lean2/src/library/unifier.cpp

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/*
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 <utility>
#include <memory>
#include <vector>
#include "util/interrupt.h"
#include "util/luaref.h"
#include "util/lazy_list_fn.h"
#include "util/sstream.h"
#include "util/lbool.h"
#include "kernel/for_each_fn.h"
#include "kernel/abstract.h"
#include "kernel/instantiate.h"
#include "kernel/type_checker.h"
#include "kernel/kernel_exception.h"
#include "kernel/error_msgs.h"
#include "library/occurs.h"
#include "library/unifier.h"
#include "library/opaque_hints.h"
#include "library/unifier_plugin.h"
#include "library/kernel_bindings.h"
namespace lean {
static name g_unifier_max_steps {"unifier", "max_steps"};
RegisterUnsignedOption(g_unifier_max_steps, LEAN_DEFAULT_UNIFIER_MAX_STEPS, "(unifier) maximum number of steps");
unsigned get_unifier_max_steps(options const & opts) { return opts.get_unsigned(g_unifier_max_steps, LEAN_DEFAULT_UNIFIER_MAX_STEPS); }
// If \c e is a metavariable ?m or a term of the form (?m l_1 ... l_n) where
// l_1 ... l_n are distinct local variables, then return ?m, and store l_1 ... l_n in args.
// Otherwise return none.
optional<expr> is_simple_meta(expr const & e, buffer<expr> & args) {
expr const & m = get_app_args(e, args);
if (!is_metavar(m))
return none_expr();
for (auto it = args.begin(); it != args.end(); it++) {
if (!is_local(*it) || std::find(args.begin(), it, *it) != it)
return none_expr();
}
return some_expr(m);
}
bool is_simple_meta(expr const & e) {
buffer<expr> args;
return (bool)is_simple_meta(e, args); // NOLINT
}
// Return true if all local constants in \c e are in locals
bool context_check(expr const & e, buffer<expr> const & locals) {
bool failed = false;
for_each(e, [&](expr const & e, unsigned) {
if (failed)
return false;
if (is_local(e) && std::find(locals.begin(), locals.end(), e) == locals.end()) {
failed = true;
return false;
}
return has_local(e);
});
return !failed;
}
// Return
// - l_undef if \c e contains a metavariable application that contains
// a local constant not in locals
// - l_true if \c e does not contain the metavariable \c m, and all local
// constants are in \c e are in \c locals.
// - l_false if \c e contains \c m or it contains a local constant \c l
// not in locals that is not in a metavariable application.
lbool occurs_context_check(substitution const & s, expr const & e, expr const & m, buffer<expr> const & locals) {
expr root = e;
lbool r = l_true;
for_each(e, [&](expr const & e, unsigned) {
if (r == l_false) {
return false;
} else if (is_local(e)) {
if (std::find(locals.begin(), locals.end(), e) == locals.end()) {
// right-hand-side contains variable that is not in the scope
// of metavariable.
r = l_false;
}
return false; // do not visit type
} else if (is_meta(e)) {
if (!context_check(e, locals) || s.occurs(m, e))
r = l_undef;
if (get_app_fn(e) == m)
r = l_false;
return false; // do not visit children
} else {
// we only need to continue exploring e if it contains
// metavariables and/or local constants.
return has_expr_metavar(e) || has_local(e);
}
});
return r;
}
// Create a lambda abstraction by abstracting the local constants \c locals in \c e
expr lambda_abstract_locals(expr const & e, buffer<expr> const & locals) {
expr v = abstract_locals(e, locals.size(), locals.data());
unsigned i = locals.size();
while (i > 0) {
--i;
expr t = abstract_locals(mlocal_type(locals[i]), i, locals.data());
v = mk_lambda(local_pp_name(locals[i]), t, v);
}
return v;
}
static std::pair<unify_status, substitution> unify_simple_core(substitution const & s, expr const & lhs, expr const & rhs,
justification const & j) {
lean_assert(is_meta(lhs));
buffer<expr> args;
auto m = is_simple_meta(lhs, args);
if (!m || is_meta(rhs)) {
return mk_pair(unify_status::Unsupported, s);
} else {
switch (occurs_context_check(s, rhs, *m, args)) {
case l_false: return mk_pair(unify_status::Failed, s);
case l_undef: mk_pair(unify_status::Unsupported, s);
case l_true: {
expr v = lambda_abstract_locals(rhs, args);
return mk_pair(unify_status::Solved, s.assign(mlocal_name(*m), v, j));
}}
}
lean_unreachable(); // LCOV_EXCL_LINE
}
std::pair<unify_status, substitution> unify_simple(substitution const & s, expr const & lhs, expr const & rhs, justification const & j) {
if (lhs == rhs)
return mk_pair(unify_status::Solved, s);
else if (!has_metavar(lhs) && !has_metavar(rhs))
return mk_pair(unify_status::Failed, s);
else if (is_meta(lhs))
return unify_simple_core(s, lhs, rhs, j);
else if (is_meta(rhs))
return unify_simple_core(s, rhs, lhs, j);
else
return mk_pair(unify_status::Unsupported, s);
}
// Return true if m occurs in e
bool occurs_meta(level const & m, level const & e) {
lean_assert(is_meta(m));
bool contains = false;
for_each(e, [&](level const & l) {
if (contains)
return false;
if (l == m) {
contains = true;
return false;
}
return has_meta(l);
});
return contains;
}
std::pair<unify_status, substitution> unify_simple_core(substitution const & s, level const & lhs, level const & rhs, justification const & j) {
lean_assert(is_meta(lhs));
bool contains = occurs_meta(lhs, rhs);
if (contains) {
if (is_succ(rhs))
return mk_pair(unify_status::Failed, s);
else
return mk_pair(unify_status::Unsupported, s);
}
return mk_pair(unify_status::Solved, s.assign(meta_id(lhs), rhs, j));
}
std::pair<unify_status, substitution> unify_simple(substitution const & s, level const & lhs, level const & rhs, justification const & j) {
if (lhs == rhs)
return mk_pair(unify_status::Solved, s);
else if (!has_meta(lhs) && !has_meta(rhs))
return mk_pair(unify_status::Failed, s);
else if (is_meta(lhs))
return unify_simple_core(s, lhs, rhs, j);
else if (is_meta(rhs))
return unify_simple_core(s, rhs, lhs, j);
else if (is_succ(lhs) && is_succ(rhs))
return unify_simple(s, succ_of(lhs), succ_of(rhs), j);
else
return mk_pair(unify_status::Unsupported, s);
}
std::pair<unify_status, substitution> unify_simple(substitution const & s, constraint const & c) {
if (is_eq_cnstr(c))
return unify_simple(s, cnstr_lhs_expr(c), cnstr_rhs_expr(c), c.get_justification());
else if (is_level_eq_cnstr(c))
return unify_simple(s, cnstr_lhs_level(c), cnstr_rhs_level(c), c.get_justification());
else
return mk_pair(unify_status::Unsupported, s);
}
static constraint g_dont_care_cnstr = mk_eq_cnstr(expr(), expr(), justification());
static unsigned g_group_size = 1u << 29;
static unsigned g_cnstr_group_first_index[6] = { 0, g_group_size, 2*g_group_size, 3*g_group_size, 4*g_group_size, 5*g_group_size};
static unsigned get_group_first_index(cnstr_group g) {
return g_cnstr_group_first_index[static_cast<unsigned>(g)];
}
/** \brief Convert choice constraint delay factor to cnstr_group */
cnstr_group get_choice_cnstr_group(constraint const & c) {
lean_assert(is_choice_cnstr(c));
unsigned f = cnstr_delay_factor(c);
if (f > static_cast<unsigned>(cnstr_group::MaxDelayed)) {
return cnstr_group::MaxDelayed;
} else {
return static_cast<cnstr_group>(f);
}
}
/** \brief Auxiliary functional object for implementing simultaneous higher-order unification */
struct unifier_fn {
typedef std::pair<constraint, unsigned> cnstr; // constraint + idx
struct cnstr_cmp {
int operator()(cnstr const & c1, cnstr const & c2) const { return c1.second < c2.second ? -1 : (c1.second == c2.second ? 0 : 1); }
};
typedef rb_tree<cnstr, cnstr_cmp> cnstr_set;
typedef rb_tree<unsigned, unsigned_cmp> cnstr_idx_set;
typedef rb_map<name, cnstr_idx_set, name_quick_cmp> name_to_cnstrs;
typedef std::unique_ptr<type_checker> type_checker_ptr;
environment m_env;
name_generator m_ngen;
substitution m_subst;
unifier_plugin m_plugin;
type_checker_ptr m_tc;
bool m_use_exception; //!< True if we should throw an exception when there are no more solutions.
