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refactor(library/unifier): move inductive datatype support to inductive_unifier_plugin

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-07-05 10:59:53 -07:00
parent e445515f2b
commit 72bce91c18
7 changed files with 221 additions and 193 deletions
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2
src/library/CMakeLists.txt
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@ -5,7 +5,7 @@ add_library(library deep_copy.cpp expr_lt.cpp io_state.cpp occurs.cpp
private.cpp placeholder.cpp aliases.cpp level_names.cpp
update_declaration.cpp choice.cpp scoped_ext.cpp locals.cpp
standard_kernel.cpp hott_kernel.cpp
unifier.cpp unifier_plugin.cpp
unifier.cpp unifier_plugin.cpp inductive_unifier_plugin.cpp
explicit.cpp num.cpp string.cpp)
# hop_match.cpp)

16
src/library/hott_kernel.cpp
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@ -5,18 +5,20 @@ Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "kernel/inductive/inductive.h"
#include "library/inductive_unifier_plugin.h"
namespace lean {
using inductive::inductive_normalizer_extension;
/** \brief Create a HoTT (Homotopy Type Theory) compatible environment */
environment mk_hott_environment(unsigned trust_lvl) {
return environment(trust_lvl,
false /* Type.{0} is proof relevant */,
true /* Eta */,
false /* Type.{0} is predicative */,
list<name>(name("Id")) /* Exact equality types are proof irrelevant */,
/* builtin support for inductive datatypes */
std::unique_ptr<normalizer_extension>(new inductive_normalizer_extension()));
environment env = environment(trust_lvl,
false /* Type.{0} is proof relevant */,
true /* Eta */,
false /* Type.{0} is predicative */,
list<name>(name("Id")) /* Exact equality types are proof irrelevant */,
/* builtin support for inductive datatypes */
std::unique_ptr<normalizer_extension>(new inductive_normalizer_extension()));
return set_unifier_plugin(env, mk_inductive_unifier_plugin());
}
}

135
src/library/inductive_unifier_plugin.cpp Normal file
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@ -0,0 +1,135 @@
/*
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/lazy_list_fn.h"
#include "kernel/inductive/inductive.h"
#include "library/unifier_plugin.h"
#include "library/unifier.h"
namespace lean {
class inductive_unifier_plugin_cell : public unifier_plugin_cell {
/** \brief Return true iff \c e is of the form (elim ... (?m ...)) */
bool is_elim_meta_app(type_checker & tc, expr const & e) const {
if (!is_app(e))
return false;
expr const & f = get_app_fn(e);
if (!is_constant(f))
return false;
auto it_name = inductive::is_elim_rule(tc.env(), const_name(f));
if (!it_name)
return false;
if (!is_meta(app_arg(e)))
return false;
if (is_pi(tc.whnf(tc.infer(e))))
return false;
return true;
}
/** \brief Return true iff the lhs or rhs of the constraint c is of the form (elim ... (?m ...)) */
bool is_elim_meta_cnstr(type_checker & tc, constraint const & c) const {
return is_eq_cnstr(c) && (is_elim_meta_app(tc, cnstr_lhs_expr(c)) || is_elim_meta_app(tc, cnstr_rhs_expr(c)));
}
/** \brief Return true iff \c e is of the form (?m ... (intro ...)) */
bool is_meta_intro_app(type_checker & tc, expr const & e) const {
if (!is_app(e) || !is_meta(e))
return false;
expr arg = get_app_fn(app_arg(e));
if (!is_constant(arg))
return false;
return (bool) inductive::is_intro_rule(tc.env(), const_name(arg)); // NOLINT
}
/** \brief Return true iff the lhs or rhs of the constraint c is of the form (?m ... (intro ...)) */
bool is_meta_intro_cnstr(type_checker & tc, constraint const & c) const {
return is_eq_cnstr(c) && (is_meta_intro_app(tc, cnstr_lhs_expr(c)) || is_meta_intro_app(tc, cnstr_rhs_expr(c)));
}
/**
\brief Given (elim args) =?= t, where elim is the eliminator/recursor for the inductive declaration \c decl,
and the last argument of args is of the form (?m ...), we create a case split where we try to assign (?m ...)
to the different constructors of decl.
