lean2/src/library/elaborator/elaborator.cpp

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/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include <memory>
#include <vector>
#include <utility>
#include "util/pdeque.h"
#include "kernel/formatter.h"
#include "kernel/free_vars.h"
#include "kernel/normalizer.h"
#include "kernel/instantiate.h"
#include "kernel/builtin.h"
#include "library/type_inferer.h"
#include "library/update_expr.h"
#include "library/reduce.h"
#include "library/elaborator/elaborator.h"
#include "library/elaborator/elaborator_trace.h"
namespace lean {
static name g_x_name("x");
class elaborator::imp {
typedef pdeque<unification_constraint> cnstr_queue;
struct state {
metavar_env m_menv;
cnstr_queue m_queue;
state(metavar_env const & menv, unsigned num_cnstrs, unification_constraint const * cnstrs):
m_menv(menv) {
for (unsigned i = 0; i < num_cnstrs; i++)
m_queue.push_back(cnstrs[i]);
}
state(metavar_env const & menv, cnstr_queue const & q):
m_menv(menv),
m_queue(q) {
}
};
/**
\brief Base class for case splits performed by the elaborator.
*/
struct case_split {
trace m_curr_assumption; // trace object used to justify current split
state m_prev_state;
std::vector<trace> m_failed_traces; // traces/justifications for failed branches
case_split(state const & prev_state):m_prev_state(prev_state) {}
virtual ~case_split() {}
virtual bool next(imp & owner) = 0;
};
/**
\brief Case-split object for choice constraints.
*/
struct choice_case_split : public case_split {
unsigned m_idx;
unification_constraint m_choice;
choice_case_split(unification_constraint const & c, state const & prev_state):
case_split(prev_state),
m_idx(0),
m_choice(c) {
}
virtual ~choice_case_split() {}
virtual bool next(imp & owner) {
return owner.next_choice_case(*this);
}
};
/**
\brief Case split object for higher-order matching
*/
struct ho_match_case_split : public case_split {
unification_constraint m_constraint;
unsigned m_idx; // current alternative
std::vector<state> m_states; // set of alternatives
ho_match_case_split(unification_constraint const & cnstr, unsigned num_states, state const * states, state const & prev_state):
case_split(prev_state),
m_constraint(cnstr),
m_idx(0),
m_states(states, states + num_states) {
}
virtual ~ho_match_case_split() {}
virtual bool next(imp & owner) {
return owner.next_ho_case(*this);
}
};
struct synthesizer_case_split : public case_split {
expr m_metavar;
std::unique_ptr<synthesizer::result> m_alternatives;
synthesizer_case_split(expr const & m, std::unique_ptr<synthesizer::result> & r, state const & prev_state):
case_split(prev_state),
m_metavar(m),
m_alternatives(std::move(r)) {
}
virtual ~synthesizer_case_split() {}
};
struct plugin_case_split : public case_split {
unification_constraint m_constraint;
std::unique_ptr<elaborator_plugin::result> m_alternatives;
plugin_case_split(unification_constraint const & cnstr, std::unique_ptr<elaborator_plugin::result> & r, state const & prev_state):
case_split(prev_state),
m_constraint(cnstr),
m_alternatives(std::move(r)) {
}
virtual ~plugin_case_split() {}
virtual bool next(imp & owner) {
return owner.next_plugin_case(*this);
}
};
environment const & m_env;
type_inferer m_type_inferer;
normalizer m_normalizer;
state m_state;
std::vector<std::unique_ptr<case_split>> m_case_splits;
std::shared_ptr<synthesizer> m_synthesizer;
std::shared_ptr<elaborator_plugin> m_plugin;
unsigned m_next_id;
int m_quota;
trace m_conflict;
bool m_interrupted;
// options
bool m_use_traces;
bool m_use_normalizer;
void set_options(options const &) {
m_use_traces = true;
m_use_normalizer = true;
}
void reset_quota() {
m_quota = m_state.m_queue.size();
}
trace mk_assumption() {
unsigned id = m_next_id;
m_next_id++;
return trace(new assumption_trace(id));
}
/** \brief Add given constraint to the front of the current constraint queue */
void push_front(unification_constraint const & c) {
reset_quota();
m_state.m_queue.push_front(c);
}
/** \brief Return true iff \c m is an assigned metavariable in the current state */
bool is_assigned(expr const & m) const {
lean_assert(is_metavar(m));
return m_state.m_menv.is_assigned(m);
}
/** \brief Return the substitution for an assigned metavariable */
expr get_mvar_subst(expr const & m) const {
lean_assert(is_metavar(m));
lean_assert(is_assigned(m));
return m_state.m_menv.get_subst(m);
}
/** \brief Return the trace/justification for an assigned metavariable */
trace get_mvar_trace(expr const & m) const {
lean_assert(is_metavar(m));
lean_assert(is_assigned(m));
return m_state.m_menv.get_trace(m);
}
/** \brief Return the type of an metavariable */
expr get_mvar_type(expr const & m) {
lean_assert(is_metavar(m));
return m_state.m_menv.get_type(m);
}
/**
\brief Return true iff \c e contains the metavariable \c m.