unsigned m_max_steps;
unsigned m_num_steps;
bool m_first; //!< True if we still have to generate the first solution.
unsigned m_next_assumption_idx; //!< Next assumption index.
unsigned m_next_cidx; //!< Next constraint index.
/**
\brief "Queue" of constraints to be solved.
We implement it using a red-black-tree because:
1- Our red-black-trees support a O(1) copy operation. So, it is cheap to create a snapshot
whenever we create a backtracking point.
2- We can easily remove any constraint from the queue in O(n log n). We do that when
a metavariable \c m is assigned, and we want to instantiate it in all constraints that
contains it.
*/
cnstr_set m_cnstrs;
/**
\brief The following map is an index. The map a metavariable name \c m to the set of constraint indices that contain \c m.
We use these indices whenever a metavariable \c m is assigned.
When the metavariable is assigned, we used this index to remove constraints that contains \c m from \c m_cnstrs,
instantiate \c m, and reprocess them.
\remark \c m_mvar_occs is for regular metavariables.
*/
name_to_cnstrs m_mvar_occs;
/**
\brief Base class for the case-splits created by the unifier.
We have three different kinds of case splits:
1- unifier plugin
2- choice constraints
3- higher-order unification
*/
struct case_split {
unsigned m_assumption_idx; // idx of the current assumption
justification m_jst;
justification m_failed_justifications; // justifications for failed branches
// snapshot of unifier's state
substitution m_subst;
cnstr_set m_cnstrs;
name_to_cnstrs m_mvar_occs;
/** \brief Save unifier's state */
case_split(unifier_fn & u, justification const & j):
m_assumption_idx(u.m_next_assumption_idx), m_jst(j), m_subst(u.m_subst), m_cnstrs(u.m_cnstrs),
m_mvar_occs(u.m_mvar_occs) {
u.m_next_assumption_idx++;
u.m_tc->push();
}
/** \brief Restore unifier's state with saved values, and update m_assumption_idx and m_failed_justifications. */
void restore_state(unifier_fn & u) {
lean_assert(u.in_conflict());
u.m_tc->pop(); // restore type checker state
u.m_tc->push();
u.m_subst = m_subst;
u.m_cnstrs = m_cnstrs;
u.m_mvar_occs = m_mvar_occs;
m_assumption_idx = u.m_next_assumption_idx;
m_failed_justifications = mk_composite1(m_failed_justifications, *u.m_conflict);
u.m_next_assumption_idx++;
u.m_conflict = optional<justification>();
}
justification get_jst() const { return m_jst; }
virtual ~case_split() {}
virtual bool next(unifier_fn & u) = 0;
};
typedef std::vector<std::unique_ptr<case_split>> case_split_stack;
struct lazy_constraints_case_split : public case_split {
lazy_list<constraints> m_tail;
lazy_constraints_case_split(unifier_fn & u, justification const & j, lazy_list<constraints> const & tail):case_split(u, j), m_tail(tail) {}
virtual bool next(unifier_fn & u) { return u.next_lazy_constraints_case_split(*this); }
};
struct simple_case_split : public case_split {
list<constraints> m_tail;
simple_case_split(unifier_fn & u, justification const & j, list<constraints> const & tail):case_split(u, j), m_tail(tail) {}
virtual bool next(unifier_fn & u) { return u.next_simple_case_split(*this); }
};
case_split_stack m_case_splits;
optional<justification> m_conflict; //!< if different from none, then there is a conflict.
unifier_fn(environment const & env, unsigned num_cs, constraint const * cs,
name_generator const & ngen, substitution const & s,
bool use_exception, unsigned max_steps):
m_env(env), m_ngen(ngen), m_subst(s), m_plugin(get_unifier_plugin(env)),
m_tc(mk_type_checker_with_hints(env, m_ngen.mk_child())),
m_use_exception(use_exception), m_max_steps(max_steps), m_num_steps(0) {
m_next_assumption_idx = 0;
m_next_cidx = 0;
m_first = true;
for (unsigned i = 0; i < num_cs; i++) {
process_constraint(cs[i]);
}
}
void check_system() {
check_interrupted();
if (m_num_steps > m_max_steps)
throw exception(sstream() << "unifier maximum number of steps (" << m_max_steps << ") exceeded, " <<
"the maximum number of steps can be increased by setting the option unifier.max_steps " <<
"(remark: the unifier uses higher order unification and unification-hints, which may trigger non-termination");
m_num_steps++;
}
bool in_conflict() const { return (bool)m_conflict; } // NOLINT
void set_conflict(justification const & j) { m_conflict = j; }
void update_conflict(justification const & j) { m_conflict = j; }
void reset_conflict() { m_conflict = optional<justification>(); lean_assert(!in_conflict()); }
expr mk_local_for(expr const & b) {
return mk_local(m_ngen.next(), binding_name(b), binding_domain(b), binding_info(b));
}
/**
\brief Update occurrence index with entry <tt>m -> cidx</tt>, where \c m is the name of a metavariable,
and \c cidx is the index of a constraint that contains \c m.