*/
lazy_list<constraints> add_elim_meta_cnstrs(type_checker & tc, name_generator ngen, inductive::inductive_decl const & decl,
expr const & elim, buffer<expr> & args, expr const & t, justification const & j) const {
lean_assert(is_constant(elim));
levels elim_lvls = const_levels(elim);
unsigned elim_num_lvls = length(elim_lvls);
unsigned num_args = args.size();
expr meta = args[num_args - 1]; // save last argument, we will update it
lean_assert(is_meta(meta));
buffer<expr> margs;
expr const & m = get_app_args(meta, margs);
expr const & mtype = mlocal_type(m);
environment const & env = tc.env();
buffer<constraints> alts;
for (auto const & intro : inductive::inductive_decl_intros(decl)) {
name const & intro_name = inductive::intro_rule_name(intro);
declaration intro_decl = env.get(intro_name);
levels intro_lvls;
if (length(intro_decl.get_univ_params()) == elim_num_lvls) {
intro_lvls = elim_lvls;
} else {
lean_assert(length(intro_decl.get_univ_params()) == elim_num_lvls - 1);
intro_lvls = tail(elim_lvls);
}
expr intro_fn = mk_constant(inductive::intro_rule_name(intro), intro_lvls);
expr hint = intro_fn;
expr intro_type = tc.whnf(inductive::intro_rule_type(intro));
while (is_pi(intro_type)) {
hint = mk_app(hint, mk_app(mk_aux_metavar_for(ngen, mtype), margs));
intro_type = tc.whnf(binding_body(intro_type));
}
constraint c1 = mk_eq_cnstr(meta, hint, j);
args[num_args - 1] = hint;
expr reduce_elim = tc.whnf(mk_app(elim, args));
constraint c2 = mk_eq_cnstr(reduce_elim, t, j);
alts.push_back(constraints({c1, c2}));
}
return to_lazy(to_list(alts.begin(), alts.end()));
}
lazy_list<constraints> process_elim_meta_core(type_checker & tc, name_generator const & ngen,
expr const & lhs, expr const & rhs, justification const & j) const {
lean_assert(is_elim_meta_app(tc, lhs));
buffer<expr> args;
expr const & elim = get_app_args(lhs, args);
environment const & env = tc.env();
auto it_name = *inductive::is_elim_rule(env, const_name(elim));
auto decls = *inductive::is_inductive_decl(env, it_name);
for (auto const & d : std::get<2>(decls)) {
if (inductive::inductive_decl_name(d) == it_name)
return add_elim_meta_cnstrs(tc, ngen, d, elim, args, rhs, j);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
public:
/**
\brief Try to solve constraint of the form (elim ... (?m ...)) =?= t, by assigning (?m ...) to the introduction rules
associated with the eliminator \c elim.
*/
virtual lazy_list<constraints> solve(type_checker & tc, constraint const & c, name_generator const & ngen) const {
expr const & lhs = cnstr_lhs_expr(c);
expr const & rhs = cnstr_rhs_expr(c);
justification const & j = c.get_justification();
if (is_elim_meta_app(tc, lhs))
return process_elim_meta_core(tc, ngen, lhs, rhs, j);
else if (is_elim_meta_app(tc, rhs))
return process_elim_meta_core(tc, ngen, rhs, lhs, j);
else
return lazy_list<constraints>();
}
virtual bool delay_constraint(type_checker & tc, constraint const & c) const {
return is_elim_meta_cnstr(tc, c) || is_meta_intro_cnstr(tc, c);
}
};
unifier_plugin mk_inductive_unifier_plugin() {
return std::make_shared<inductive_unifier_plugin_cell>();
}
}

12
src/library/inductive_unifier_plugin.h Normal file
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@ -0,0 +1,12 @@
/*
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#pragma once
#include "library/unifier_plugin.h"
namespace lean {
/** \brief Return a unifier plugin that handles constraints containing eliminators and introductions */
unifier_plugin mk_inductive_unifier_plugin();
}

16
src/library/standard_kernel.cpp
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@ -5,18 +5,20 @@ Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "kernel/inductive/inductive.h"
#include "library/inductive_unifier_plugin.h"
namespace lean {
using inductive::inductive_normalizer_extension;
/** \brief Create standard Lean environment */
environment mk_environment(unsigned trust_lvl) {
return environment(trust_lvl,
true /* Type.{0} is proof irrelevant */,
true /* Eta */,
true /* Type.{0} is impredicative */,
list<name>() /* No type class has proof irrelevance */,
/* builtin support for inductive datatypes */
std::unique_ptr<normalizer_extension>(new inductive_normalizer_extension()));
environment env = environment(trust_lvl,
true /* Type.{0} is proof irrelevant */,
true /* Eta */,
