
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m_to.insert(D, list<name>(C));
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else if (std::find(it2->begin(), it2->end(), C) == it2->end())
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m_to.insert(D, list<name>(C, *it2));
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}
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};
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static void check_pi(name const & f, expr const & t) {
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if (!is_pi(t))
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throw exception(sstream() << "invalid coercion, '" << f << "' is not function");
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}
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/** \brief Return true iff args contains Var(0), Var(1), ..., Var(args.size() - 1) */
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static bool check_var_args(buffer<expr> const & args) {
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for (unsigned i = 0; i < args.size(); i++) {
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if (!is_var(args[i]) || var_idx(args[i]) != i)
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return false;
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}
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return true;
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}
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/** \brief Return true iff param_id(levels[i]) == level_params[i] */
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static bool check_levels(levels ls, level_param_names ps) {
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while (!is_nil(ls) && !is_nil(ps)) {
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if (!is_param(head(ls)))
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return false;
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if (param_id(head(ls)) != head(ps))
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return false;
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ls = tail(ls);
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ps = tail(ps);
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}
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return is_nil(ls) && is_nil(ps);
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}
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optional<coercion_class> type_to_coercion_class(expr const & t) {
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if (is_sort(t)) {
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return optional<coercion_class>(coercion_class::mk_sort());
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} else if (is_pi(t)) {
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return optional<coercion_class>(coercion_class::mk_fun());
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} else {
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expr const & C = get_app_fn(t);
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if (is_constant(C))
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return optional<coercion_class>(coercion_class::mk_user(const_name(C)));
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else
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return optional<coercion_class>();
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}
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}
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typedef list<std::pair<name, coercion_class>> arrows;
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static bool contains(arrows const & a, name const & C, coercion_class const & D) {
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return std::find(a.begin(), a.end(), mk_pair(C, D)) != a.end();
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}
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static arrows insert(arrows const & a, name const & C, coercion_class const & D) {
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return arrows(mk_pair(C, D), a);
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}
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struct add_coercion_fn {
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coercion_state m_state;
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arrows m_visited;
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io_state const & m_ios;
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void add_coercion_trans(name const & C,
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level_param_names const & f_level_params, expr const & f, expr const & f_type, unsigned f_num_args,
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level_param_names const & g_level_params, expr g, expr const & g_type, unsigned g_num_args,
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coercion_class const & g_class) {
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expr t = f_type;
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buffer<expr> args;
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for (unsigned i = 0; i <= f_num_args; i++)
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args.push_back(mk_var(i));
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expr f_app = apply_beta(f, args.size(), args.data());
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buffer<name> f_arg_names;
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buffer<expr> f_arg_types;
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while (is_pi(t)) {
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f_arg_names.push_back(binding_name(t));
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f_arg_types.push_back(binding_domain(t));
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t = binding_body(t);
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}
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expr D_app = t;
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buffer<expr> gf_args;
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gf_args.push_back(f_app);
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expr D_cnst = get_app_rev_args(D_app, gf_args);
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if (gf_args.size() != g_num_args + 1)
