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feat(kernel/inductive): finish inductive datatype declaration validation

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-05-17 19:19:32 -07:00
parent 5c7d3c79c4
commit 8fcb84c8f2
2 changed files with 280 additions and 64 deletions
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335
src/kernel/inductive/inductive.cpp
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@ -5,10 +5,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "util/name_generator.h"
#include "util/sstream.h"
#include "util/list_fn.h"
#include "kernel/type_checker.h"
#include "kernel/kernel_exception.h"
#include "kernel/instantiate.h"
#include "kernel/inductive/inductive.h"
#include "kernel/find_fn.h"
namespace lean {
namespace inductive {
@ -19,74 +22,278 @@ environment add_inductive(environment const & env, name const & ind_name, level_
return add_inductive(env, level_params, num_params, list<inductive_decl>(inductive_decl(ind_name, type, intro_rules)));
}
struct add_inductive_fn {
environment m_env;
level_param_names m_level_names;
unsigned m_num_params;
list<inductive_decl> m_decls;
unsigned m_decls_sz;
list<level> m_levels; // m_level_names ==> m_levels
name_generator m_ngen;
type_checker m_tc;
buffer<expr> m_param_types;
buffer<expr> m_param_consts;
buffer<level> m_it_levels; // the levels for each inductive datatype in m_decls
buffer<expr> m_it_consts; // the constants for each inductive datatype in m_decls
buffer<unsigned> m_it_num_args; // total number of arguments (params + indices) for each inductive datatype in m_decls
add_inductive_fn(environment env,
level_param_names const & level_params,
unsigned num_params,
list<inductive_decl> const & decls):
m_env(env), m_level_names(level_params), m_num_params(num_params), m_decls(decls),
m_ngen(g_tmp_prefix), m_tc(m_env) {
m_decls_sz = length(m_decls);
m_levels = map2<level>(level_params, [](name const & n) { return mk_param_univ(n); });
}
/** \brief Return the number of inductive datatypes being defined. */
unsigned get_num_its() const { return m_decls_sz; }
/** \brief Make sure the latest environment is being used by m_tc */
void updt_type_checker() {
type_checker tc(m_env);
m_tc.swap(tc);
}
/** \brief Display types being declared */
void display(std::ostream & out) {
out << "\nadd_inductive\n";
if (!is_nil(m_level_names)) {
out << "level params: ";
for (auto l : m_level_names) { out << l << " "; }
out << "\n";
}
out << "num params: " << m_num_params << "\n";
for (auto d : m_decls) {
out << inductive_decl_name(d) << " : " << inductive_decl_type(d) << "\n";
for (auto ir : inductive_decl_intros(d)) {
out << " " << intro_rule_name(ir) << " : " << intro_rule_type(ir) << "\n";
}
}
}
name mk_fresh_name() { return m_ngen.next(); }
/** \brief Create a local constant for the given binding. */
expr mk_local_for(expr const & b) {
return mk_local(mk_fresh_name(), binding_name(b), binding_domain(b));
}
/**
\brief Check if the type of datatypes is well typed, all inductive datatypes have the same parameters,
and the number of parameters match the argument num_params.
This method also populates the fields m_param_types and m_param_consts, m_it_levels, m_it_consts.
*/
void check_inductive_types() {
bool first = true;
bool to_prop = false; // set to true if the inductive datatypes live in Bool/Prop (Type 0)
for (auto d : m_decls) {
expr t = inductive_decl_type(d);
m_tc.check(t, m_level_names);
unsigned i = 0;
m_it_num_args.push_back(0);
while (is_pi(t)) {
if (i < m_num_params) {
if (first) {
m_param_types.push_back(binding_domain(t));
expr l = mk_local_for(t);
m_param_consts.push_back(l);
t = instantiate(binding_body(t), l);
} else {
if (!m_tc.is_def_eq(binding_domain(t), m_param_types[i]))
throw kernel_exception(m_env, "parameters of all inductive datatypes must match");
t = instantiate(binding_body(t), m_param_consts[i]);
}
i++;
} else {
t = binding_body(t);
}
m_it_num_args.back()++;
}
if (i != m_num_params)
throw kernel_exception(m_env, "number of parameters mismatch in inductive datatype declaration");
t = m_tc.ensure_sort(t);
if (m_env.impredicative()) {
// if the environment is impredicative, then the resultant universe is 0 (Bool/Prop),
// or is never zero (under any parameter assignment).