true /* Type.{0} is impredicative */,
list<name>() /* No type class has proof irrelevance */,
/* builtin support for inductive datatypes */
std::unique_ptr<normalizer_extension>(new inductive_normalizer_extension()));
return set_unifier_plugin(env, mk_inductive_unifier_plugin());
}
}

232
src/library/unifier.cpp
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@ -16,7 +16,6 @@ Author: Leonardo de Moura
#include "kernel/abstract.h"
#include "kernel/instantiate.h"
#include "kernel/type_checker.h"
#include "kernel/inductive/inductive.h"
#include "library/occurs.h"
#include "library/unifier.h"
#include "library/unifier_plugin.h"
@ -193,6 +192,55 @@ std::pair<unify_status, substitution> unify_simple(substitution const & s, const
return mk_pair(unify_status::Unsupported, s);
}
/** \brief Given \c type of the form <tt>(Pi ctx, r)</tt>, return <tt>(Pi ctx, new_range)</tt> */
static expr replace_range(expr const & type, expr const & new_range) {
if (is_pi(type))
return update_binding(type, binding_domain(type), replace_range(binding_body(type), new_range));
else
return new_range;
}
/** \brief Return the "arity" of the given type. The arity is the number of nested pi-expressions. */
static unsigned get_arity(expr type) {
unsigned r = 0;
while (is_pi(type)) {
type = binding_body(type);
r++;
}
return r;
}
/**
\brief Given a type \c t of the form
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), B[x_1, ..., x_n]</tt>
return a new metavariable \c m1 with type
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), Type.{u}</tt>
where \c u is a new universe metavariable.
*/
expr mk_aux_type_metavar_for(name_generator & ngen, expr const & t) {
expr new_type = replace_range(t, mk_sort(mk_meta_univ(ngen.next())));
name n = ngen.next();
return mk_metavar(n, new_type);
}
/**
\brief Given a type \c t of the form
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), B[x_1, ..., x_n]</tt>
return a new metavariable \c m1 with type
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), (m2 x_1 ... x_n)</tt>
where \c m2 is a new metavariable with type
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), Type.{u}</tt>
where \c u is a new universe metavariable.
*/
expr mk_aux_metavar_for(name_generator & ngen, expr const & t) {
unsigned num = get_arity(t);
expr r = mk_app_vars(mk_aux_type_metavar_for(ngen, t), num);
expr new_type = replace_range(t, r);
name n = ngen.next();
return mk_metavar(n, new_type);
}
static constraint g_dont_care_cnstr = mk_eq_cnstr(expr(), expr(), justification());
/**
@ -356,65 +404,6 @@ struct unifier_fn {
void update_conflict(justification const & j) { m_conflict = j; }
void reset_conflict() { m_conflict = optional<justification>(); lean_assert(!in_conflict()); }
/** \brief Given \c type of the form <tt>(Pi ctx, r)</tt>, return <tt>(Pi ctx, new_range)</tt> */
static expr replace_range(expr const & type, expr const & new_range) {
if (is_pi(type))
return update_binding(type, binding_domain(type), replace_range(binding_body(type), new_range));
else
return new_range;
}
/** \brief Return the "arity" of the given type. The arity is the number of nested pi-expressions. */
static unsigned get_arity(expr type) {
unsigned r = 0;
while (is_pi(type)) {
type = binding_body(type);
r++;
}
return r;
}
/** \brief Return the term (f #n-1 ... #0) */
static expr mk_app_vars(expr const & f, unsigned n) {
expr r = f;
unsigned i = n;
while (i > 0) {
--i;
r = r(mk_var(i));
}
return r;
}
/**
\brief Given a type \c t of the form
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), B[x_1, ..., x_n]</tt>
return a new metavariable \c m1 with type
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), Type.{u}</tt>
where \c u is a new universe metavariable.
*/
expr mk_aux_type_metavar_for(expr const & t) {
expr new_type = replace_range(t, mk_sort(mk_meta_univ(m_ngen.next())));
name n = m_ngen.next();
return mk_metavar(n, new_type);
}
/**
\brief Given a type \c t of the form
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), B[x_1, ..., x_n]</tt>
return a new metavariable \c m1 with type
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), (m2 x_1 ... x_n)</tt>
where \c m2 is a new metavariable with type
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), Type.{u}</tt>
where \c u is a new universe metavariable.