*/
void add_mvar_occ(name const & m, unsigned cidx) {
cnstr_idx_set s;
auto it = m_mvar_occs.find(m);
if (it)
s = *it;
if (!s.contains(cidx)) {
s.insert(cidx);
m_mvar_occs.insert(m, s);
}
}
void add_meta_occ(expr const & m, unsigned cidx) {
lean_assert(is_meta(m));
add_mvar_occ(mlocal_name(get_app_fn(m)), cidx);
}
void add_meta_occs(expr const & e, unsigned cidx) {
if (has_expr_metavar(e)) {
for_each(e, [&](expr const & e, unsigned) {
if (is_meta(e)) {
add_meta_occ(e, cidx);
return false;
}
if (is_local(e))
return false;
return has_expr_metavar(e);
});
}
}
/** \brief Add constraint to the constraint queue */
unsigned add_cnstr(constraint const & c, cnstr_group g) {
unsigned cidx = m_next_cidx + get_group_first_index(g);
m_cnstrs.insert(cnstr(c, cidx));
m_next_cidx++;
return cidx;
}
/** \brief Check if \c t1 and \c t2 are definitionally equal, if they are not, set a conflict with justification \c j */
bool is_def_eq(expr const & t1, expr const & t2, justification const & j) {
if (m_tc->is_def_eq(t1, t2, j)) {
return true;
} else {
set_conflict(j);
return false;
}
}
/** \brief Check if \c t1 and \c t2 are definitionally, and accumulate constraints in \c new_cs
\pre m_tc must not have pending constraints
*/
bool is_def_eq(expr const & t1, expr const & t2, justification const & j, buffer<constraint> & new_cs) {
type_checker::scope s(*m_tc);
lean_assert(!m_tc->next_cnstr());
if (m_tc->is_def_eq(t1, t2, j)) {
while (auto c = m_tc->next_cnstr())
new_cs.push_back(*c);
return true;
} else {
return false;
}
}
/**
\brief Assign \c v to metavariable \c m with justification \c j.
The type of v and m are inferred, and is_def_eq is invoked.
Any constraint that contains \c m is revisited.
*/
bool assign(expr const & m, expr const & v, justification const & j) {
lean_assert(is_metavar(m));
m_subst.d_assign(m, v, j);
expr m_type = mlocal_type(m);
expr v_type;
try {
v_type = m_tc->infer(v);
} catch (kernel_exception & e) {
set_conflict(j);
return false;
}
if (in_conflict())
return false;
justification j1 = mk_justification(m, [=](formatter const & fmt, substitution const & subst) {
return pp_type_mismatch(fmt, subst.instantiate(m_type), subst.instantiate(v_type));
});
if (!is_def_eq(m_type, v_type, mk_composite1(j1, j)))
return false;
auto it = m_mvar_occs.find(mlocal_name(m));
if (it) {
cnstr_idx_set s = *it;
m_mvar_occs.erase(mlocal_name(m));
s.for_each([&](unsigned cidx) {
process_constraint_cidx(cidx);
});
return !in_conflict();
} else {
return true;
}
}
/**
\brief Assign \c v to universe metavariable \c m with justification \c j.
Any constraint that contains \c m is revisted.
*/
bool assign(level const & m, level const & v, justification const & j) {
lean_assert(is_meta(m));
m_subst.d_assign(m, v, j);
return true;
}
enum status { Solved, Failed, Continue };
/**
\brief Process constraints of the form <tt>lhs =?= rhs</tt> where lhs is of the form <tt>?m</tt> or <tt>(?m l_1 .... l_n)</tt>,
where all \c l_i are distinct local variables. In this case, the method returns Solved, if the method assign succeeds.
The method returns \c Failed if \c rhs contains <tt>?m</tt>, or it contains a local constant not in <tt>{l_1, ..., l_n}</tt>.
Otherwise, it returns \c Continue.
*/
status process_metavar_eq(expr const & lhs, expr const & rhs, justification const & j) {
if (!is_meta(lhs))
return Continue;
buffer<expr> locals;
auto m = is_simple_meta(lhs, locals);
if (!m || is_meta(rhs))
return Continue;
switch (occurs_context_check(m_subst, rhs, *m, locals)) {
case l_false:
set_conflict(j);
return Failed;
case l_undef:
return Continue;
case l_true:
lean_assert(!m_subst.is_assigned(*m));
if (assign(*m, lambda_abstract_locals(rhs, locals), j)) {
return Solved;
} else {
return Failed;
}
}
lean_unreachable(); // LCOV_EXCL_LINE
}
optional<declaration> is_delta(expr const & e) { return ::lean::is_delta(m_env, e); }
/** \brief Return true if lhs and rhs are of the form (f ...) where f can be expanded */
bool is_eq_deltas(expr const & lhs, expr const & rhs) {
auto lhs_d = is_delta(lhs);
auto rhs_d = is_delta(rhs);
return lhs_d && rhs_d && is_eqp(*lhs_d, *rhs_d);
}
/** \brief Return true if the constraint is of the form (f ...) =?= (f ...), where f can be expanded. */
bool is_delta_cnstr(constraint const & c) {
return is_eq_cnstr(c) && is_eq_deltas(cnstr_lhs_expr(c), cnstr_rhs_expr(c));
}
std::pair<constraint, bool> instantiate_metavars(constraint const & c) {
if (is_eq_cnstr(c)) {
auto lhs_jst = m_subst.d_instantiate_metavars(cnstr_lhs_expr(c));
auto rhs_jst = m_subst.d_instantiate_metavars(cnstr_rhs_expr(c));
expr lhs = lhs_jst.first;
expr rhs = rhs_jst.first;
if (lhs != cnstr_lhs_expr(c) || rhs != cnstr_rhs_expr(c)) {
return mk_pair(mk_eq_cnstr(lhs, rhs,
mk_composite1(mk_composite1(c.get_justification(), lhs_jst.second), rhs_jst.second)),
true);
}
} else if (is_level_eq_cnstr(c)) {
auto lhs_jst = m_subst.d_instantiate_metavars(cnstr_lhs_level(c));
auto rhs_jst = m_subst.d_instantiate_metavars(cnstr_rhs_level(c));
level lhs = lhs_jst.first;
level rhs = rhs_jst.first;
if (lhs != cnstr_lhs_level(c) || rhs != cnstr_rhs_level(c)) {
return mk_pair(mk_level_eq_cnstr(lhs, rhs,
mk_composite1(mk_composite1(c.get_justification(), lhs_jst.second), rhs_jst.second)),
true);
}
}
return mk_pair(c, false);
}
status process_eq_constraint_core(constraint const & c) {
expr const & lhs = cnstr_lhs_expr(c);
expr const & rhs = cnstr_rhs_expr(c);
justification const & jst = c.get_justification();
if (lhs == rhs)
return Solved; // trivial constraint
// Update justification using the justification of the instantiated metavariables
if (!has_metavar(lhs) && !has_metavar(rhs)) {
return is_def_eq(lhs, rhs, jst) ? Solved : Failed;
}
// Handle higher-order pattern matching.