The substitutions in the current state are taken into account.
*/
bool has_metavar(expr const & e, expr const & m) const {
return ::lean::has_metavar(e, m, m_state.m_menv.get_substitutions());
}
/**
\brief Return a unassigned metavariable in the current state.
Return the anonymous name if the state does not contain unassigned metavariables.
*/
name find_unassigned_metavar() const {
return m_state.m_menv.find_unassigned_metavar();
}
/** \brief Return true if \c a is of the form <tt>(?m ...)</tt> */
static bool is_meta_app(expr const & a) {
return is_app(a) && is_metavar(arg(a, 0));
}
/** \brief Return true iff \c a is a metavariable or if \c a is an application where the function is a metavariable */
static bool is_meta(expr const & a) {
return is_metavar(a) || is_meta_app(a);
}
/** \brief Return true iff \c a is a metavariable and has a meta context. */
static bool is_metavar_with_context(expr const & a) {
return is_metavar(a) && has_local_context(a);
}
/** \brief Return true if \c a is of the form <tt>(?m[...] ...)</tt> */
static bool is_meta_app_with_context(expr const & a) {
return is_meta_app(a) && has_local_context(arg(a, 0));
}
static expr mk_lambda(name const & n, expr const & d, expr const & b) {
return ::lean::mk_lambda(n, d, b);
}
/**
\brief Create the term (fun (x_0 : types[0]) ... (x_{n-1} : types[n-1]) body)
*/
expr mk_lambda(buffer<expr> const & types, expr const & body) {
expr r = body;
unsigned i = types.size();
while (i > 0) {
--i;
r = mk_lambda(name(g_x_name, i), types[i], r);
}
return r;
}
/**
\brief Auxiliary method for pushing a new constraint to the constraint queue.
The new constraint is based on the constraint \c c. The constraint \c c may be a equality or convertability constraint.
The update is justified by \c new_tr.
*/
void push_updated_constraint(unification_constraint const & c, expr const & new_a, expr const & new_b, trace const & new_tr) {
lean_assert(is_eq(c) || is_convertible(c));
context const & ctx = get_context(c);
if (is_eq(c))
push_front(mk_eq_constraint(ctx, new_a, new_b, new_tr));
else
push_front(mk_convertible_constraint(ctx, new_a, new_b, new_tr));
}
/**
\brief Auxiliary method for pushing a new constraint to the constraint queue.
The new constraint is based on the constraint \c c. The constraint \c c may be a equality or convertability constraint.
The flag \c is_lhs says if the left-hand-side or right-hand-side are being updated with \c new_a.
The update is justified by \c new_tr.
