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feat(kernel): add difference constraint solver with backtracking support, and justification generation, this solver will be used to check the satisfiability of universe level constraints

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-02-14 14:29:33 -08:00
parent 9f93b5d97e
commit 76b1ddb967
5 changed files with 510 additions and 4 deletions
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2
src/kernel/CMakeLists.txt
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add_library(kernel level.cpp
add_library(kernel level.cpp diff_cnstrs.cpp
# expr.cpp
# free_vars.cpp abstract.cpp instantiate.cpp
# normalizer.cpp context.cpp level.cpp object.cpp environment.cpp

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src/kernel/diff_cnstrs.cpp Normal file
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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 <algorithm>
#include <utility>
#include <unordered_map>
#include <vector>
#include "util/hash.h"
#include "util/safe_arith.h"
#include "kernel/diff_cnstrs.h"
namespace lean {
struct diff_cnstrs::imp {
typedef int edge_id;
static constexpr edge_id null_edge_id = -1;
struct edge_jst {
bool m_propagation;
union {
justification m_asserted;
edge_id m_implied_by;
};
edge_jst():m_propagation(false), m_asserted(nullptr) {}
edge_jst(justification jst):m_propagation(false), m_asserted(jst) {}
edge_jst(edge_id e_id):m_propagation(true), m_implied_by(e_id) {}
};
struct edge {
node m_source;
node m_target;
distance m_distance;
edge_jst m_justification;
edge(node s, node t, distance d, edge_jst const & j):
m_source(s), m_target(t), m_distance(d), m_justification(j) {}
};
enum class trail_kind { MkNode, AddEdge, DisableNode };
struct trail {
trail_kind m_kind;
union {
edge_id m_old_edge_id;
node m_disabled_node; // node that was disabled
};
trail(trail_kind k):m_kind(k) {}
};
typedef std::pair<node, node> node_pair;
struct node_pair_hash { unsigned operator()(node_pair const & p) const { return hash(p.first, p.second); } };
typedef std::unordered_map<std::pair<node, node>, edge_id, node_pair_hash, std::equal_to<node_pair>> distances;
typedef std::vector<edge_id> edge_ids;
new_eq_eh m_eh;
std::vector<edge> m_edges; // vector/trail of all edges
std::vector<bool> m_enabled; // map node -> bool
std::vector<edge_ids> m_incoming_edges; // map node -> incoming edges
std::vector<edge_ids> m_outgoing_edges; // map node -> outgoing edges
distances m_distances; // map node*node -> edge
std::vector<trail> m_trail_stack; // trail/undo stack
std::vector<unsigned> m_scopes;
imp(new_eq_eh const & eh):m_eh(eh) {}
imp(imp const & s, new_eq_eh const & eh):
m_eh(eh),
m_edges(s.m_edges),
m_enabled(s.m_enabled),
m_incoming_edges(s.m_incoming_edges),
m_outgoing_edges(s.m_outgoing_edges),
m_distances(s.m_distances) {
// the trail (aka backtracking stack) is not copied
}
void push_mk_node_trail() {
m_trail_stack.push_back(trail(trail_kind::MkNode));
}
void push_new_edge_trail(edge_id old_edge = null_edge_id) {
trail t(trail_kind::AddEdge);
t.m_old_edge_id = old_edge;
m_trail_stack.push_back(t);
}
void push_disable_node_trail(node n) {
trail t(trail_kind::DisableNode);
t.m_disabled_node = n;
m_trail_stack.push_back(t);
}
void undo_mk_node() {
lean_assert(!m_enabled.empty());
lean_assert(!m_incoming_edges.empty());
lean_assert(!m_outgoing_edges.empty());
lean_assert(m_incoming_edges.back().empty());
lean_assert(m_outgoing_edges.back().empty());
m_incoming_edges.pop_back();
m_outgoing_edges.pop_back();
m_enabled.pop_back();
}
void undo_disable_node(node n) {
lean_assert(n < m_enabled.size());
lean_assert(!m_enabled[n]);
m_enabled[n] = true;
}
void undo_add_edge(edge_id old_e_id) {
lean_assert(!m_edges.empty());
edge_id e_id = m_edges.size() - 1;
auto & e = m_edges.back();
node s = e.m_source;
node t = e.m_target;
auto & out = m_outgoing_edges[s];
auto & in = m_incoming_edges[t];