status st = process_metavar_eq(lhs, rhs, jst);
if (st != Continue) return st;
st = process_metavar_eq(rhs, lhs, jst);
if (st != Continue) return st;
return Continue;
}
expr instantiate_meta(expr e, justification & j) {
while (true) {
expr const & f = get_app_fn(e);
if (!is_metavar(f))
return e;
name const & f_name = mlocal_name(f);
auto f_value = m_subst.get_expr(f_name);
if (!f_value)
return e;
j = mk_composite1(j, m_subst.get_expr_jst(f_name));
buffer<expr> args;
get_app_rev_args(e, args);
e = apply_beta(*f_value, args.size(), args.data());
}
}
expr instantiate_meta_args(expr const & e, justification & j) {
if (!is_app(e))
return e;
buffer<expr> args;
bool modified = false;
expr const & f = get_app_rev_args(e, args);
unsigned i = args.size();
while (i > 0) {
--i;
expr new_arg = instantiate_meta(args[i], j);
if (new_arg != args[i]) {
modified = true;
args[i] = new_arg;
}
}
if (!modified)
return e;
return mk_rev_app(f, args.size(), args.data());
}
status instantiate_eq_cnstr(constraint const & c) {
justification j = c.get_justification();
expr lhs = instantiate_meta(cnstr_lhs_expr(c), j);
expr rhs = instantiate_meta(cnstr_rhs_expr(c), j);
if (lhs != cnstr_lhs_expr(c) || rhs != cnstr_rhs_expr(c))
return is_def_eq(lhs, rhs, j) ? Solved : Failed;
lhs = instantiate_meta_args(lhs, j);
rhs = instantiate_meta_args(rhs, j);
if (lhs != cnstr_lhs_expr(c) || rhs != cnstr_rhs_expr(c))
return is_def_eq(lhs, rhs, j) ? Solved : Failed;
return Continue;
}
/** \brief Process an equality constraints. */
bool process_eq_constraint(constraint const & c) {
lean_assert(is_eq_cnstr(c));
// instantiate assigned metavariables
status st = instantiate_eq_cnstr(c);
if (st != Continue) return st == Solved;
st = process_eq_constraint_core(c);
if (st != Continue) return st == Solved;
expr const & lhs = cnstr_lhs_expr(c);
expr const & rhs = cnstr_rhs_expr(c);
if (is_eq_deltas(lhs, rhs)) {
// we need to create a backtracking point for this one
add_cnstr(c, cnstr_group::Basic);
} else if (m_plugin->delay_constraint(*m_tc, c)) {
unsigned cidx = add_cnstr(c, cnstr_group::PluginDelayed);
add_meta_occs(lhs, cidx);
add_meta_occs(rhs, cidx);
} else if (is_meta(lhs) && is_meta(rhs)) {
// flex-flex constraints are delayed the most.
unsigned cidx = add_cnstr(c, cnstr_group::FlexFlex);
add_meta_occ(lhs, cidx);
add_meta_occ(rhs, cidx);
} else if (is_meta(lhs)) {
// flex-rigid constraints are delayed.
unsigned cidx = add_cnstr(c, cnstr_group::FlexRigid);
add_meta_occ(lhs, cidx);
} else if (is_meta(rhs)) {
// flex-rigid constraints are delayed.
unsigned cidx = add_cnstr(c, cnstr_group::FlexRigid);
add_meta_occ(rhs, cidx);
} else {
// this constraints require the unifier plugin to be solved
add_cnstr(c, cnstr_group::Basic);
}
return true;
}
/**
\brief Process a universe level constraints of the form <tt>?m =?= rhs</tt>. It fails if rhs contains \c ?m and
is definitely bigger than \c ?m.
TODO(Leo): we should improve this method in the future. It is doing only very basic things.
*/
status process_metavar_eq(level const & lhs, level const & rhs, justification const & j) {
if (!is_meta(lhs))
return Continue;
bool contains = occurs_meta(lhs, rhs);
if (contains) {
if (is_succ(rhs))
return Failed;
else
return Continue;
}
lean_assert(!m_subst.is_assigned(lhs));
if (assign(lhs, rhs, j)) {
return Solved;
} else {
return Failed;
}
}
/** \brief Process a universe level contraints. */
bool process_level_eq_constraint(constraint const & c) {
lean_assert(is_level_eq_cnstr(c));
// instantiate assigned metavariables
constraint new_c = instantiate_metavars(c).first;
level lhs = cnstr_lhs_level(new_c);
level rhs = cnstr_rhs_level(new_c);
justification jst = new_c.get_justification();
// normalize lhs and rhs
lhs = normalize(lhs);
rhs = normalize(rhs);
// eliminate outermost succs
while (is_succ(lhs) && is_succ(rhs)) {
lhs = succ_of(lhs);
rhs = succ_of(rhs);
}
if (lhs == rhs)
return true; // trivial constraint
if (!has_meta(lhs) && !has_meta(rhs)) {
set_conflict(jst);
return false; // trivial failure
}
status st = process_metavar_eq(lhs, rhs, jst);
if (st != Continue) return st == Solved;
st = process_metavar_eq(rhs, lhs, jst);
if (st != Continue) return st == Solved;
add_cnstr(new_c, cnstr_group::FlexRigid);
return true;
}
/**
\brief Process the given constraint \c c. "Easy" constraints are solved, and the remaining ones
are added to the constraint queue m_cnstrs. By "easy", see the methods
#process_eq_constraint and #process_level_eq_constraint.
*/
bool process_constraint(constraint const & c) {
if (in_conflict())
return false;
check_system();
switch (c.kind()) {
case constraint_kind::Choice:
// Choice constraints are never considered easy.
add_cnstr(c, get_choice_cnstr_group(c));
return true;
case constraint_kind::Eq:
return process_eq_constraint(c);
case constraint_kind::LevelEq:
return process_level_eq_constraint(c);
}
lean_unreachable(); // LCOV_EXCL_LINE
}
/**
\brief Process constraint with index \c cidx. The constraint is removed
from the constraint queue, and the method #process_constraint is invoked.
*/
bool process_constraint_cidx(unsigned cidx) {
if (in_conflict())
return false;
cnstr c(g_dont_care_cnstr, cidx);
if (auto it = m_cnstrs.find(c)) {
constraint c2 = it->first;
m_cnstrs.erase(c);
return process_constraint(c2);
}
return true;
}
void add_case_split(std::unique_ptr<case_split> && cs) {
m_case_splits.push_back(std::move(cs));
}
// This method is used only for debugging purposes.
