feat(kernel/inductive): finish inductive datatype declaration validation
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura
parent
5c7d3c79c4
commit
8fcb84c8f2
2 changed files with 280 additions and 64 deletions
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@ -5,10 +5,13 @@ 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 "util/name_generator.h"
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#include "util/sstream.h"
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#include "util/list_fn.h"
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#include "kernel/type_checker.h"
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#include "kernel/kernel_exception.h"
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#include "kernel/instantiate.h"
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#include "kernel/inductive/inductive.h"
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#include "kernel/find_fn.h"
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namespace lean {
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namespace inductive {
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@ -19,74 +22,278 @@ environment add_inductive(environment const & env, name const & ind_name, level_
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return add_inductive(env, level_params, num_params, list<inductive_decl>(inductive_decl(ind_name, type, intro_rules)));
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}
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environment add_inductive(environment env,
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struct add_inductive_fn {
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environment m_env;
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level_param_names m_level_names;
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unsigned m_num_params;
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list<inductive_decl> m_decls;
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unsigned m_decls_sz;
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list<level> m_levels; // m_level_names ==> m_levels
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name_generator m_ngen;
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type_checker m_tc;
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buffer<expr> m_param_types;
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buffer<expr> m_param_consts;
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buffer<level> m_it_levels; // the levels for each inductive datatype in m_decls
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buffer<expr> m_it_consts; // the constants for each inductive datatype in m_decls
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buffer<unsigned> m_it_num_args; // total number of arguments (params + indices) for each inductive datatype in m_decls
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add_inductive_fn(environment env,
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level_param_names const & level_params,
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unsigned num_params,
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list<inductive_decl> const & decls) {
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// TODO(Leo)
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std::cout << "\nadd_inductive\n";
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if (!is_nil(level_params)) {
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std::cout << "level params: ";
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for (auto l : level_params) { std::cout << l << " "; }
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std::cout << "\n";
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list<inductive_decl> const & decls):
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m_env(env), m_level_names(level_params), m_num_params(num_params), m_decls(decls),
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m_ngen(g_tmp_prefix), m_tc(m_env) {
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m_decls_sz = length(m_decls);
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m_levels = map2<level>(level_params, [](name const & n) { return mk_param_univ(n); });
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}
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std::cout << "num params: " << num_params << "\n";
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for (auto d : decls) {
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std::cout << inductive_decl_name(d) << " : " << inductive_decl_type(d) << "\n";
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/** \brief Return the number of inductive datatypes being defined. */
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unsigned get_num_its() const { return m_decls_sz; }
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/** \brief Make sure the latest environment is being used by m_tc */
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void updt_type_checker() {
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type_checker tc(m_env);
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m_tc.swap(tc);
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}
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/** \brief Display types being declared */
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void display(std::ostream & out) {
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out << "\nadd_inductive\n";
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if (!is_nil(m_level_names)) {
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out << "level params: ";
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for (auto l : m_level_names) { out << l << " "; }
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out << "\n";
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}
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out << "num params: " << m_num_params << "\n";
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for (auto d : m_decls) {
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out << inductive_decl_name(d) << " : " << inductive_decl_type(d) << "\n";
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for (auto ir : inductive_decl_intros(d)) {
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std::cout << " " << intro_rule_name(ir) << " : " << intro_rule_type(ir) << "\n";
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out << " " << intro_rule_name(ir) << " : " << intro_rule_type(ir) << "\n";
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}
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}
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}
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if (is_nil(decls))
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throw kernel_exception(env, "at least one inductive datatype declaration expected");
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type_checker tc(env);
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name mk_fresh_name() { return m_ngen.next(); }
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/** \brief Create a local constant for the given binding. */
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expr mk_local_for(expr const & b) {
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return mk_local(mk_fresh_name(), binding_name(b), binding_domain(b));
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}
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/**
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\brief Check if the type of datatypes is well typed, all inductive datatypes have the same parameters,
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and the number of parameters match the argument num_params.
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This method also populates the fields m_param_types and m_param_consts, m_it_levels, m_it_consts.