*/
void push_updated_constraint(unification_constraint const & c, bool is_lhs, expr const & new_a, trace const & new_tr) {
lean_assert(is_eq(c) || is_convertible(c));
context const & ctx = get_context(c);
if (is_eq(c)) {
if (is_lhs)
push_front(mk_eq_constraint(ctx, new_a, eq_rhs(c), new_tr));
else
push_front(mk_eq_constraint(ctx, eq_lhs(c), new_a, new_tr));
} else {
if (is_lhs)
push_front(mk_convertible_constraint(ctx, new_a, convertible_to(c), new_tr));
else
push_front(mk_convertible_constraint(ctx, convertible_from(c), new_a, new_tr));
}
}
/**
\brief Auxiliary method for pushing a new constraint to the constraint queue.
The new constraint is obtained from \c c by one or more normalization steps that produce \c new_a and \c new_b
*/
void push_normalized_constraint(unification_constraint const & c, expr const & new_a, expr const & new_b) {
push_updated_constraint(c, new_a, new_b, trace(new normalize_trace(c)));
}
/**
\brief Assign \c v to \c m with justification \c tr in the current state.
*/
void assign(expr const & m, expr const & v, trace const & tr) {
lean_assert(is_metavar(m));
metavar_env & menv = m_state.m_menv;
m_state.m_menv.assign(m, v, tr);
if (menv.has_type(m)) {
}
}
bool process(unification_constraint const & c) {
m_quota--;
switch (c.kind()) {
case unification_constraint_kind::Eq: return process_eq(c);
case unification_constraint_kind::Convertible: return process_convertible(c);
case unification_constraint_kind::Max: return process_max(c);
case unification_constraint_kind::Choice: return process_choice(c);
}
lean_unreachable();
return true;
}
bool process_eq(unification_constraint const & c) {
return process_eq_convertible(get_context(c), eq_lhs(c), eq_rhs(c), c);
}
bool process_convertible(unification_constraint const & c) {
return process_eq_convertible(get_context(c), convertible_from(c), convertible_to(c), c);
}
/**
Process <tt>ctx |- a == b</tt> and <tt>ctx |- a << b</tt> when:
1- \c a is an assigned metavariable
2- \c a is a unassigned metavariable without a metavariable context.
3- \c a is a unassigned metavariable of the form <tt>?m[lift:s:n, ...]</tt>, and \c b does not have
a free variable in the range <tt>[s, s+n)</tt>.
4- \c a is an application of the form <tt>(?m ...)</tt> where ?m is an assigned metavariable.
*/
enum status { Processed, Failed, Continue };
status process_metavar(unification_constraint const & c, expr const & a, expr const & b, bool is_lhs, bool allow_assignment) {
if (is_metavar(a)) {
if (is_assigned(a)) {
// Case 1
trace new_tr(new substitution_trace(c, get_mvar_trace(a)));
push_updated_constraint(c, is_lhs, get_mvar_subst(a), new_tr);
return Processed;
} else if (!has_local_context(a)) {
// Case 2
if (has_metavar(b, a)) {
m_conflict = trace(new unification_failure_trace(c));
return Failed;
} else if (allow_assignment) {
assign(a, b, trace(new assignment_trace(c)));
reset_quota();
return Processed;
}
} else {
local_entry const & me = head(metavar_lctx(a));
if (me.is_lift() && !has_free_var(b, me.s(), me.s() + me.n())) {
// Case 3
trace new_tr(new substitution_trace(c, get_mvar_trace(a)));
expr new_a = pop_meta_context(a);
expr new_b = lower_free_vars(b, me.s() + me.n(), me.n());
if (!is_lhs)
swap(new_a, new_b);
push_updated_constraint(c, new_a, new_b, new_tr);
return Processed;
}
}
}
if (is_app(a) && is_metavar(arg(a, 0)) && is_assigned(arg(a, 0))) {
// Case 4
trace new_tr(new substitution_trace(c, get_mvar_trace(arg(a, 0))));
expr new_a = update_app(a, 0, get_mvar_subst(arg(a, 0)));