lean_assert_eq(m_distances[node_pair(s, t)], e_id);
if (old_e_id == null_edge_id) {
m_distances.erase(node_pair(s, t));
in.erase(std::remove(in.begin(), in.end(), e_id), in.end());
out.erase(std::remove(out.begin(), out.end(), e_id), out.end());
} else {
m_distances[node_pair(s, t)] = old_e_id;
std::replace(in.begin(), in.end(), e_id, old_e_id);
std::replace(out.begin(), out.end(), e_id, old_e_id);
}
m_edges.pop_back();
}
void push() {
m_scopes.push_back(m_trail_stack.size());
}
void pop(unsigned num_scopes) {
unsigned lvl = m_scopes.size();
lean_assert(num_scopes <= lvl);
unsigned new_lvl = lvl - num_scopes;
unsigned old_trail_sz = m_scopes[new_lvl];
unsigned i = m_trail_stack.size();
while (i > old_trail_sz) {
--i;
trail const & t = m_trail_stack.back();
switch (t.m_kind) {
case trail_kind::MkNode: undo_mk_node(); break;
case trail_kind::AddEdge: undo_add_edge(t.m_old_edge_id); break;
case trail_kind::DisableNode: undo_disable_node(t.m_disabled_node); break;
}
m_trail_stack.pop_back();
}
lean_assert(m_trail_stack.size() == old_trail_sz);
m_scopes.resize(new_lvl);
}
void disable_node(node n) {
lean_assert(n < m_enabled.size());
lean_assert(m_enabled[n]);
m_enabled[n] = false;
push_disable_node_trail(n);
}
bool is_enabled(node n) const {
lean_assert(n < m_enabled.size());
return m_enabled[n];
}
optional<distance> get_distance(node s, node t) const {
auto it = m_distances.find(node_pair(s, t));
if (it == m_distances.end())
return optional<distance>();
else
return optional<distance>(m_edges[it->second].m_distance);
}
bool is_implied(node s, node t, distance d) const {
auto d1 = get_distance(s, t);
return d1 && *d1 >= d;
}
bool is_consistent(node s, node t, distance d) const {
// we just check if t >= s - d + 1 is not implied
return !is_implied(t, s, safe_sub(1, d));
}
void check_new_eq(edge const & e) {
if (e.m_distance == 0 && e.m_source != e.m_target) {
auto d = get_distance(e.m_target, e.m_source);
if (d && *d == 0) {
// new implied equality
m_eh(e.m_source, e.m_target);
}
}
}
bool add_edge_core(edge const & e) {
node s = e.m_source;
node t = e.m_target;
auto it = m_distances.find(node_pair(s, t));
if (it == m_distances.end()) {
edge_id e_id = m_edges.size();
m_edges.push_back(e);
m_distances[node_pair(s, t)] = e_id;
m_incoming_edges[t].push_back(e_id);
m_outgoing_edges[s].push_back(e_id);
push_new_edge_trail(null_edge_id);
check_new_eq(e);
return true;
} else {
edge_id old_e_id = it->second;
distance d = e.m_distance;
if (d > m_edges[old_e_id].m_distance) {
edge_id e_id = m_edges.size();
m_edges.push_back(e);
it->second = e_id;
auto & in = m_incoming_edges[t];
auto & out = m_outgoing_edges[s];
std::replace(in.begin(), in.end(), old_e_id, e_id);
std::replace(out.begin(), out.end(), old_e_id, e_id);
push_new_edge_trail(old_e_id);
check_new_eq(e);
return true;
} else {
return false; // redundant edge
}
}
}
bool add_edge_core(node s, node t, distance d, edge_jst const & j) {
return add_edge_core(edge(s, t, d, j));
}
node mk_node() {
node n = m_enabled.size();
m_enabled.push_back(true);
m_incoming_edges.push_back(edge_ids());
m_outgoing_edges.push_back(edge_ids());
push_mk_node_trail();
add_edge_core(n, n, 0, edge_jst());
lean_assert(*get_distance(n, n) == 0);
return n;
}
void add_edge(node s, node t, distance d, justification j) {
lean_assert(is_enabled(s));
lean_assert(is_enabled(t));
lean_assert(is_consistent(s, t, d));
if (is_implied(s, t, d))
return; // redundant
edge_id new_e_id = m_edges.size();
edge_jst prop_jst(new_e_id);
buffer<edge> to_add;
to_add.push_back(edge(s, t, d, edge_jst(j)));
for (auto in_id : m_incoming_edges[s]) {
edge & e = m_edges[in_id];
if (is_enabled(e.m_source) && e.m_source != s)
to_add.emplace_back(e.m_source, t, safe_add(e.m_distance, d), prop_jst);
}
for (auto out_id : m_outgoing_edges[t]) {
edge & e = m_edges[out_id];
if (is_enabled(e.m_target) && t != e.m_target)
to_add.emplace_back(s, e.m_target, safe_add(e.m_distance, d), prop_jst);
}