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return;
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if (length(const_levels(D_cnst)) != length(g_level_params))
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return;
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// C >-> D >-> E
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g = instantiate_univ_params(g, g_level_params, const_levels(D_cnst));
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expr gf = apply_beta(g, gf_args.size(), gf_args.data());
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expr gf_type = g_type;
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while (is_pi(gf_type))
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gf_type = binding_body(gf_type);
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gf_type = instantiate(instantiate_univ_params(gf_type, g_level_params, const_levels(D_cnst)), gf_args.size(), gf_args.data());
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unsigned i = f_arg_types.size();
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while (i > 0) {
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--i;
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gf = mk_lambda(f_arg_names[i], f_arg_types[i], gf);
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gf_type = mk_pi(f_arg_names[i], f_arg_types[i], gf_type);
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}
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add_coercion(C, gf, gf_type, f_level_params, f_num_args, g_class);
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}
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void add_coercion_trans_to(name const & C, expr const & f, expr const & f_type,
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level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
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// apply transitivity using ext.m_to
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coercion_class C_cls = coercion_class::mk_user(C);
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auto it1 = m_state.m_to.find(C_cls);
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if (!it1)
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return;
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for (name const & B : *it1) {
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coercion_info info = m_state.get_info(B, C_cls);
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// B >-> C >-> D
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add_coercion_trans(B, info.m_level_params, info.m_fun, info.m_fun_type, info.m_num_args,
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ls, f, f_type, num_args, cls);
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}
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}
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void add_coercion_trans_from(name const & C, expr const & f, expr const & f_type,
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level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
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// apply transitivity using ext.m_from
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if (cls.kind() != coercion_class_kind::User)
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return; // nothing to do Sort and Fun classes are terminal
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name const & D = cls.get_name();
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auto it = m_state.m_from.find(D);
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if (!it)
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return;
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for (coercion_class E : *it) {
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coercion_info info = m_state.get_info(D, E);
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// C >-> D >-> E
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add_coercion_trans(C, ls, f, f_type, num_args,
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info.m_level_params, info.m_fun, info.m_fun_type, info.m_num_args, info.m_to);
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}
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}
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void add_coercion_core(name const & C, expr const & f, expr const & f_type,
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level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
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auto it = m_state.m_coercion_info.find(C);
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if (!it) {
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list<coercion_info> infos(coercion_info(f, f_type, ls, num_args, cls));
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m_state.m_coercion_info.insert(C, infos);
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} else {
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list<coercion_info> infos = *it;
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infos = filter(infos, [&](coercion_info const & info) { return info.m_to != cls; });
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infos = list<coercion_info>(coercion_info(f, f_type, ls, num_args, cls), infos);
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m_state.m_coercion_info.insert(C, infos);
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}
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if (is_constant(f))
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m_state.m_coercions.insert(const_name(f));
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}
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void add_coercion(name const & C, expr const & f, expr const & f_type,
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level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
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if (contains(m_visited, C, cls))
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return;
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if (cls.kind() == coercion_class_kind::User && cls.get_name() == C)
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return;
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m_visited = insert(m_visited, C, cls);