*/
expr mk_aux_metavar_for(expr const & t) {
unsigned num = get_arity(t);
expr r = mk_app_vars(mk_aux_type_metavar_for(t), num);
expr new_type = replace_range(t, r);
name n = m_ngen.next();
return mk_metavar(n, new_type);
}
/**
\brief Given t
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), B[x_1, ..., x_n]</tt>
@ -603,7 +592,7 @@ struct unifier_fn {
}
// We delay constraints where lhs or rhs are of the form (elim ... (?m ...))
if (is_elim_meta_app(lhs) || is_elim_meta_app(rhs) || is_meta_intro_app(lhs) || is_meta_intro_app(rhs) || m_plugin->delay_constraint(m_tc, c)) {
if (m_plugin->delay_constraint(m_tc, c)) {
add_cnstr(c, &unassigned_lvls, &unassigned_exprs, cnstr_group::Reduction);
} else if (is_meta(lhs) && is_meta(rhs)) {
// flex-flex constraints are delayed the most.
@ -821,117 +810,6 @@ struct unifier_fn {
return process_lazy_constraints(alts, mk_composite1(c.get_justification(), m_type_jst.second));
}
/** \brief Return true iff \c e is of the form (elim ... (?m ...)) */
bool is_elim_meta_app(expr const & e) {
if (!is_app(e))
return false;
expr const & f = get_app_fn(e);
if (!is_constant(f))
return false;
auto it_name = inductive::is_elim_rule(m_env, const_name(f));
if (!it_name)
return false;
if (!is_meta(app_arg(e)))
return false;
if (is_pi(m_tc.whnf(m_tc.infer(e))))
return false;
return true;
}
/** \brief Return true iff the lhs or rhs of the constraint c is of the form (elim ... (?m ...)) */
bool is_elim_meta_cnstr(constraint const & c) {
return is_eq_cnstr(c) && (is_elim_meta_app(cnstr_lhs_expr(c)) || is_elim_meta_app(cnstr_rhs_expr(c)));
}
/** \brief Return true iff \c e is of the form (?m ... (intro ...)) */
bool is_meta_intro_app(expr const & e) {
if (!is_app(e) || !is_meta(e))
return false;
expr arg = get_app_fn(app_arg(e));
if (!is_constant(arg))
return false;
return (bool) inductive::is_intro_rule(m_env, const_name(arg)); // NOLINT
}
/**
\brief Given (elim args) =?= t, where elim is the eliminator/recursor for the inductive declaration \c decl,
and the last argument of args is of the form (?m ...), we create a case split where we try to assign (?m ...)
to the different constructors of decl.
*/
bool add_elim_meta_cnstrs(inductive::inductive_decl const & decl, expr const & elim, buffer<expr> & args, expr const & t,
justification const & j) {
lean_assert(is_constant(elim));
levels elim_lvls = const_levels(elim);
unsigned elim_num_lvls = length(elim_lvls);
unsigned num_args = args.size();
expr meta = args[num_args - 1]; // save last argument, we will update it
lean_assert(is_meta(meta));
buffer<expr> margs;
expr const & m = get_app_args(meta, margs);
expr const & mtype = mlocal_type(m);
buffer<constraints> alts;
for (auto const & intro : inductive::inductive_decl_intros(decl)) {
name const & intro_name = inductive::intro_rule_name(intro);
declaration intro_decl = m_env.get(intro_name);
levels intro_lvls;
if (length(intro_decl.get_univ_params()) == elim_num_lvls) {
intro_lvls = elim_lvls;
} else {
lean_assert(length(intro_decl.get_univ_params()) == elim_num_lvls - 1);
intro_lvls = tail(elim_lvls);
}
expr intro_fn = mk_constant(inductive::intro_rule_name(intro), intro_lvls);
expr hint = intro_fn;
expr intro_type = m_tc.whnf(inductive::intro_rule_type(intro));
while (is_pi(intro_type)) {
hint = mk_app(hint, mk_app(mk_aux_metavar_for(mtype), margs));
intro_type = m_tc.whnf(binding_body(intro_type));
}
constraint c1 = mk_eq_cnstr(meta, hint, j);
args[num_args - 1] = hint;
expr reduce_elim = m_tc.whnf(mk_app(elim, args));
constraint c2 = mk_eq_cnstr(reduce_elim, t, j);
alts.push_back(constraints({c1, c2}));
}
if (alts.empty()) {
set_conflict(j);
return false;
} else if (alts.size() == 1) {
return process_constraints(alts[0], justification());
} else {
justification a = mk_assumption_justification(m_next_assumption_idx);
add_case_split(std::unique_ptr<case_split>(new ho_case_split(*this, to_list(alts.begin() + 1, alts.end()))));
return process_constraints(alts[0], a);
}
}
bool process_elim_meta_core(expr const & lhs, expr const & rhs, justification const & j) {
lean_assert(is_elim_meta_app(lhs));
buffer<expr> args;
expr const & elim = get_app_args(lhs, args);
auto it_name = *inductive::is_elim_rule(m_env, const_name(elim));
auto decls = *inductive::is_inductive_decl(m_env, it_name);
for (auto const & d : std::get<2>(decls)) {
if (inductive::inductive_decl_name(d) == it_name)
return add_elim_meta_cnstrs(d, elim, args, rhs, j);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
/**
\brief Try to solve constraint of the form (elim ... (?m ...)) =?= t, by assigning (?m ...) to the introduction rules
associated with the eliminator \c elim.