for (auto const & e : to_add) {
auto old_d = get_distance(e.m_source, e.m_target);
if (!old_d || e.m_distance > *old_d)
add_edge_core(e);
}
}
void explain(node s, node t, buffer<justification> & js) const {
if (s != t) {
buffer<node_pair> todo;
todo.push_back(node_pair(s, t));
while (!todo.empty()) {
node s = todo.back().first;
node t = todo.back().second;
edge_id e_id = m_distances.find(todo.back())->second;
todo.pop_back();
edge const & e = m_edges[e_id];
edge_jst j = e.m_justification;
if (!j.m_propagation && j.m_asserted != nullptr) {
js.push_back(j.m_asserted);
} else {
edge const & e1 = m_edges[j.m_implied_by];
if (e1.m_source != e1.m_target)
todo.push_back(node_pair(e1.m_source, e1.m_target));
if (s != e1.m_source)
todo.push_back(node_pair(s, e1.m_source));
if (e1.m_target != t)
todo.push_back(node_pair(e1.m_target, t));
}
}
}
}
void display(std::ostream & out) const {
for (node n = 0; n < m_outgoing_edges.size(); n++) {
if (is_enabled(n)) {
for (edge_id e_id : m_outgoing_edges[n]) {
auto const & e = m_edges[e_id];
lean_assert(e.m_source == n);
if (e.m_target != n && is_enabled(e.m_target))
out << "n" << n << " + " << e.m_distance << " <= n" << e.m_target << "\n";
}
}
}
}
};
diff_cnstrs::diff_cnstrs(new_eq_eh const & eh):m_ptr(new imp(eh)) {}
diff_cnstrs::diff_cnstrs(diff_cnstrs const & s, new_eq_eh const & eh):m_ptr(new imp(*s.m_ptr, eh)) {}
diff_cnstrs::~diff_cnstrs() {}
diff_cnstrs::node diff_cnstrs::mk_node() { return m_ptr->mk_node(); }
void diff_cnstrs::add_edge(node s, node t, distance d, justification j) { m_ptr->add_edge(s, t, d, j); }
void diff_cnstrs::disable_node(node n) { m_ptr->disable_node(n); }
void diff_cnstrs::push() { m_ptr->push(); }
void diff_cnstrs::pop(unsigned num_scopes) { m_ptr->pop(num_scopes); }
optional<diff_cnstrs::distance> diff_cnstrs::get_distance(node s, node t) const { return m_ptr->get_distance(s, t); }
bool diff_cnstrs::is_enabled(node n) const { return m_ptr->is_enabled(n); }
void diff_cnstrs::explain(node s, node t, buffer<justification> & js) const { m_ptr->explain(s, t, js); }
bool diff_cnstrs::is_implied(node s, node t, distance d) const { return m_ptr->is_implied(s, t, d); }
bool diff_cnstrs::is_consistent(node s, node t, distance d) const { return m_ptr->is_consistent(s, t, d); }
void diff_cnstrs::display(std::ostream & out) const { m_ptr->display(out); }
}

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src/kernel/diff_cnstrs.h Normal file
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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
*/
#pragma once
#include <memory>
#include "util/optional.h"
#include "util/buffer.h"
namespace lean {
class diff_cnstrs {
struct imp;
std::unique_ptr<imp> m_ptr;
public:
typedef unsigned node;
/**
\brief The justifications are "opaque" to this module.
From the point of view of this module, they are just markers.
*/
typedef void * justification;
typedef int distance;
/**
\brief Event handler for implied equalities.
*/
typedef std::function<void(node, node)> new_eq_eh;
/**
\brief Create an empty set of constraints. The "customer" can provide
an event handler that will be invoked whenever an equality between two nodes
is inferred.
*/
diff_cnstrs(new_eq_eh const & eh = [](node, node) {});
diff_cnstrs(diff_cnstrs const & s, new_eq_eh const & eh = [](node, node) {});
~diff_cnstrs();
/**
\brief Create a new node.
*/
node mk_node();
/**
\brief Disable a node created using \c mk_node.
\remark We cannot add edges between disabled nodes.
\pre is_enabled(n)
*/
void disable_node(node n);
/**
\brief Return true iff the given node is enabled.
*/
bool is_enabled(node n) const;
/**
\brief Add an edge <tt>s -d-> t</tt> with justification \c j.
The edge can be viewed as an inequality <tt>s + d <= t</tt>.
\remark This method assumes that the new edge would not produce
a "positive cycle". A positive cycle in the graph is an "inconsistency"
of the form <tt>k <= 0</tt>, where \c k is a positive number.