push_updated_constraint(c, is_lhs, new_a, new_tr);
return Processed;
}
return Continue;
}
/** \brief Unfold let-expression */
void process_let(expr & a) {
if (is_let(a))
a = instantiate(let_body(a), let_value(a));
}
/** \brief Replace variables by their definition if the context contains it. */
void process_var(context const & ctx, expr & a) {
if (is_var(a)) {
try {
context_entry const & e = lookup(ctx, var_idx(a));
if (e.get_body())
a = e.get_body();
} catch (exception&) {
}
}
}
expr normalize(context const & ctx, expr const & a) {
return m_normalizer(a, ctx, &(m_state.m_menv));
}
void process_app(context const & ctx, expr & a) {
if (is_app(a)) {
expr f = arg(a, 0);
if (is_value(f) && m_use_normalizer) {
// if f is a semantic attachment, we keep normalizing children from
// left to right until the semantic attachment is applicable
buffer<expr> new_args;
new_args.append(num_args(a), &(arg(a, 0)));
bool modified = false;
expr r;
for (unsigned i = 1; i < new_args.size(); i++) {
expr const & curr = new_args[i];
expr new_curr = normalize(ctx, curr);
if (curr != new_curr) {
modified = true;
new_args[i] = new_curr;
if (to_value(f).normalize(new_args.size(), new_args.data(), r)) {
a = r;
return;
}
}
}
if (modified) {
a = mk_app(new_args.size(), new_args.data());
return;
}
} else {
process_let(f);
process_var(ctx, f);
f = head_beta_reduce(f);
a = update_app(a, 0, f);
a = head_beta_reduce(a);
}
}
}
void process_eq(context const & ctx, expr & a) {
if (is_eq(a) && m_use_normalizer) {
a = normalize(ctx, a);
}
}
expr normalize_step(context const & ctx, expr const & a) {
expr new_a = a;
process_let(new_a);
process_var(ctx, new_a);
process_app(ctx, new_a);
process_eq(ctx, new_a);
return new_a;
}
int get_const_weight(expr const & a) {
lean_assert(is_constant(a));
object const & obj = m_env.find_object(const_name(a));
if (obj && obj.is_definition() && !obj.is_opaque())
return obj.get_weight();
else
return -1;
}
/**
\brief Return a number >= 0 if \c a is a defined constant or the application of a defined constant.
In this case, the value is the weight of the definition.
*/
int get_unfolding_weight(expr const & a) {
if (is_constant(a))
return get_const_weight(a);
else if (is_app(a) && is_constant(arg(a, 0)))
return get_const_weight(arg(a, 0));
else
return -1;
}
expr unfold(expr const & a) {
lean_assert(is_constant(a) || (is_app(a) && is_constant(arg(a, 0))));
if (is_constant(a)) {
return m_env.find_object(const_name(a)).get_value();
} else {
return update_app(a, 0, m_env.find_object(const_name(arg(a, 0))).get_value());
}
}
bool normalize_head(expr a, expr b, unification_constraint const & c) {
context const & ctx = get_context(c);
bool modified = false;
while (true) {
check_interrupted(m_interrupted);
expr new_a = normalize_step(ctx, a);
expr new_b = normalize_step(ctx, b);
if (new_a == a && new_b == b) {
int w_a = get_unfolding_weight(a);
int w_b = get_unfolding_weight(b);
if (w_a >= 0 || w_b >= 0) {
if (w_a >= w_b)
new_a = unfold(a);
if (w_b >= w_a)
new_b = unfold(b);
if (new_a == a && new_b == b)
break;
} else {
break;
}
}
modified = true;
a = new_a;
b = new_b;
if (a == b) {
return true;
}
}
if (modified) {
push_normalized_constraint(c, a, b);
return true;
} else {
return false;
}
}
bool process_eq_convertible(context const & ctx, expr const & a, expr const & b, unification_constraint const & c) {
bool eq = is_eq(c);
if (a == b) {
return true;
}
status r;
bool allow_assignment = eq; // at this point, we only assign metavariables if the constraint is an equational constraint.