void display(std::ostream & out, justification const & j, unsigned indent = 0) {
for (unsigned i = 0; i < indent; i++)
out << " ";
out << j.pp(mk_simple_formatter_factory()(m_env, options()), nullptr, m_subst) << "\n";
if (j.is_composite()) {
display(out, composite_child1(j), indent+2);
display(out, composite_child2(j), indent+2);
}
}
void pop_case_split() {
m_tc->pop();
m_case_splits.pop_back();
}
bool resolve_conflict() {
lean_assert(in_conflict());
while (!m_case_splits.empty()) {
justification conflict = *m_conflict;
std::unique_ptr<case_split> & d = m_case_splits.back();
if (depends_on(conflict, d->m_assumption_idx)) {
d->m_failed_justifications = mk_composite1(d->m_failed_justifications, conflict);
if (d->next(*this)) {
reset_conflict();
return true;
}
} else {
pop_case_split();
}
}
return false;
}
optional<substitution> failure() {
lean_assert(in_conflict());
if (m_use_exception)
throw unifier_exception(*m_conflict, m_subst);
else
return optional<substitution>();
}
/** \brief Process constraints in \c cs, and append justification \c j to them. */
bool process_constraints(constraints const & cs, justification const & j) {
for (constraint const & c : cs)
process_constraint(update_justification(c, mk_composite1(c.get_justification(), j)));
return !in_conflict();
}
bool next_lazy_constraints_case_split(lazy_constraints_case_split & cs) {
auto r = cs.m_tail.pull();
if (r) {
cs.restore_state(*this);
lean_assert(!in_conflict());
cs.m_tail = r->second;
return process_constraints(r->first, mk_composite1(cs.get_jst(), mk_assumption_justification(cs.m_assumption_idx)));
} else {
// update conflict
update_conflict(mk_composite1(*m_conflict, cs.m_failed_justifications));
pop_case_split();
return false;
}
}
bool process_lazy_constraints(lazy_list<constraints> const & l, justification const & j) {
auto r = l.pull();
if (r) {
if (r->second.is_nil()) {
// there is only one alternative
return process_constraints(r->first, j);
} else {
justification a = mk_assumption_justification(m_next_assumption_idx);
add_case_split(std::unique_ptr<case_split>(new lazy_constraints_case_split(*this, j, r->second)));
return process_constraints(r->first, mk_composite1(j, a));
}
} else {
set_conflict(j);
return false;
}
}
bool process_plugin_constraint(constraint const & c) {
lean_assert(!is_choice_cnstr(c));
lazy_list<constraints> alts = m_plugin->solve(*m_tc, c, m_ngen.mk_child());
return process_lazy_constraints(alts, c.get_justification());
}
bool process_choice_constraint(constraint const & c) {
lean_assert(is_choice_cnstr(c));
expr const & m = cnstr_expr(c);
choice_fn const & fn = cnstr_choice_fn(c);
expr m_type;
try {
m_type = m_tc->infer(m);
} catch (kernel_exception &) {
set_conflict(c.get_justification());
return false;
}
auto m_type_jst = m_subst.d_instantiate_metavars(m_type);
lazy_list<constraints> alts = fn(m, m_type_jst.first, m_subst, m_ngen.mk_child());
return process_lazy_constraints(alts, mk_composite1(c.get_justification(), m_type_jst.second));
}
bool next_simple_case_split(simple_case_split & cs) {
if (!is_nil(cs.m_tail)) {
cs.restore_state(*this);
lean_assert(!in_conflict());
constraints c = head(cs.m_tail);
cs.m_tail = tail(cs.m_tail);
return process_constraints(c, mk_composite1(cs.get_jst(), mk_assumption_justification(cs.m_assumption_idx)));
} else {
// update conflict
update_conflict(mk_composite1(*m_conflict, cs.m_failed_justifications));
pop_case_split();
return false;
}
}
/**
\brief Solve constraints of the form (f a_1 ... a_n) =?= (f b_1 ... b_n) where f can be expanded.
We consider two possible solutions:
1) a_1 =?= b_1, ..., a_n =?= b_n
2) t =?= s, where t and s are the terms we get after expanding f
*/
bool process_delta(constraint const & c) {
lean_assert(is_delta_cnstr(c));
expr const & lhs = cnstr_lhs_expr(c);
expr const & rhs = cnstr_rhs_expr(c);
buffer<expr> lhs_args, rhs_args;
justification j = c.get_justification();
expr lhs_fn = get_app_rev_args(lhs, lhs_args);
expr rhs_fn = get_app_rev_args(rhs, rhs_args);
declaration d = *m_env.find(const_name(lhs_fn));
levels lhs_lvls = const_levels(lhs_fn);
levels rhs_lvls = const_levels(lhs_fn);
if (lhs_args.size() != rhs_args.size() ||
length(lhs_lvls) != length(rhs_lvls) ||
length(d.get_univ_params()) != length(lhs_lvls)) {
// the constraint is not well-formed, this can happen when users are abusing the API
return false;
}
justification a;
// add case_split for t =?= s
expr lhs_fn_val = instantiate_univ_params(d.get_value(), d.get_univ_params(), const_levels(lhs_fn));
expr rhs_fn_val = instantiate_univ_params(d.get_value(), d.get_univ_params(), const_levels(rhs_fn));
expr t = apply_beta(lhs_fn_val, lhs_args.size(), lhs_args.data());
expr s = apply_beta(rhs_fn_val, rhs_args.size(), rhs_args.data());
buffer<constraint> cs2;
if (is_def_eq(t, s, j, cs2)) {
// create a case split
a = mk_assumption_justification(m_next_assumption_idx);
add_case_split(std::unique_ptr<case_split>(new simple_case_split(*this, j, to_list(cs2.begin(), cs2.end()))));
}
// process first case
justification new_j = mk_composite1(j, a);
while (!is_nil(lhs_lvls)) {
level lhs = head(lhs_lvls);
level rhs = head(rhs_lvls);
if (!process_constraint(mk_level_eq_cnstr(lhs, rhs, new_j)))
return false;
lhs_lvls = tail(lhs_lvls);
rhs_lvls = tail(rhs_lvls);
}
unsigned i = lhs_args.size();
while (i > 0) {
--i;
if (!is_def_eq(lhs_args[i], rhs_args[i], new_j))
return false;
}
return true;
}
/** \brief Return true iff \c c is a flex-rigid constraint. */
static bool is_flex_rigid(constraint const & c) {
if (!is_eq_cnstr(c))
return false;
bool is_lhs_meta = is_meta(cnstr_lhs_expr(c));
bool is_rhs_meta = is_meta(cnstr_rhs_expr(c));
return is_lhs_meta != is_rhs_meta;
}
/** \brief Return true iff \c c is a flex-flex constraint */
static bool is_flex_flex(constraint const & c) {
return is_eq_cnstr(c) && is_meta(cnstr_lhs_expr(c)) && is_meta(cnstr_rhs_expr(c));
}
/**
\brief Given t
<tt>Pi (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), B[x_1, ..., x_n]</tt>
return
<tt>fun (x_1 : A_1) ... (x_n : A_n[x_1, ..., x_{n-1}]), v[x_1, ... x_n]</tt>
\remark v has free variables.
*/
expr mk_lambda_for(expr const & t, expr const & v) {
if (is_pi(t)) {
return mk_lambda(binding_name(t), binding_domain(t), mk_lambda_for(binding_body(t), v), binding_info(t));
} else {
return v;
}
}
/** \see ensure_sufficient_args */
optional<expr> ensure_sufficient_args_core(expr mtype, unsigned i, buffer<expr> const & margs) {
if (i == margs.size())
return some_expr(mtype);
mtype = m_tc->ensure_pi(mtype);
try {
if (!m_tc->is_def_eq(binding_domain(mtype), m_tc->infer(margs[i])))
return none_expr();
} catch (kernel_exception &) {
return none_expr();
}
expr local = mk_local_for(mtype);
expr body = instantiate(binding_body(mtype), local);
auto new_body = ensure_sufficient_args_core(body, i+1, margs);
if (!new_body)
return none_expr();
return some_expr(Pi(local, *new_body));
}
/**
\brief Make sure mtype is a Pi of size at least margs.size().
If it is not, we use ensure_pi and (potentially) add new constaints to enforce it.