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add_coercion_core(C, f, f_type, ls, num_args, cls);
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add_coercion_trans_to(C, f, f_type, ls, num_args, cls);
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add_coercion_trans_from(C, f, f_type, ls, num_args, cls);
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}
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add_coercion_fn(coercion_state const & s, io_state const & ios):
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m_state(s), m_ios(ios) {}
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coercion_state operator()(name const & C, expr const & f, expr const & f_type,
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level_param_names const & ls, unsigned num_args, coercion_class const & cls) {
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add_coercion(C, f, f_type, ls, num_args, cls);
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m_state.update_from_to(C, cls, m_ios);
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return m_state;
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}
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};
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coercion_state add_coercion(environment const & env, io_state const & ios, coercion_state const & st, name const & f, name const & C) {
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declaration d = env.get(f);
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unsigned num = 0;
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buffer<expr> args;
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expr t = d.get_type();
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check_pi(f, t);
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while (true) {
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args.clear();
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expr const & C_fn = get_app_rev_args(binding_domain(t), args);
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if (is_constant(C_fn) &&
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const_name(C_fn) == C &&
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num == args.size() &&
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check_var_args(args) &&
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check_levels(const_levels(C_fn), d.get_univ_params())) {
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expr fn = mk_constant(f, const_levels(C_fn));
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optional<coercion_class> cls = type_to_coercion_class(binding_body(t));
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if (!cls)
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throw exception(sstream() << "invalid coercion, '" << f << "' cannot be used as a coercion from '" << C << "'");
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else if (cls->kind() == coercion_class_kind::User && cls->get_name() == C)
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throw exception(sstream() << "invalid coercion, '" << f << "' is a coercion from '" << C << "' to itself");
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return add_coercion_fn(st, ios)(C, fn, d.get_type(), d.get_univ_params(), num, *cls);
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}
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t = binding_body(t);
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num++;
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check_pi(f, t);
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}
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}
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typedef std::pair<name, name> coercion_entry;
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struct coercion_config {
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typedef coercion_state state;
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typedef coercion_entry entry;
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static void add_entry(environment const & env, io_state const & ios, state & s, entry const & e) {
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s = add_coercion(env, ios, s, e.first, e.second);
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}
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static name const & get_class_name() {
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static name g_class_name("coercion");
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return g_class_name;
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}
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static std::string const & get_serialization_key() {
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static std::string g_key("coerce");
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return g_key;
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}
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static void write_entry(serializer & s, entry const & e) {
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s << e.first << e.second;
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}
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static entry read_entry(deserializer & d) {
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entry e;
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d >> e.first >> e.second;
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return e;
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}
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};
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template class scoped_ext<coercion_config>;
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typedef scoped_ext<coercion_config> coercion_ext;
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environment add_coercion(environment const & env, name const & f, name const & C, io_state const & ios) {
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return coercion_ext::add_entry(env, ios, coercion_entry(f, C));
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}
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environment add_coercion(environment const & env, name const & f, io_state const & ios) {