\pre is_consistent(s, t, d)
\pre is_enabled(s)
\pre is_enabled(t)
*/
void add_edge(node s, node t, distance d, justification j);
/**
\brief Create a backtracking point.
*/
void push();
/**
\brief Restore backtracking point. This method undoes the \c mk_node,
\c disable_node and \c add_edge operations between
this call and the matching \c push.
*/
void pop(unsigned num_scopes = 1);
/**
\brief Return the distance between \c s and \c t.
If the result is none, then the distance is "infinite", i.e.,
there is no path between \c s and \c t.
The distance \c d between \c s and \c t can be viewed as
an inequality <tt>s + d <= t</tt>, and this is the "best"
inequality implied by the already added edges. By best,
we mean, forall d1 > d, !is_implied(s, t, d1)
*/
optional<distance> get_distance(node s, node t) const;
/**
\brief Return true iff the already added edges imply
that distance between \c s and \c t is at least \c d
*/
bool is_implied(node s, node t, distance d) const;
/**
\brief Return true iff by adding the edge s -d-> t we don't
create a positive cycle.
This method is equivalent to <tt>!is_implied(t, s, 1-d)</tt>
*/
bool is_consistent(node s, node t, distance d) const;
/**
\brief Return a "justification" for <tt>get_distance(s, t)</tt>.
The distance is implied by a subset of edges added using
\c add_edge. This method collect the justification for each one
of theses edges in \c js.
*/
void explain(node s, node t, buffer<justification> & js) const;
/**
\brief Display the distances between all ones. This used only
for debugging purposes.
*/
void display(std::ostream & out) const;
};
}

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src/tests/kernel/CMakeLists.txt
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@ -1,3 +1,9 @@
add_executable(level level.cpp)
target_link_libraries(level ${EXTRA_LIBS})
add_test(level ${CMAKE_CURRENT_BINARY_DIR}/level)
add_executable(diff_cnstrs diff_cnstrs.cpp)
target_link_libraries(diff_cnstrs ${EXTRA_LIBS})
add_test(diff_cnstrs ${CMAKE_CURRENT_BINARY_DIR}/diff_cnstrs)
# add_executable(expr expr.cpp)
# target_link_libraries(expr ${EXTRA_LIBS})
# add_test(expr ${CMAKE_CURRENT_BINARY_DIR}/expr)
@ -12,9 +18,6 @@
# add_executable(free_vars free_vars.cpp)
# target_link_libraries(free_vars ${EXTRA_LIBS})
# add_test(free_vars ${CMAKE_CURRENT_BINARY_DIR}/free_vars)
add_executable(level level.cpp)
target_link_libraries(level ${EXTRA_LIBS})
add_test(level ${CMAKE_CURRENT_BINARY_DIR}/level)
# add_executable(replace replace.cpp)
# target_link_libraries(replace ${EXTRA_LIBS})
# add_test(replace ${CMAKE_CURRENT_BINARY_DIR}/replace)

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src/tests/kernel/diff_cnstrs.cpp Normal file
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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 "util/test.h"
#include "kernel/diff_cnstrs.h"
using namespace lean;
typedef diff_cnstrs::node node;
static void tst1() {
diff_cnstrs c([](node n1, node n2) { std::cout << "New equality: n" << n1 << " n" << n2 << "\n";});
node n0 = c.mk_node();
node n1 = c.mk_node();
node n2 = c.mk_node();
int j1; int j2;
c.add_edge(n0, n1, 10, &j1);
c.display(std::cout);
std::cout << "====\n";
c.add_edge(n1, n2, 20, &j2);
c.push();
c.display(std::cout);
node n3 = c.mk_node();
node n4 = c.mk_node();
int j3, j4, j5;
c.add_edge(n2, n3, 0, &j3);
c.add_edge(n3, n4, 0, &j4);
c.add_edge(n4, n2, 0, &j5);
std::cout << "====\n";
c.display(std::cout);
buffer<void *> js;
c.explain(n2, n4, js);
lean_assert(js.size() == 2);
lean_assert(js[0] == &j3 || js[0] == &j4);
lean_assert(js[1] == &j3 || js[1] == &j4);
lean_assert(c.is_implied(n1, n4, 10));
lean_assert(c.is_consistent(n1, n4, 100));
lean_assert(!c.is_consistent(n4, n1, 0));
c.disable_node(n1);
lean_assert(c.is_enabled(n0));
lean_assert(!c.is_enabled(n1));
node n5 = c.mk_node();
c.add_edge(n2, n5, 100, &j5);
std::cout << "====\n";
c.display(std::cout);
c.pop();
std::cout << "====\n";
c.display(std::cout);
}
int main() {
save_stack_info();
tst1();
return has_violations() ? 1 : 0;
}