*/
optional<expr> ensure_sufficient_args(expr const & mtype, buffer<expr> const & margs, buffer<constraint> & cs, justification const & j) {
expr t = mtype;
unsigned num = 0;
while (is_pi(t)) {
num++;
t = binding_body(t);
}
if (num == margs.size())
return some_expr(mtype);;
lean_assert(!m_tc->next_cnstr()); // make sure there are no pending constraints
// We must create a scope to make sure no constraints "leak" into the current state.
type_checker::scope scope(*m_tc);
auto new_mtype = ensure_sufficient_args_core(mtype, 0, margs);
if (!new_mtype)
return none_expr();
while (auto c = m_tc->next_cnstr())
cs.push_back(update_justification(*c, mk_composite1(c->get_justification(), j)));
return new_mtype;
}
/**
\see mk_flex_rigid_app_cnstrs
When using "imitation" for solving a constraint
?m l_1 ... l_k =?= f a_1 ... a_n
We say argument a_i is "easy" if
1) it is a local constant
2) there is only one l_j equal to a_i.
3) none of the l_j's is of the form (?m ...)
In our experiments, the vast majority (> 2/3 of all cases) of the arguments are easy.
margs contains l_1 ... l_k
arg is the argument we are testing
Result: none if it is not an easy argument, and variable #k-i-1 if it is easy.
The variable is the "solution".
*/
optional<expr> is_easy_flex_rigid_arg(buffer<expr> const & margs, expr const & arg) {
if (!is_local(arg))
return none_expr();
optional<expr> v;
unsigned num_margs = margs.size();
for (unsigned j = 0; j < num_margs; j++) {
if (is_meta(margs[j]))
return none_expr();
if (is_local(margs[j]) && mlocal_name(arg) == mlocal_name(margs[j])) {
if (v)
return none_expr(); // failed, there is more than one possibility
v = mk_var(num_margs - j - 1);
}
}
return v;
}
/**
\brief Given
m := a metavariable ?m
margs := [a_1 ... a_k]
rhs := (g b_1 ... b_n)
Then create the constraints
(?m_1 a_1 ... a_k) =?= b_1
...
(?m_n a_1 ... a_k) =?= b_n
?m =?= fun (x_1 ... x_k), f (?m_1 x_1 ... x_k) ... (?m_n x_1 ... x_k)
Remark: we try to minimize the number of constraints (?m_i a_1 ... a_k) =?= b_i by detecting "easy" cases
that can be solved immediately. See \c is_easy_flex_rigid_arg
Remark: The term f is:
- g (if g is a constant), OR
- variable (if g is a local constant equal to a_i)
*/
void mk_flex_rigid_app_cnstrs(expr const & m, buffer<expr> const & margs, expr const & f, expr const & rhs, justification const & j,
buffer<constraints> & alts) {
lean_assert(is_metavar(m));
lean_assert(is_app(rhs));
lean_assert(is_constant(f) || is_var(f));
buffer<constraint> cs;
expr mtype = mlocal_type(m);
auto new_mtype = ensure_sufficient_args(mtype, margs, cs, j);
if (!new_mtype) return;
mtype = *new_mtype;
buffer<expr> rargs;
get_app_args(rhs, rargs);
buffer<expr> sargs;
for (expr const & rarg : rargs) {
if (auto v = is_easy_flex_rigid_arg(margs, rarg)) {
sargs.push_back(*v);
} else {
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()));
}
}
expr v = mk_app(f, sargs);
v = mk_lambda_for(mtype, v);
cs.push_back(mk_eq_cnstr(m, v, j));
alts.push_back(to_list(cs.begin(), cs.end()));
}
/**
\brief Given
m := a metavariable ?m
margs := [a_1 ... a_k]
rhs := (fun/Pi (y : A), B y)
Then create the constraints
(?m_1 a_1 ... a_k) =?= A
(?m_2 a_1 ... a_k l) =?= B l
?m =?= fun (x_1 ... x_k), fun/Pi (y : ?m_1 x_1 ... x_k), ?m_2 x_1 ... x_k y
where l is a fresh local constant.
*/
void mk_bindings_imitation(expr const & m, buffer<expr> const & margs, expr const & rhs, justification const & j,
buffer<constraints> & alts) {
lean_assert(is_metavar(m));
lean_assert(is_binding(rhs));
buffer<constraint> cs;
expr mtype = mlocal_type(m);
auto new_mtype = ensure_sufficient_args(mtype, margs, cs, j);
if (!new_mtype) return;
mtype = *new_mtype;
expr maux1 = mk_aux_metavar_for(m_ngen, mtype);
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(m_ngen, mtype2);
expr new_local = mk_local_for(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));
v = mk_lambda_for(mtype, v);
cs.push_back(mk_eq_cnstr(m, v, j));
alts.push_back(to_list(cs.begin(), cs.end()));
}
/**
\brief Given
m := a metavariable ?m
rhs := sort, constant
Then solve (?m a_1 ... a_k) =?= rhs, by returning the constraint
?m =?= fun (x1 ... x_k), rhs
*/
void mk_simple_imitation(expr const & m, expr const & rhs, justification const & j, buffer<constraints> & alts) {
lean_assert(is_metavar(m));
lean_assert(is_sort(rhs) || is_constant(rhs));
expr const & mtype = mlocal_type(m);
buffer<constraint> cs;
cs.push_back(mk_eq_cnstr(m, mk_lambda_for(mtype, rhs), j));
alts.push_back(to_list(cs.begin(), cs.end()));
}
/**
\brief Given
m := a metavariable ?m
margs := [a_1 ... a_k]
rhs := M(b_1 ... b_n) where M is a macro with arguments b_1 ... b_n
Then create the constraints
(?m_1 a_1 ... a_k) =?= b_1
...
(?m_n a_1 ... a_k) =?= b_n
?m =?= fun (x_1 ... x_k), M((?m_1 x_1 ... x_k) ... (?m_n x_1 ... x_k))
*/
void mk_macro_imitation(expr const & m, buffer<expr> const & margs, expr const & rhs, justification const & j,
buffer<constraints> & alts) {
lean_assert(is_metavar(m));
lean_assert(is_macro(rhs));
buffer<constraint> cs;
expr mtype = mlocal_type(m);
auto new_mtype = ensure_sufficient_args(mtype, margs, cs, j);
if (!new_mtype) return;
mtype = *new_mtype;
// 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(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()));
}
expr v = mk_macro(macro_def(rhs), sargs.size(), sargs.data());
v = mk_lambda_for(mtype, v);
cs.push_back(mk_eq_cnstr(m, v, j));
alts.push_back(to_list(cs.begin(), cs.end()));
}
/**
Given,
m := a metavariable ?m
margs := [a_1 ... a_k]
We say a unification problem (?m a_1 ... a_k) =?= rhs uses "simple projections" when
If (rhs and a_i are *not* local constants) OR (rhs is a local constant and a_i is a metavariable application),
then we add the constraints
a_i =?= rhs
?m =?= fun x_1 ... x_k, x_i
to alts as a possible solution.