r = process_metavar(c, a, b, true, allow_assignment);
if (r != Continue) { return r == Processed; }
r = process_metavar(c, b, a, false, allow_assignment);
if (r != Continue) { return r == Processed; }
if (normalize_head(a, b, c)) { return true; }
r = process_metavar(c, a, b, true, !is_type(b) && !is_meta(b));
if (r != Continue) { return r == Processed; }
r = process_metavar(c, b, a, false, !is_type(a) && !is_meta(a) && a != Bool);
if (r != Continue) { return r == Processed; }
if (a.kind() == b.kind()) {
switch (a.kind()) {
case expr_kind::Constant: case expr_kind::Var: case expr_kind::Value:
return a == b;
case expr_kind::Type:
if ((!eq && m_env.is_ge(ty_level(b), ty_level(a))) || (eq && a == b)) {
return true;
} else {
m_conflict = trace(new unification_failure_trace(c));
return false;
}
case expr_kind::Eq: {
trace new_trace(new destruct_trace(c));
push_front(mk_eq_constraint(ctx, eq_lhs(a), eq_lhs(b), new_trace));
push_front(mk_eq_constraint(ctx, eq_rhs(a), eq_rhs(b), new_trace));
return true;
}
case expr_kind::Pi: {
trace new_trace(new destruct_trace(c));
push_front(mk_eq_constraint(ctx, abst_domain(a), abst_domain(b), new_trace));
context new_ctx = extend(ctx, abst_name(a), abst_domain(a));
if (eq)
push_front(mk_eq_constraint(new_ctx, abst_body(a), abst_body(b), new_trace));
else
push_front(mk_convertible_constraint(new_ctx, abst_body(a), abst_body(b), new_trace));
return true;
}
case expr_kind::Lambda: {
trace new_trace(new destruct_trace(c));
push_front(mk_eq_constraint(ctx, abst_domain(a), abst_domain(b), new_trace));
context new_ctx = extend(ctx, abst_name(a), abst_domain(a));
push_front(mk_eq_constraint(new_ctx, abst_body(a), abst_body(b), new_trace));
return true;
}
case expr_kind::App:
if (!is_meta_app(a) && !is_meta_app(b)) {
if (num_args(a) == num_args(b)) {
trace new_trace(new destruct_trace(c));
for (unsigned i = 0; i < num_args(a); i++)
push_front(mk_eq_constraint(ctx, arg(a, i), arg(b, i), new_trace));
return true;
} else {
return false;
}
}
break;
case expr_kind::Let:
lean_unreachable();
return true;
default:
break;
}
}
if (!is_meta(a) && !is_meta(b) && a.kind() != b.kind())
return false;
std::cout << "Postponed: "; display(std::cout, c);
return true;
}
bool process_max(unification_constraint const &) {
// TODO(Leo)
return true;
}
bool process_choice(unification_constraint const &) {
// TODO(Leo)
return true;
}
void resolve_conflict() {
lean_assert(m_conflict);
while (!m_case_splits.empty()) {
std::unique_ptr<case_split> & d = m_case_splits.back();
if (depends_on(m_conflict, d->m_curr_assumption)) {
d->m_failed_traces.push_back(m_conflict);
if (d->next(*this)) {
m_conflict = trace();
reset_quota();
return;
}
}
m_case_splits.pop_back();
}
throw elaborator_exception(m_conflict);
}
bool next_choice_case(choice_case_split & s) {
unification_constraint & choice = s.m_choice;
unsigned idx = s.m_idx;
if (idx < choice_size(choice)) {
s.m_idx++;
s.m_curr_assumption = mk_assumption();
m_state = s.m_prev_state;
push_front(mk_eq_constraint(get_context(choice), choice_mvar(choice), choice_ith(choice, idx), s.m_curr_assumption));
s.m_idx++;
return true;
} else {
m_conflict = trace(new unification_failure_by_cases_trace(choice, s.m_failed_traces.size(), s.m_failed_traces.data()));
return false;
}
}
bool next_ho_case(ho_match_case_split &) {
#if 0
unification_constraint & cnstr = s.m_constraint;
context const & ctx = get_context(cnstr);
expr const & a = eq_lhs(cnstr);