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declaration d = env.get(f);
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expr t = d.get_type();
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check_pi(f, t);
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while (is_pi(binding_body(t)))
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t = binding_body(t);
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expr C = get_app_fn(binding_domain(t));
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if (!is_constant(C))
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throw exception(sstream() << "invalid coercion, '" << f << "' cannot be used as a coercion");
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return add_coercion(env, f, const_name(C), ios);
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}
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bool is_coercion(environment const & env, name const & f) {
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coercion_state const & ext = coercion_ext::get_state(env);
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return ext.m_coercions.contains(f);
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}
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bool is_coercion(environment const & env, expr const & f) {
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return is_constant(f) && is_coercion(env, const_name(f));
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}
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bool has_coercions_to(environment const & env, name const & D) {
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coercion_state const & ext = coercion_ext::get_state(env);
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auto it = ext.m_to.find(coercion_class::mk_user(D));
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return it && !is_nil(*it);
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}
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bool has_coercions_from(environment const & env, name const & C) {
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coercion_state const & ext = coercion_ext::get_state(env);
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return ext.m_coercion_info.contains(C);
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}
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bool has_coercions_from(environment const & env, expr const & C) {
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expr const & C_fn = get_app_fn(C);
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if (!is_constant(C_fn))
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return false;
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coercion_state const & ext = coercion_ext::get_state(env);
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auto it = ext.m_coercion_info.find(const_name(C_fn));
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if (!it)
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return false;
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list<coercion_info> const & cs = *it;
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return
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head(cs).m_num_args == get_app_num_args(C) &&
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length(head(cs).m_level_params) == length(const_levels(C_fn));
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}
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optional<expr> get_coercion(environment const & env, expr const & C, coercion_class const & D) {
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buffer<expr> args;
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expr const & C_fn = get_app_rev_args(C, args);
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if (!is_constant(C_fn))
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return none_expr();
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coercion_state const & ext = coercion_ext::get_state(env);
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auto it = ext.m_coercion_info.find(const_name(C_fn));
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if (!it)
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return none_expr();
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for (coercion_info const & info : *it) {
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if (info.m_to == D && info.m_num_args == args.size() && length(info.m_level_params) == length(const_levels(C_fn))) {
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expr f = instantiate_univ_params(info.m_fun, info.m_level_params, const_levels(C_fn));
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return some_expr(apply_beta(f, args.size(), args.data()));
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}
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}
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return none_expr();
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}
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optional<expr> get_coercion(environment const & env, expr const & C, name const & D) {
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return get_coercion(env, C, coercion_class::mk_user(D));
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}
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optional<expr> get_coercion_to_sort(environment const & env, expr const & C) {
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return get_coercion(env, C, coercion_class::mk_sort());
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}
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optional<expr> get_coercion_to_fun(environment const & env, expr const & C) {
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return get_coercion(env, C, coercion_class::mk_fun());
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}
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bool get_user_coercions(environment const & env, expr const & C, buffer<std::tuple<name, expr, expr>> & result) {
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buffer<expr> args;
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expr const & C_fn = get_app_rev_args(C, args);
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if (!is_constant(C_fn))