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*/
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void check_inductive_types() {
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bool first = true;
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buffer<expr> param_types;
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buffer<expr> local_consts;
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buffer<level> Ilevels; // level of each inductive datatype
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name_generator ngen(g_tmp_prefix);
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// Check if the type of datatypes is well typed
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for (auto d : decls) {
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expr t = tc.whnf(inductive_decl_type(d));
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tc.check(t, level_params);
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bool to_prop = false; // set to true if the inductive datatypes live in Bool/Prop (Type 0)
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for (auto d : m_decls) {
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expr t = inductive_decl_type(d);
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m_tc.check(t, m_level_names);
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unsigned i = 0;
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m_it_num_args.push_back(0);
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while (is_pi(t)) {
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if (i < num_params) {
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if (i < m_num_params) {
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if (first) {
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param_types.push_back(binding_domain(t));
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expr l = mk_local(ngen.next(), binding_name(t), binding_domain(t));
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local_consts.push_back(l);
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m_param_types.push_back(binding_domain(t));
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expr l = mk_local_for(t);
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m_param_consts.push_back(l);
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t = instantiate(binding_body(t), l);
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} else {
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if (!tc.is_def_eq(binding_domain(t), param_types[i]))
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throw kernel_exception(env, "parameters of all inductive datatypes must match");
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t = instantiate(binding_body(t), local_consts[i]);
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if (!m_tc.is_def_eq(binding_domain(t), m_param_types[i]))
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throw kernel_exception(m_env, "parameters of all inductive datatypes must match");
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t = instantiate(binding_body(t), m_param_consts[i]);
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}
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i++;
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} else {
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t = binding_body(t);
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}
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t = tc.whnf(t);
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m_it_num_args.back()++;
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}
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if (i != m_num_params)
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throw kernel_exception(m_env, "number of parameters mismatch in inductive datatype declaration");
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t = m_tc.ensure_sort(t);
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if (m_env.impredicative()) {
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// if the environment is impredicative, then the resultant universe is 0 (Bool/Prop),
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// or is never zero (under any parameter assignment).
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if (!is_zero(sort_level(t)) && !is_not_zero(sort_level(t)))
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throw kernel_exception(m_env,
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"the resultant universe must be 0 or different"
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"from zero for all parameter/global level assignments");
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if (first) {
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to_prop = is_zero(sort_level(t));
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} else {
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if (is_zero(sort_level(t)) != to_prop)
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throw kernel_exception(m_env,
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"for impredicative environments, if one datatype is in Bool/Prop, "
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"then all of them must be in Bool/Prop");
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}
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}
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m_it_levels.push_back(sort_level(t));
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m_it_consts.push_back(mk_constant(inductive_decl_name(d), m_levels));
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first = false;
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if (i != num_params)
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throw kernel_exception(env, "number of parameters mismatch in inductive datatype declaration");
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t = tc.ensure_sort(t);
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Ilevels.push_back(sort_level(t));
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}
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}
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// Add all datatype declarations to environment
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for (auto d : decls) {
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env = env.add(check(env, mk_var_decl(inductive_decl_name(d), level_params, inductive_decl_type(d))));
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/** \brief Add all datatype declarations to environment. */
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void declare_inductive_types() {
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for (auto d : m_decls) {
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m_env = m_env.add(check(m_env, mk_var_decl(inductive_decl_name(d), m_level_names, inductive_decl_type(d))));
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}
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// Add all introduction rules (aka constructors) to environment
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for (auto d : decls) {
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updt_type_checker();
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}
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/**
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\brief Return true iff \c t is a term of ther form
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(I As t)
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where I is the d_idx inductive datatype being declared and
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As are the global parameters of this declaration.
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*/
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bool is_valid_it_app(expr const & t, unsigned d_idx) {
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buffer<expr> args;
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expr I = get_app_args(t, args);
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if (!m_tc.is_def_eq(I, m_it_consts[d_idx]) || args.size() != m_it_num_args[d_idx])
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return false;
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for (unsigned i = 0; i < m_num_params; i++) {
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if (m_param_consts[i] != args[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 \c t is a valid occurrence of one of the datatypes being defined. */
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bool is_valid_it_app(expr const & t) {
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for (unsigned i = 0; i < get_num_its(); i++)
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if (is_valid_it_app(t, i))
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return true;
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return false;
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}
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/** \brief Return true iff \c e is one of the inductive datatype being declared. */
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bool is_it_occ(expr const & e) {
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return
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is_constant(e) &&
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std::any_of(m_it_consts.begin(), m_it_consts.end(), [&](expr const & c) { return const_name(e) == const_name(c); });
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}
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/** \brief Return true if \c t does not contain any occurrence of a datatype being declared */
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bool has_it_occ(expr const & t) {
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return (bool)find(t, [&](expr const & e, unsigned) { return is_it_occ(e); }); // NOLINT
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}
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/**
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\brief Check if \c t contains only positive occurrences of the inductive datatypes being declared.
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Return true iff it is a recursive argument.
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*/
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bool check_positivity(expr t, name const & intro_name, int arg_idx) {
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t = m_tc.whnf(t);
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if (!has_it_occ(t)) {
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return false; // nonrecursive argument
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} else if (is_pi(t)) {
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if (has_it_occ(binding_domain(t)))
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throw kernel_exception(m_env, sstream() << "arg #" << arg_idx << " of '" << intro_name << "' "
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"has a non positive occurrence of the datatypes being declared");
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return check_positivity(instantiate(binding_body(t), mk_local_for(t)), intro_name, arg_idx);
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} else if (is_valid_it_app(t)) {
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return true; // recursive argument
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} else {
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throw kernel_exception(m_env, sstream() << "arg #" << arg_idx << " of '" << intro_name << "' "
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"contain a non valid occurrence of the datatypes being declared");
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}
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}
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/**
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\brief Check the intro_rule \c ir of the given inductive decl. \c d_idx is the position of \c d in m_decls.