If rhs is a local constant and a_i == rhs, then we add the constraint
?m =?= fun x_1 ... x_k, x_i
to alts as a possible solution when a_i is the same local constant or a metavariable application
*/
void mk_simple_projections(expr const & m, buffer<expr> const & margs, expr const & rhs, justification const & j,
buffer<constraints> & alts) {
lean_assert(is_metavar(m));
lean_assert(!is_meta(rhs));
expr const & mtype = mlocal_type(m);
unsigned i = margs.size();
while (i > 0) {
unsigned vidx = margs.size() - i;
--i;
expr const & marg = margs[i];
if ((!is_local(marg) && !is_local(rhs)) || (is_meta(marg) && is_local(rhs))) {
// if rhs is not local, then we only add projections for the nonlocal arguments of lhs
buffer<constraint> cs;
if (auto new_mtype = ensure_sufficient_args(mtype, margs, cs, j)) {
cs.push_back(mk_eq_cnstr(marg, rhs, j));
expr v = mk_lambda_for(*new_mtype, mk_var(vidx));
cs.push_back(mk_eq_cnstr(m, v, j));
alts.push_back(to_list(cs.begin(), cs.end()));
}
} else if (is_local(marg) && is_local(rhs) && mlocal_name(marg) == mlocal_name(rhs)) {
// if the argument is local, and rhs is equal to it, then we also add a projection
buffer<constraint> cs;
if (auto new_mtype = ensure_sufficient_args(mtype, margs, cs, j)) {
expr v = mk_lambda_for(*new_mtype, mk_var(vidx));
cs.push_back(mk_eq_cnstr(m, v, j));
alts.push_back(to_list(cs.begin(), cs.end()));
}
}
}
}
/** \brief Process a flex rigid constraint */
bool process_flex_rigid(expr const & lhs, expr const & rhs, justification const & j) {
lean_assert(is_meta(lhs));
lean_assert(!is_meta(rhs));
buffer<expr> margs;
expr m = get_app_args(lhs, margs);
for (expr & marg : margs)
marg = m_tc->whnf(marg);
buffer<constraints> alts;
switch (rhs.kind()) {
case expr_kind::Var: case expr_kind::Meta:
lean_unreachable(); // LCOV_EXCL_LINE
case expr_kind::Local:
mk_simple_projections(m, margs, rhs, j, alts);
break;
case expr_kind::Sort: case expr_kind::Constant:
mk_simple_projections(m, margs, rhs, j, alts);
mk_simple_imitation(m, rhs, j, alts);
break;
case expr_kind::Pi: case expr_kind::Lambda:
mk_simple_projections(m, margs, rhs, j, alts);
mk_bindings_imitation(m, margs, rhs, j, alts);
break;
case expr_kind::Macro:
mk_simple_projections(m, margs, rhs, j, alts);
mk_macro_imitation(m, margs, rhs, j, alts);
break;
case expr_kind::App: {
expr const & f = get_app_fn(rhs);
if (is_local(f)) {
unsigned i = margs.size();
while (i > 0) {
unsigned vidx = margs.size() - i;
--i;
expr const & marg = margs[i];
if (is_local(marg) && mlocal_name(marg) == mlocal_name(f))
mk_flex_rigid_app_cnstrs(m, margs, mk_var(vidx), rhs, j, alts);
}
} else if (is_constant(f)) {
mk_simple_projections(m, margs, rhs, j, alts);
mk_flex_rigid_app_cnstrs(m, margs, f, rhs, j, alts);
} else {
expr new_rhs = m_tc->whnf(rhs);
lean_assert(new_rhs != rhs);
return is_def_eq(lhs, new_rhs, j);
}
break;
}}
if (alts.empty()) {
set_conflict(j);
return false;
} else if (alts.size() == 1) {
// we don't need to create a backtracking point
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 simple_case_split(*this, j, to_list(alts.begin() + 1, alts.end()))));
return process_constraints(alts[0], a);
}
}
/** \brief Process a flex rigid constraint */
bool process_flex_rigid(constraint const & c) {
lean_assert(is_flex_rigid(c));
expr lhs = cnstr_lhs_expr(c);
expr rhs = cnstr_rhs_expr(c);
if (is_meta(lhs))
return process_flex_rigid(lhs, rhs, c.get_justification());
else
return process_flex_rigid(rhs, lhs, c.get_justification());
}
bool process_flex_flex(constraint const & c) {
expr const & lhs = cnstr_lhs_expr(c);
expr const & rhs = cnstr_rhs_expr(c);
// We ignore almost all flex-flex constraints.
// We just handle flex_flex "first-order" case
// ?M_1 l_1 ... l_k =?= ?M_2 l_1 ... l_k
if (!is_simple_meta(lhs) || !is_simple_meta(rhs))
return true;
buffer<expr> lhs_args, rhs_args;
expr ml = get_app_args(lhs, lhs_args);
expr mr = get_app_args(rhs, rhs_args);
if (ml == mr || lhs_args.size() != rhs_args.size())
return true;
lean_assert(!m_subst.is_assigned(ml));
lean_assert(!m_subst.is_assigned(mr));
unsigned i = 0;
for (; i < lhs_args.size(); i++)
if (lhs_args[i] != rhs_args[i])
break;
if (i == lhs_args.size())
return assign(ml, mr, c.get_justification());
return true;
}
void consume_tc_cnstrs() {
while (true) {
if (in_conflict())
return;
if (auto c = m_tc->next_cnstr()) {
process_constraint(*c);
} else {
break;
}
}
}
/** \brief Process the next constraint in the constraint queue m_cnstrs */
bool process_next() {
lean_assert(!m_cnstrs.empty());
constraint c = m_cnstrs.min()->first;
m_cnstrs.erase_min();
if (is_choice_cnstr(c)) {
return process_choice_constraint(c);
} else {
auto r = instantiate_metavars(c);
c = r.first;
lean_assert(!m_tc->next_cnstr());
bool modified = r.second;
if (is_level_eq_cnstr(c)) {
if (modified)
return process_constraint(c);
else
return process_plugin_constraint(c);
} else {
lean_assert(is_eq_cnstr(c));
if (is_delta_cnstr(c))
return process_delta(c);
else if (modified)
return is_def_eq(cnstr_lhs_expr(c), cnstr_rhs_expr(c), c.get_justification());
else if (is_flex_rigid(c))
return process_flex_rigid(c);
else if (is_flex_flex(c))
return process_flex_flex(c);
else
return process_plugin_constraint(c);
}
}
}
/** \brief Return true if unifier may be able to produce more solutions */
bool more_solutions() const {
return !in_conflict() || !m_case_splits.empty();
}
/** \brief Produce the next solution */
optional<substitution> next() {
if (!more_solutions())
return failure();
if (!m_first && !m_case_splits.empty()) {
justification all_assumptions;
for (auto const & cs : m_case_splits)
all_assumptions = mk_composite1(all_assumptions, mk_assumption_justification(cs->m_assumption_idx));
set_conflict(all_assumptions);
if (!resolve_conflict())
return failure();
} else if (m_first) {
m_first = false;
} else {
// This is not the first run, and there are no case-splits.