expr const & b = eq_rhs(cnstr);
lean_assert(is_meta_app(a));
lean_assert(!has_local_context(arg(a, 0)));
lean_assert(!is_meta_app(b));
expr f_a = arg(a, 0);
lean_assert(is_metavar(f_a));
unsigned num_a = num_args(a);
// unification_constraints_wrapper ucw;
buffer<expr> arg_types;
for (unsigned i = 1; i < num_a; i++) {
arg_types.push_back(m_type_inferer(arg(a, i), ctx, &s, &ucw));
}
#endif
return true;
}
bool next_plugin_case(plugin_case_split & s) {
try {
s.m_curr_assumption = mk_assumption();
std::pair<metavar_env, list<unification_constraint>> r = s.m_alternatives->next(s.m_curr_assumption);
m_state.m_queue = s.m_prev_state.m_queue;
m_state.m_menv = r.first;
for (auto c : r.second) {
push_front(c);
}
return true;
} catch (exception & ex) {
m_conflict = trace(new unification_failure_by_cases_trace(s.m_constraint, s.m_failed_traces.size(), s.m_failed_traces.data()));
return false;
}
}
public:
imp(environment const & env, metavar_env const & menv, unsigned num_cnstrs, unification_constraint const * cnstrs,
options const & opts, std::shared_ptr<synthesizer> const & s, std::shared_ptr<elaborator_plugin> const & p):
m_env(env),
m_type_inferer(env),
m_normalizer(env),
m_state(menv, num_cnstrs, cnstrs),
m_synthesizer(s),
m_plugin(p) {
set_options(opts);
m_next_id = 0;
m_quota = 0;
m_interrupted = false;
display(std::cout);
}
substitution next() {
check_interrupted(m_interrupted);
if (m_conflict)
throw elaborator_exception(m_conflict);
if (!m_case_splits.empty()) {
buffer<trace> assumptions;
for (std::unique_ptr<case_split> const & cs : m_case_splits)
assumptions.push_back(cs->m_curr_assumption);
m_conflict = trace(new next_solution_trace(assumptions.size(), assumptions.data()));
resolve_conflict();
}
reset_quota();
while (true) {
check_interrupted(m_interrupted);
cnstr_queue & q = m_state.m_queue;
if (q.empty()) {
name m = find_unassigned_metavar();
std::cout << "Queue is empty\n"; display(std::cout);
if (m) {
// TODO(Leo)
// erase the following line, and implement interface with synthesizer
return m_state.m_menv.get_substitutions();
} else {
return m_state.m_menv.get_substitutions();
}
} else {
unification_constraint c = q.front();
std::cout << "Processing "; display(std::cout, c);
q.pop_front();
if (!process(c)) {
resolve_conflict();
}
}
}
}
void interrupt() {
m_interrupted = true;
m_type_inferer.set_interrupt(true);
m_normalizer.set_interrupt(true);
}
void display(std::ostream & out, unification_constraint const & c) const {
formatter fmt = mk_simple_formatter();
out << c.pp(fmt, options(), nullptr, false) << "\n";
}
void display(std::ostream & out) const {
m_state.m_menv.get_substitutions().for_each([&](name const & m, expr const & e) {
out << m << " <- " << e << "\n";
});
for (auto c : m_state.m_queue)
display(out, c);
}
};
elaborator::elaborator(environment const & env,
metavar_env const & menv,
unsigned num_cnstrs,
unification_constraint const * cnstrs,
options const & opts,
std::shared_ptr<synthesizer> const & s,
std::shared_ptr<elaborator_plugin> const & p):
m_ptr(new imp(env, menv, num_cnstrs, cnstrs, opts, s, p)) {
}
elaborator::elaborator(environment const & env,
metavar_env const & menv,
context const & ctx, expr const & lhs, expr const & rhs):
elaborator(env, menv, { mk_eq_constraint(ctx, lhs, rhs, trace()) }) {
}
elaborator::~elaborator() {
}
substitution elaborator::next() {
return m_ptr->next();
}
void elaborator::interrupt() {
m_ptr->interrupt();
}
}