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\see check_intro_rules
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*/
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void check_intro_rule(inductive_decl const &, unsigned d_idx, intro_rule const & ir) {
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expr t = intro_rule_type(ir);
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name n = intro_rule_name(ir);
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m_tc.check(t, m_level_names);
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unsigned i = 0;
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bool found_rec = false;
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while (is_pi(t)) {
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if (i < m_num_params) {
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if (!m_tc.is_def_eq(binding_domain(t), m_param_types[i]))
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throw kernel_exception(m_env, sstream() << "arg #" << i << " of '" << n << "' "
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<< "does not match inductive datatypes parameters'");
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t = instantiate(binding_body(t), m_param_consts[i]);
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} else {
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expr s = m_tc.ensure_sort(m_tc.infer(binding_domain(t)));
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// the sort is ok IF
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// 1- its level is <= inductive datatype level, OR
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// 2- m_env is impredicative and inductive datatype is at level 0
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if (!(is_geq(m_it_levels[d_idx], sort_level(s)) || (is_zero(m_it_levels[d_idx]) && m_env.impredicative())))
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throw kernel_exception(m_env, sstream() << "universe level of type_of(arg #" << i << ") "
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<< "of '" << n << "' is too big for the corresponding inductive datatype");
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bool is_rec = check_positivity(binding_domain(t), n, i);
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if (found_rec && !is_rec)
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throw kernel_exception(m_env, sstream() << "arg #" << i << " of '" << n << "' "
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<< "is not recursive, but it occurs after recursive arguments");
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if (is_rec)
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found_rec = true;
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if (!found_rec) {
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t = instantiate(binding_body(t), mk_local_for(t));
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} else {
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t = binding_body(t);
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if (!closed(t))
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throw kernel_exception(m_env, sstream() << "invalid occurrence of recursive arg#" << i <<
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" of '" << n << "' the body of the functional type depends on it.");
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}
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}
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i++;
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}
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if (!is_valid_it_app(t, d_idx))
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throw kernel_exception(m_env, sstream() << "invalid return type for '" << n << "'");
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}
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/**
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\brief Check if
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- all introduction rules start with the same parameters
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- the type of all arguments (which are not datatype global params) live in universes <= level of the corresponding datatype
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- all inductive datatype occurrences are positive
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- all introduction rules are well typed
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\remark this method must be executed after declare_inductive_types
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*/
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void check_intro_rules() {
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unsigned i = 0;
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for (auto d : m_decls) {
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for (auto ir : inductive_decl_intros(d))
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env = env.add(check(env, mk_var_decl(intro_rule_name(ir), level_params, intro_rule_type(ir))));
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check_intro_rule(d, i, ir);
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i++;
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}
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return env;
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}
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/** \brief Add all introduction rules (aka constructors) to environment */
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void declare_intro_rules() {
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for (auto d : m_decls) {
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for (auto ir : inductive_decl_intros(d))
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m_env = m_env.add(check(m_env, mk_var_decl(intro_rule_name(ir), m_level_names, intro_rule_type(ir))));
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}
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}
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environment operator()() {
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display(std::cout);
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if (get_num_its() == 0)
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throw kernel_exception(m_env, "at least one inductive datatype declaration expected");
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check_inductive_types();
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declare_inductive_types();
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check_intro_rules();
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declare_intro_rules();
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return m_env;
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}
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};
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environment add_inductive(environment env,
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level_param_names const & level_params,
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unsigned num_params,
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list<inductive_decl> const & decls) {
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return add_inductive_fn(env, level_params, num_params, decls)();
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}
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}
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}
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@ -53,3 +53,12 @@ local tc = type_checker(env)
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print(tc:check(Const("forest", {mk_level_zero()})))
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print(tc:check(Const("vcons", {mk_level_zero()})))
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print(tc:check(Const("consf", {mk_level_zero()})))
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local Even = Const("Even")
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local Odd = Const("Odd")
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local b = Const("b")
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env = add_inductive(env, {},
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{"Even", mk_arrow(Nat, Bool),
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"zero_is_even", Even(zero),
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"succ_odd", Pi(b, Nat, mk_arrow(Odd(b), Even(succ(b))))},
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{"Odd", mk_arrow(Nat, Bool),
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"succ_even", Pi(b, Nat, mk_arrow(Even(b), Odd(succ(b))))})
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