*/
bool process_elim_meta_cnstr(constraint const & c) {
expr const & lhs = cnstr_lhs_expr(c);
expr const & rhs = cnstr_rhs_expr(c);
justification const & j = c.get_justification();
if (is_elim_meta_app(lhs))
return process_elim_meta_core(lhs, rhs, j);
else
return process_elim_meta_core(rhs, lhs, j);
}
bool next_ho_case_split(ho_case_split & cs) {
if (!is_nil(cs.m_tail)) {
cs.restore_state(*this);
@ -986,7 +864,7 @@ struct unifier_fn {
get_app_args(rhs, rargs);
buffer<expr> sargs;
for (expr const & rarg : rargs) {
expr maux = mk_aux_metavar_for(mtype);
expr maux = mk_aux_metavar_for(m_ngen, mtype);
cs.push_back(mk_eq_cnstr(mk_app(maux, margs), rarg, j));
sargs.push_back(mk_app_vars(maux, margs.size()));
}
@ -1011,13 +889,13 @@ struct unifier_fn {
lean_assert(is_metavar(m));
lean_assert(is_binding(rhs));
expr const & mtype = mlocal_type(m);
expr maux1 = mk_aux_metavar_for(mtype);
expr maux1 = mk_aux_metavar_for(m_ngen, mtype);
buffer<constraint> cs;
cs.push_back(mk_eq_cnstr(mk_app(maux1, margs), binding_domain(rhs), j));
expr dontcare;
expr tmp_pi = mk_pi(binding_name(rhs), mk_app_vars(maux1, margs.size()), dontcare); // trick for "extending" the context
expr mtype2 = replace_range(mtype, tmp_pi); // trick for "extending" the context
expr maux2 = mk_aux_metavar_for(mtype2);
expr maux2 = mk_aux_metavar_for(m_ngen, mtype2);
expr new_local = mk_local(m_ngen.next(), binding_name(rhs), binding_domain(rhs), binding_info(rhs));
cs.push_back(mk_eq_cnstr(mk_app(mk_app(maux2, margs), new_local), instantiate(binding_body(rhs), new_local), j));
expr v = update_binding(rhs, mk_app_vars(maux1, margs.size()), mk_app_vars(maux2, margs.size() + 1));
@ -1060,7 +938,7 @@ struct unifier_fn {
// create an auxiliary metavariable for each macro argument
buffer<expr> sargs;
for (unsigned i = 0; i < macro_num_args(rhs); i++) {
expr maux = mk_aux_metavar_for(mtype);
expr maux = mk_aux_metavar_for(m_ngen, mtype);
cs.push_back(mk_eq_cnstr(mk_app(maux, margs), macro_arg(rhs, i), j));
sargs.push_back(mk_app_vars(maux, margs.size()));
}
@ -1209,8 +1087,6 @@ struct unifier_fn {
return process_flex_rigid(c);
else if (is_flex_flex(c))
return process_flex_flex(c);
else if (is_elim_meta_cnstr(c))
return process_elim_meta_cnstr(c);
else
return process_plugin_constraint(c);
}

1
src/library/unifier.h
View file

@ -28,6 +28,7 @@ unsigned get_unifier_max_steps(options const & opts);
bool get_unifier_unfold_opaque(options const & opts);
bool is_simple_meta(expr const & e);
expr mk_aux_metavar_for(name_generator & ngen, expr const & t);
enum class unify_status { Solved, Failed, Unsupported };
/**