if (!is_zero(sort_level(t)) && !is_not_zero(sort_level(t)))
throw kernel_exception(m_env,
"the resultant universe must be 0 or different"
"from zero for all parameter/global level assignments");
if (first) {
to_prop = is_zero(sort_level(t));
} else {
if (is_zero(sort_level(t)) != to_prop)
throw kernel_exception(m_env,
"for impredicative environments, if one datatype is in Bool/Prop, "
"then all of them must be in Bool/Prop");
}
}
m_it_levels.push_back(sort_level(t));
m_it_consts.push_back(mk_constant(inductive_decl_name(d), m_levels));
first = false;
}
}
/** \brief Add all datatype declarations to environment. */
void declare_inductive_types() {
for (auto d : m_decls) {
m_env = m_env.add(check(m_env, mk_var_decl(inductive_decl_name(d), m_level_names, inductive_decl_type(d))));
}
updt_type_checker();
}
/**
\brief Return true iff \c t is a term of ther form
(I As t)
where I is the d_idx inductive datatype being declared and
As are the global parameters of this declaration.
*/
bool is_valid_it_app(expr const & t, unsigned d_idx) {
buffer<expr> args;
expr I = get_app_args(t, args);
if (!m_tc.is_def_eq(I, m_it_consts[d_idx]) || args.size() != m_it_num_args[d_idx])
return false;
for (unsigned i = 0; i < m_num_params; i++) {
if (m_param_consts[i] != args[i])
return false;
}
return true;
}
/** \brief Return true iff \c t is a valid occurrence of one of the datatypes being defined. */
bool is_valid_it_app(expr const & t) {
for (unsigned i = 0; i < get_num_its(); i++)
if (is_valid_it_app(t, i))
return true;
return false;
}
/** \brief Return true iff \c e is one of the inductive datatype being declared. */
bool is_it_occ(expr const & e) {
return
is_constant(e) &&
std::any_of(m_it_consts.begin(), m_it_consts.end(), [&](expr const & c) { return const_name(e) == const_name(c); });
}
/** \brief Return true if \c t does not contain any occurrence of a datatype being declared */
bool has_it_occ(expr const & t) {
return (bool)find(t, [&](expr const & e, unsigned) { return is_it_occ(e); }); // NOLINT
}
/**
\brief Check if \c t contains only positive occurrences of the inductive datatypes being declared.
Return true iff it is a recursive argument.
*/
bool check_positivity(expr t, name const & intro_name, int arg_idx) {
t = m_tc.whnf(t);
if (!has_it_occ(t)) {
return false; // nonrecursive argument
} else if (is_pi(t)) {
if (has_it_occ(binding_domain(t)))
throw kernel_exception(m_env, sstream() << "arg #" << arg_idx << " of '" << intro_name << "' "
"has a non positive occurrence of the datatypes being declared");
return check_positivity(instantiate(binding_body(t), mk_local_for(t)), intro_name, arg_idx);
} else if (is_valid_it_app(t)) {
return true; // recursive argument
} else {
throw kernel_exception(m_env, sstream() << "arg #" << arg_idx << " of '" << intro_name << "' "
"contain a non valid occurrence of the datatypes being declared");
}
}
/**
\brief Check the intro_rule \c ir of the given inductive decl. \c d_idx is the position of \c d in m_decls.
\see check_intro_rules
*/
void check_intro_rule(inductive_decl const &, unsigned d_idx, intro_rule const & ir) {
expr t = intro_rule_type(ir);
name n = intro_rule_name(ir);
m_tc.check(t, m_level_names);
unsigned i = 0;
bool found_rec = false;
while (is_pi(t)) {
if (i < m_num_params) {
if (!m_tc.is_def_eq(binding_domain(t), m_param_types[i]))
throw kernel_exception(m_env, sstream() << "arg #" << i << " of '" << n << "' "
<< "does not match inductive datatypes parameters'");
t = instantiate(binding_body(t), m_param_consts[i]);
} else {
expr s = m_tc.ensure_sort(m_tc.infer(binding_domain(t)));
// the sort is ok IF
// 1- its level is <= inductive datatype level, OR
// 2- m_env is impredicative and inductive datatype is at level 0
if (!(is_geq(m_it_levels[d_idx], sort_level(s)) || (is_zero(m_it_levels[d_idx]) && m_env.impredicative())))
throw kernel_exception(m_env, sstream() << "universe level of type_of(arg #" << i << ") "
<< "of '" << n << "' is too big for the corresponding inductive datatype");
bool is_rec = check_positivity(binding_domain(t), n, i);
if (found_rec && !is_rec)
throw kernel_exception(m_env, sstream() << "arg #" << i << " of '" << n << "' "
<< "is not recursive, but it occurs after recursive arguments");
if (is_rec)
