lean2/src/library/definitional/cases_on.cpp

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7.5 KiB
C++

/*
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "util/sstream.h"
#include "kernel/environment.h"
#include "kernel/instantiate.h"
#include "kernel/abstract.h"
#include "kernel/inductive/inductive.h"
#include "kernel/type_checker.h"
#include "library/module.h"
#include "library/protected.h"
namespace lean {
static void throw_corrupted(name const & n) {
throw exception(sstream() << "error in 'cases_on' generation, '" << n << "' inductive datatype declaration is corrupted");
}
/** \brief Given a C := As -> Type, return (fun (xs : As), unit) */
static expr mk_fun_unit(expr const & C, expr const & unit) {
if (is_pi(C)) {
return mk_lambda(binding_name(C), binding_domain(C), mk_fun_unit(binding_body(C), unit));
} else {
return unit;
}
}
static bool is_type_former_arg(buffer<name> const & C_names, expr const & arg) {
expr const & fn = get_app_fn(arg);
return is_local(fn) && std::find(C_names.begin(), C_names.end(), mlocal_name(fn)) != C_names.end();
}
/** \brief Given minor premise (Pi (a_1 : A_1) ... (a_n : A_n), B)
return fun (a_1 : A_1') ... (a_n : A_n'), star),
and A_i' is A_i if A_i is not the main type former C_main.
*/
static expr mk_fun_star(expr const & minor, buffer<name> const & C_names, name const & C_main,
expr const & unit, expr const & star) {
if (is_pi(minor)) {
expr const & domain = binding_domain(minor);
expr const & body = binding_body(minor);
if (is_type_former_arg(C_names, domain) && mlocal_name(get_app_fn(domain)) != C_main)
return mk_lambda(binding_name(minor), unit, mk_fun_star(body, C_names, C_main, unit, star));
else
return mk_lambda(binding_name(minor), binding_domain(minor), mk_fun_star(body, C_names, C_main, unit, star));
} else {
return star;
}
}
environment mk_cases_on(environment const & env, name const & n) {
optional<inductive::inductive_decls> decls = inductive::is_inductive_decl(env, n);
if (!decls)
throw exception(sstream() << "error in 'cases_on' generation, '" << n << "' is not an inductive datatype");
name cases_on_name(n, "cases_on");
name_generator ngen;
name rec_name = inductive::get_elim_name(n);
declaration rec_decl = env.get(rec_name);
declaration ind_decl = env.get(n);
unsigned num_idx_major = *inductive::get_num_indices(env, n) + 1;
unsigned num_minors = *inductive::get_num_minor_premises(env, n);
auto idecls = std::get<2>(*decls);
unsigned num_types = length(idecls);
unsigned num_params = std::get<1>(*decls);
buffer<expr> rec_params;
expr rec_type = rec_decl.get_type();
while (is_pi(rec_type)) {
expr local = mk_local(ngen.next(), binding_name(rec_type), binding_domain(rec_type), binding_info(rec_type));
rec_type = instantiate(binding_body(rec_type), local);
rec_params.push_back(local);
}
levels lvls = param_names_to_levels(rec_decl.get_univ_params());
bool elim_to_prop = length(rec_decl.get_univ_params()) == length(ind_decl.get_univ_params());
level elim_univ = elim_to_prop ? mk_level_zero() : head(lvls);
optional<expr> unit;
optional<expr> star;
// we use unit if num_types > 1
if (num_types > 1) {
unit = mk_constant(name("unit"), to_list(elim_univ));
star = mk_constant(name({"unit", "star"}), to_list(elim_univ));
}
// rec_params order
// As Cs minor_premises indices major-premise
// cases_on has
// As C[i] indices major-premise minor_premises[i]
// That is, it only contains its type former and minor_premises
buffer<expr> cases_on_params;
expr rec_cnst = mk_constant(rec_name, lvls);
buffer<expr> rec_args; // arguments for rec used to define cases_on
// Add params: As
for (unsigned i = 0; i < num_params; i++) {
cases_on_params.push_back(rec_params[i]);
rec_args.push_back(rec_params[i]);
}
// Add C[i]
buffer<name> C_names;
bool found = false;
unsigned i = num_params;
name C_main; // name of the main type former
for (auto const & d : idecls) {
C_names.push_back(mlocal_name(rec_params[i]));
if (inductive::inductive_decl_name(d) == n) {
cases_on_params.push_back(rec_params[i]);
rec_args.push_back(rec_params[i]);
C_main = mlocal_name(rec_params[i]);
found = true;
} else {
rec_args.push_back(mk_fun_unit(mlocal_type(rec_params[i]), *unit));
}
i++;
}
if (!found)
throw_corrupted(n);
// Add indices and major-premise to rec_params
for (unsigned i = 0; i < num_idx_major; i++)
cases_on_params.push_back(rec_params[num_params + num_types + num_minors + i]);
// Add minor premises to rec_params and rec_args
i = num_params + num_types;
for (auto const & d : idecls) {
bool is_main = inductive::inductive_decl_name(d) == n;
for (auto ir : inductive::inductive_decl_intros(d)) {
expr const & minor = rec_params[i];
if (is_main) {
// A cases_on minor premise does not contain "recursive" arguments
buffer<expr> minor_non_rec_params;
buffer<expr> minor_params;
expr minor_type = mlocal_type(minor);
while (is_pi(minor_type)) {
expr local = mk_local(ngen.next(), binding_name(minor_type), binding_domain(minor_type),
binding_info(minor_type));
expr curr_type = mlocal_type(local);
while (is_pi(curr_type))
curr_type = binding_body(curr_type);
if (is_type_former_arg(C_names, curr_type)) {
if (mlocal_name(get_app_fn(curr_type)) == C_main) {
minor_params.push_back(local);
} else {
minor_params.push_back(update_mlocal(local, *unit));
}
} else {
minor_params.push_back(local);
minor_non_rec_params.push_back(local);
}
minor_type = instantiate(binding_body(minor_type), local);
}
expr new_C = update_mlocal(minor, Pi(minor_non_rec_params, minor_type));
cases_on_params.push_back(new_C);
expr new_C_app = mk_app(new_C, minor_non_rec_params);
expr rec_arg = Fun(minor_params, new_C_app);
rec_args.push_back(rec_arg);
} else {
rec_args.push_back(mk_fun_star(mlocal_type(minor), C_names, C_main, *unit, *star));
}
i++;
}
}
// Add indices and major-premise to rec_args
for (unsigned i = 0; i < num_idx_major; i++)
rec_args.push_back(rec_params[num_params + num_types + num_minors + i]);
expr cases_on_type = Pi(cases_on_params, rec_type);
expr cases_on_value = Fun(cases_on_params, mk_app(rec_cnst, rec_args));
bool opaque = false;
bool use_conv_opt = true;
declaration new_d = mk_definition(env, cases_on_name, rec_decl.get_univ_params(), cases_on_type, cases_on_value,
opaque, rec_decl.get_module_idx(), use_conv_opt);
environment new_env = module::add(env, check(env, new_d));
return add_protected(new_env, cases_on_name);
}
}