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return false;
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coercion_state const & ext = coercion_ext::get_state(env);
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auto it = ext.m_coercion_info.find(const_name(C_fn));
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if (!it)
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return false;
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bool r = false;
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|
for (coercion_info const & info : *it) {
|
|
if (info.m_to.kind() == coercion_class_kind::User &&
|
|
info.m_num_args == args.size() &&
|
|
length(info.m_level_params) == length(const_levels(C_fn))) {
|
|
expr f = instantiate_univ_params(info.m_fun, info.m_level_params, const_levels(C_fn));
|
|
expr c = apply_beta(f, args.size(), args.data());
|
|
expr t = instantiate_univ_params(info.m_fun_type, info.m_level_params, const_levels(C_fn));
|
|
for (unsigned i = 0; i < args.size(); i++) t = binding_body(t);
|
|
t = instantiate(t, args.size(), args.data());
|
|
result.emplace_back(info.m_to.get_name(), c, t);
|
|
r = true;
|
|
}
|
|
}
|
|
return r;
|
|
}
|
|
|
|
template<typename F>
|
|
void for_each_coercion(environment const & env, F && f) {
|
|
coercion_state const & ext = coercion_ext::get_state(env);
|
|
ext.m_coercion_info.for_each([&](name const & C, list<coercion_info> const & infos) {
|
|
for (auto const & info : infos) {
|
|
f(C, info);
|
|
}
|
|
});
|
|
}
|
|
|
|
void for_each_coercion_user(environment const & env,
|
|
std::function<void(name const &, name const &, expr const &, level_param_names const &, unsigned)> const & f) {
|
|
for_each_coercion(env, [&](name const & C, coercion_info const & info) {
|
|
if (info.m_to.kind() == coercion_class_kind::User) f(C, info.m_to.get_name(), info.m_fun, info.m_level_params, info.m_num_args);
|
|
});
|
|
}
|
|
|
|
void for_each_coercion_sort(environment const & env,
|
|
std::function<void(name const &, expr const &, level_param_names const &, unsigned)> const & f) {
|
|
for_each_coercion(env, [&](name const & C, coercion_info const & info) {
|
|
if (info.m_to.kind() == coercion_class_kind::Sort) f(C, info.m_fun, info.m_level_params, info.m_num_args);
|
|
});
|
|
}
|
|
|
|
void for_each_coercion_fun(environment const & env,
|
|
std::function<void(name const &, expr const &, level_param_names const &, unsigned)> const & f) {
|
|
for_each_coercion(env, [&](name const & C, coercion_info const & info) {
|
|
if (info.m_to.kind() == coercion_class_kind::Fun) f(C, info.m_fun, info.m_level_params, info.m_num_args);
|
|
});
|
|
}
|
|
|
|
static int add_coercion(lua_State * L) {
|
|
int nargs = lua_gettop(L);
|
|
if (nargs == 2)
|
|
return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), get_io_state(L)));
|
|
else if (nargs == 3 && is_io_state(L, 3))
|
|
return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), to_io_state(L, 3)));
|
|
else if (nargs == 3)
|
|
return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), to_name_ext(L, 3), get_io_state(L)));
|
|
else
|
|
return push_environment(L, add_coercion(to_environment(L, 1), to_name_ext(L, 2), to_name_ext(L, 3), to_io_state(L, 4)));
|
|
}
|
|
static int is_coercion(lua_State * L) {
|
|
if (is_expr(L, 2))
|
|
return push_boolean(L, is_coercion(to_environment(L, 1), to_expr(L, 2)));
|
|
else
|
|
return push_boolean(L, is_coercion(to_environment(L, 1), to_name_ext(L, 2)));
|
|
}
|
|
static int has_coercions_from(lua_State * L) {
|
|
if (is_expr(L, 2))
|
|
return push_boolean(L, has_coercions_from(to_environment(L, 1), to_expr(L, 2)));
|
|
else
|
|
return push_boolean(L, has_coercions_from(to_environment(L, 1), to_name_ext(L, 2)));
|
|
}
|
|
static int get_coercion(lua_State * L) { return push_optional_expr(L, get_coercion(to_environment(L, 1), to_expr(L, 2), to_name_ext(L, 3))); }
|
|
static int get_coercion_to_sort(lua_State * L) { return push_optional_expr(L, get_coercion_to_sort(to_environment(L, 1), to_expr(L, 2))); }
|
|
static int get_coercion_to_fun(lua_State * L) { return push_optional_expr(L, get_coercion_to_fun(to_environment(L, 1), to_expr(L, 2))); }
|
|
static int get_user_coercions(lua_State * L) {
|
|
buffer<std::tuple<name, expr, expr>> r;
|
|
get_user_coercions(to_environment(L, 1), to_expr(L, 2), r);
|
|
lua_newtable(L);
|
|
int i = 1;
|
|
for (auto p : r) {
|
|
lua_newtable(L);
|
|
push_name(L, std::get<0>(p));
|
|
lua_rawseti(L, -2, 1);
|
|
push_expr(L, std::get<1>(p));
|
|
lua_rawseti(L, -2, 2);
|
|
push_expr(L, std::get<2>(p));
|
|
lua_rawseti(L, -2, 3);
|
|
lua_rawseti(L, -2, i);
|
|
i = i + 1;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
static int for_each_coercion(lua_State * L, coercion_class_kind k) {
|
|
environment env = to_environment(L, 1);
|
|
luaL_checktype(L, 2, LUA_TFUNCTION); // user-fun
|
|
for_each_coercion(env, [&](name const & C, coercion_info const & info) {
|
|
if (info.m_to.kind() != k)
|
|
return;
|
|
lua_pushvalue(L, 2); // push user-fun
|
|
push_name(L, C);
|
|
int nargs = 4;
|
|
if (info.m_to.kind() == coercion_class_kind::User) {
|
|
push_name(L, info.m_to.get_name());
|
|
nargs++;
|
|
}
|
|
push_expr(L, info.m_fun);
|
|
push_list_name(L, info.m_level_params);
|
|
push_integer(L, info.m_num_args);
|
|
pcall(L, nargs, 0, 0);
|
|
});
|
|
return 0;
|
|
}
|
|
|
|
static int for_each_coercion_user(lua_State * L) { return for_each_coercion(L, coercion_class_kind::User); }
|
|
static int for_each_coercion_sort(lua_State * L) { return for_each_coercion(L, coercion_class_kind::Sort); }
|
|
static int for_each_coercion_fun(lua_State * L) { return for_each_coercion(L, coercion_class_kind::Fun); }
|
|
|
|
void open_coercion(lua_State * L) {
|
|
SET_GLOBAL_FUN(add_coercion, "add_coercion");
|
|
SET_GLOBAL_FUN(is_coercion, "is_coercion");
|
|
SET_GLOBAL_FUN(has_coercions_from, "has_coercions_from");
|
|
SET_GLOBAL_FUN(get_coercion, "get_coercion");
|
|
SET_GLOBAL_FUN(get_coercion_to_sort, "get_coercion_to_sort");
|
|
SET_GLOBAL_FUN(get_coercion_to_fun, "get_coercion_to_fun");
|
|
SET_GLOBAL_FUN(get_user_coercions, "get_user_coercions");
|
|
SET_GLOBAL_FUN(for_each_coercion_user, "for_each_coercion_user");
|
|
SET_GLOBAL_FUN(for_each_coercion_sort, "for_each_coercion_sort");
|
|
SET_GLOBAL_FUN(for_each_coercion_fun, "for_each_coercion_fun");
|
|
}
|
|
}
|