found_rec = true;
if (!found_rec) {
t = instantiate(binding_body(t), mk_local_for(t));
} else {
t = binding_body(t);
if (!closed(t))
throw kernel_exception(m_env, sstream() << "invalid occurrence of recursive arg#" << i <<
" of '" << n << "' the body of the functional type depends on it.");
}
}
i++;
}
if (!is_valid_it_app(t, d_idx))
throw kernel_exception(m_env, sstream() << "invalid return type for '" << n << "'");
}
/**
\brief Check if
- all introduction rules start with the same parameters
- the type of all arguments (which are not datatype global params) live in universes <= level of the corresponding datatype
- all inductive datatype occurrences are positive
- all introduction rules are well typed
\remark this method must be executed after declare_inductive_types
*/
void check_intro_rules() {
unsigned i = 0;
for (auto d : m_decls) {
for (auto ir : inductive_decl_intros(d))
check_intro_rule(d, i, ir);
i++;
}
}
/** \brief Add all introduction rules (aka constructors) to environment */
void declare_intro_rules() {
for (auto d : m_decls) {
for (auto ir : inductive_decl_intros(d))
m_env = m_env.add(check(m_env, mk_var_decl(intro_rule_name(ir), m_level_names, intro_rule_type(ir))));
}
}
environment operator()() {
display(std::cout);
if (get_num_its() == 0)
throw kernel_exception(m_env, "at least one inductive datatype declaration expected");
check_inductive_types();
declare_inductive_types();
check_intro_rules();
declare_intro_rules();
return m_env;
}
};
environment add_inductive(environment env,
level_param_names const & level_params,
unsigned num_params,
list<inductive_decl> const & decls) {
// TODO(Leo)
std::cout << "\nadd_inductive\n";
if (!is_nil(level_params)) {
std::cout << "level params: ";
for (auto l : level_params) { std::cout << l << " "; }
std::cout << "\n";
}
std::cout << "num params: " << num_params << "\n";
for (auto d : decls) {
std::cout << inductive_decl_name(d) << " : " << inductive_decl_type(d) << "\n";
for (auto ir : inductive_decl_intros(d)) {
std::cout << " " << intro_rule_name(ir) << " : " << intro_rule_type(ir) << "\n";
}
}
if (is_nil(decls))
throw kernel_exception(env, "at least one inductive datatype declaration expected");
type_checker tc(env);
bool first = true;
buffer<expr> param_types;
buffer<expr> local_consts;
buffer<level> Ilevels; // level of each inductive datatype
name_generator ngen(g_tmp_prefix);
// Check if the type of datatypes is well typed
for (auto d : decls) {
expr t = tc.whnf(inductive_decl_type(d));
tc.check(t, level_params);
unsigned i = 0;
while (is_pi(t)) {
if (i < num_params) {
if (first) {
param_types.push_back(binding_domain(t));
expr l = mk_local(ngen.next(), binding_name(t), binding_domain(t));
local_consts.push_back(l);
t = instantiate(binding_body(t), l);
} else {
if (!tc.is_def_eq(binding_domain(t), param_types[i]))
throw kernel_exception(env, "parameters of all inductive datatypes must match");
t = instantiate(binding_body(t), local_consts[i]);
}
i++;
} else {
t = binding_body(t);
}
t = tc.whnf(t);
}
first = false;
if (i != num_params)
throw kernel_exception(env, "number of parameters mismatch in inductive datatype declaration");
t = tc.ensure_sort(t);
Ilevels.push_back(sort_level(t));
}
// Add all datatype declarations to environment
for (auto d : decls) {
env = env.add(check(env, mk_var_decl(inductive_decl_name(d), level_params, inductive_decl_type(d))));
}
// Add all introduction rules (aka constructors) to environment
for (auto d : decls) {
for (auto ir : inductive_decl_intros(d))
env = env.add(check(env, mk_var_decl(intro_rule_name(ir), level_params, intro_rule_type(ir))));
}
return env;
return add_inductive_fn(env, level_params, num_params, decls)();
}
}
}

9
tests/lua/ind1.lua
View file

@ -53,3 +53,12 @@ local tc = type_checker(env)
print(tc:check(Const("forest", {mk_level_zero()})))
print(tc:check(Const("vcons", {mk_level_zero()})))
print(tc:check(Const("consf", {mk_level_zero()})))
local Even = Const("Even")
local Odd = Const("Odd")
local b = Const("b")
env = add_inductive(env, {},
{"Even", mk_arrow(Nat, Bool),
"zero_is_even", Even(zero),
"succ_odd", Pi(b, Nat, mk_arrow(Odd(b), Even(succ(b))))},
{"Odd", mk_arrow(Nat, Bool),
"succ_even", Pi(b, Nat, mk_arrow(Even(b), Odd(succ(b))))})