// We don't throw an exception since there are no more solutions.
return optional<substitution>();
}
while (true) {
consume_tc_cnstrs();
if (!in_conflict()) {
if (m_cnstrs.empty())
break;
process_next();
}
if (in_conflict() && !resolve_conflict())
return failure();
}
lean_assert(!in_conflict());
lean_assert(m_cnstrs.empty());
return optional<substitution>(m_subst.forget_justifications());
}
};
lazy_list<substitution> unify(std::shared_ptr<unifier_fn> u) {
if (!u->more_solutions()) {
u->failure(); // make sure exception is thrown if u->m_use_exception is true
return lazy_list<substitution>();
} else {
return mk_lazy_list<substitution>([=]() {
auto s = u->next();
if (s)
return some(mk_pair(*s, unify(u)));
else
return lazy_list<substitution>::maybe_pair();
});
}
}
lazy_list<substitution> unify(environment const & env, unsigned num_cs, constraint const * cs, name_generator const & ngen,
bool use_exception, unsigned max_steps) {
return unify(std::make_shared<unifier_fn>(env, num_cs, cs, ngen, substitution(), use_exception, max_steps));
}
lazy_list<substitution> unify(environment const & env, unsigned num_cs, constraint const * cs, name_generator const & ngen,
bool use_exception, options const & o) {
return unify(env, num_cs, cs, ngen, use_exception, get_unifier_max_steps(o));
}
lazy_list<substitution> unify(environment const & env, expr const & lhs, expr const & rhs, name_generator const & ngen, substitution const & s,
unsigned max_steps) {
substitution new_s = s;
expr _lhs = new_s.d_instantiate(lhs);
expr _rhs = new_s.d_instantiate(rhs);
auto u = std::make_shared<unifier_fn>(env, 0, nullptr, ngen, new_s, false, max_steps);
if (!u->m_tc->is_def_eq(_lhs, _rhs))
return lazy_list<substitution>();
else
return unify(u);
}
lazy_list<substitution> unify(environment const & env, expr const & lhs, expr const & rhs, name_generator const & ngen,
substitution const & s, options const & o) {
return unify(env, lhs, rhs, ngen, s, get_unifier_max_steps(o));
}
static int unify_simple(lua_State * L) {
int nargs = lua_gettop(L);
std::pair<unify_status, substitution> r;
if (nargs == 2)
r = unify_simple(to_substitution(L, 1), to_constraint(L, 2));
else if (nargs == 3 && is_expr(L, 2))
r = unify_simple(to_substitution(L, 1), to_expr(L, 2), to_expr(L, 3), justification());
else if (nargs == 3 && is_level(L, 2))
r = unify_simple(to_substitution(L, 1), to_level(L, 2), to_level(L, 3), justification());
else if (is_expr(L, 2))
r = unify_simple(to_substitution(L, 1), to_expr(L, 2), to_expr(L, 3), to_justification(L, 4));
else
r = unify_simple(to_substitution(L, 1), to_level(L, 2), to_level(L, 3), to_justification(L, 4));
push_integer(L, static_cast<unsigned>(r.first));
push_substitution(L, r.second);
return 2;
}
typedef lazy_list<substitution> substitution_seq;
DECL_UDATA(substitution_seq)
static const struct luaL_Reg substitution_seq_m[] = {
{"__gc", substitution_seq_gc},
{0, 0}
};
static int substitution_seq_next(lua_State * L) {
substitution_seq seq = to_substitution_seq(L, lua_upvalueindex(1));
substitution_seq::maybe_pair p;
p = seq.pull();
if (p) {
push_substitution_seq(L, p->second);
lua_replace(L, lua_upvalueindex(1));
push_substitution(L, p->first);
} else {
lua_pushnil(L);
}
return 1;
}
static int push_substitution_seq_it(lua_State * L, substitution_seq const & seq) {
push_substitution_seq(L, seq);
lua_pushcclosure(L, &safe_function<substitution_seq_next>, 1); // create closure with 1 upvalue
return 1;
}
static void to_constraint_buffer(lua_State * L, int idx, buffer<constraint> & cs) {
luaL_checktype(L, idx, LUA_TTABLE);
lua_pushvalue(L, idx); // put table on top of the stack
int n = objlen(L, idx);
for (int i = 1; i <= n; i++) {
lua_rawgeti(L, -1, i);
cs.push_back(to_constraint(L, -1));
lua_pop(L, 1);
}
lua_pop(L, 1);
}
#if 0
static constraints to_constraints(lua_State * L, int idx) {
buffer<constraint> cs;
to_constraint_buffer(L, idx, cs);
return to_list(cs.begin(), cs.end());
}
static unifier_plugin to_unifier_plugin(lua_State * L, int idx) {
luaL_checktype(L, idx, LUA_TFUNCTION); // user-fun
luaref f(L, idx);
return unifier_plugin([=](constraint const & c, name_generator const & ngen) {
lua_State * L = f.get_state();
f.push();
push_constraint(L, c);
push_name_generator(L, ngen);
pcall(L, 2, 1, 0);
lazy_list<constraints> r;
if (is_constraint(L, -1)) {
// single constraint
r = lazy_list<constraints>(constraints(to_constraint(L, -1)));
} else if (lua_istable(L, -1)) {
int num = objlen(L, -1);
if (num == 0) {
// empty table
r = lazy_list<constraints>();
} else {
lua_rawgeti(L, -1, 1);
if (is_constraint(L, -1)) {
// array of constraints case
lua_pop(L, 1);
r = lazy_list<constraints>(to_constraints(L, -1));
} else {
lua_pop(L, 1);
buffer<constraints> css;
// array of array of constraints
for (int i = 1; i <= num; i++) {
lua_rawgeti(L, -1, i);
css.push_back(to_constraints(L, -1));
lua_pop(L, 1);
}
r = to_lazy(to_list(css.begin(), css.end()));
}
}
} else if (lua_isnil(L, -1)) {
// nil case
r = lazy_list<constraints>();
} else {
throw exception("invalid unifier plugin, the result value must be a constrant, "
"nil, an array of constraints, or an array of arrays of constraints");
}
lua_pop(L, 1);
return r;
});
}
#endif
static name g_tmp_prefix = name::mk_internal_unique_name();
static int unify(lua_State * L) {
int nargs = lua_gettop(L);
lazy_list<substitution> r;
environment const & env = to_environment(L, 1);
if (is_expr(L, 2)) {
if (nargs == 6)
r = unify(env, to_expr(L, 2), to_expr(L, 3), to_name_generator(L, 4), to_substitution(L, 5), to_options(L, 6));
else
r = unify(env, to_expr(L, 2), to_expr(L, 3), to_name_generator(L, 4), to_substitution(L, 5), options());
} else {
buffer<constraint> cs;
to_constraint_buffer(L, 2, cs);
if (nargs == 4)
r = unify(env, cs.size(), cs.data(), to_name_generator(L, 3), false, to_options(L, 4));
else
r = unify(env, cs.size(), cs.data(), to_name_generator(L, 3), false, options());
}
return push_substitution_seq_it(L, r);
}
void open_unifier(lua_State * L) {
luaL_newmetatable(L, substitution_seq_mt);
lua_pushvalue(L, -1);
lua_setfield(L, -2, "__index");
setfuncs(L, substitution_seq_m, 0);
SET_GLOBAL_FUN(substitution_seq_pred, "is_substitution_seq");
SET_GLOBAL_FUN(unify_simple, "unify_simple");
SET_GLOBAL_FUN(unify, "unify");
lua_newtable(L);
SET_ENUM("Solved", unify_status::Solved);
SET_ENUM("Failed", unify_status::Failed);
SET_ENUM("Unsupported", unify_status::Unsupported);
lua_setglobal(L, "unify_status");
}
}