diff options
Diffstat (limited to 'src/theory/bv/equality_engine.h')
-rw-r--r-- | src/theory/bv/equality_engine.h | 564 |
1 files changed, 564 insertions, 0 deletions
diff --git a/src/theory/bv/equality_engine.h b/src/theory/bv/equality_engine.h new file mode 100644 index 000000000..03895a598 --- /dev/null +++ b/src/theory/bv/equality_engine.h @@ -0,0 +1,564 @@ +#include "cvc4_private.h" + +#pragma once + +#include <vector> +#include <ext/hash_map> + +#include "expr/node.h" +#include "context/cdo.h" +#include "util/output.h" + +namespace CVC4 { +namespace theory { +namespace bv { + +struct NodeIdTraits { + /** The null id */ + static const size_t null; // Defined in the cpp file (GCC bug) + /** Number of bits we use for the id */ + static const size_t s_id_bits = 24; + /** Number of bits we use for the size the equivalence class */ + static const size_t s_size_bits = 16; +}; + +class EqualityNode { + +public: + + /** The size of this equivalence class (if it's a representative) */ + size_t d_size : NodeIdTraits::s_size_bits; + + /** The id (in the eq-manager) of the representative equality node */ + size_t d_findId : NodeIdTraits::s_id_bits; + + /** The next equality node in this class */ + size_t d_nextId : NodeIdTraits::s_id_bits; + +public: + + /** + * Creates a new node, which is in a list of it's own. + */ + EqualityNode(size_t nodeId = NodeIdTraits::null) + : d_size(1), d_findId(nodeId), d_nextId(nodeId) {} + + inline void init(size_t nodeId) { + d_size = 1; + d_findId = d_nextId = nodeId; + } + + /** + * Returns the next node in the class circural list. + */ + inline size_t getNext() const { + return d_nextId; + } + + /** + * Returns the size of this equivalence class (only valid if this is the representative). + */ + inline size_t getSize() const { + return d_size; + } + + /** + * Merges the two lists. If add size is true the size of this node is increased by the size of + * the other node, otherwise the size is decreased by the size of the other node. + */ + template<bool addSize> + inline void merge(EqualityNode& other) { + size_t tmp = d_nextId; d_nextId = other.d_nextId; other.d_nextId = tmp; + if (addSize) { + Assert(d_size + other.d_size > d_size); + d_size += other.d_size; + } else { + Assert(d_size > other.d_size); + d_size -= other.d_size; + } + } + + /** + * Returns the class representative. + */ + inline size_t getFind() const { return d_findId; } + + /** + * Set the class representative. + */ + inline void setFind(size_t findId) { d_findId = findId; } + +}; + + +template <typename OwnerClass, typename NotifyClass> +class EqualityEngine { + + /** The class to notify when a representative changes for a term */ + NotifyClass d_notify; + + /** Map from nodes to their ids */ + __gnu_cxx::hash_map<TNode, size_t, TNodeHashFunction> d_nodeIds; + + /** Map from ids to the nodes */ + std::vector<Node> d_nodes; + + /** Map from ids to the equality nodes */ + std::vector<EqualityNode> d_equalityNodes; + + /** Number of asserted equalities we have so far */ + context::CDO<size_t> d_assertedEqualitiesCount; + + /** + * We keep a list of asserted equalities. Not among original terms, but + * among the class representatives. + */ + struct Equality { + /** Left hand side of the equality */ + size_t lhs : NodeIdTraits::s_id_bits; + /** Right hand side of the equality */ + size_t rhs : NodeIdTraits::s_id_bits; + /** Equality constructor */ + Equality(size_t lhs = NodeIdTraits::null, size_t rhs = NodeIdTraits::null) + : lhs(lhs), rhs(rhs) {} + }; + + /** The ids of the classes we have merged */ + std::vector<Equality> d_assertedEqualities; + + /** + * An edge in the equality graph. This graph is an undirected graph (both edges added) + * containing the actual asserted equalities. + */ + class EqualityEdge { + + // The id of the RHS of this equality + size_t d_nodeId : NodeIdTraits::s_id_bits; + // The next edge + size_t d_nextId : NodeIdTraits::s_id_bits; + + public: + + EqualityEdge(size_t nodeId = NodeIdTraits::null, size_t nextId = NodeIdTraits::null) + : d_nodeId(nodeId), d_nextId(nextId) {} + + /** Returns the id of the next edge */ + inline size_t getNext() const { return d_nextId; } + + /** Returns the id of the target edge node */ + inline size_t getNodeId() const { return d_nodeId; } + }; + + /** + * All the equality edges (twice as many as the number of asserted equalities. If an equality + * t1 = t2 is asserted, the edges added are -> t2, -> t1 (in this order). Hance, having the index + * of one of the edges you can reconstruct the original equality. + */ + std::vector<EqualityEdge> d_equalityEdges; + + /** + * Map from a node to it's first edge in the equality graph. Edges are added to the front of the + * list which makes the insertion/backtracking easy. + */ + std::vector<size_t> d_equalityGraph; + + /** Add an edge to the equality graph */ + inline void addGraphEdge(size_t t1, size_t t2); + + /** Returns the equality node of the given node */ + inline EqualityNode& getEqualityNode(TNode node); + + /** Returns the equality node of the given node */ + inline EqualityNode& getEqualityNode(size_t nodeId); + + /** Returns the id of the node */ + inline size_t getNodeId(TNode node) const; + + /** Merge the class2 into class1 */ + void merge(EqualityNode& class1, EqualityNode& class2); + + /** Undo the mereg of class2 into class1 */ + void undoMerge(EqualityNode& class1, EqualityNode& class2, size_t class2Id); + + /** Backtrack the information if necessary */ + void backtrack(); + + /** + * Data used in the BFS search through the equality graph. + */ + struct BfsData { + // The current node + size_t nodeId : NodeIdTraits::s_id_bits; + // The index of the edge we traversed + size_t edgeId : NodeIdTraits::s_id_bits; + // Index in the queue of the previous node. Shouldn't be too much of them, at most the size + // of the biggest equivalence class + size_t previousIndex : NodeIdTraits::s_size_bits; + + BfsData(size_t nodeId = NodeIdTraits::null, size_t edgeId = NodeIdTraits::null, size_t prev = 0) + : nodeId(nodeId), edgeId(edgeId), previousIndex(prev) {} + }; + + /** + * Trigger that will + */ + struct Trigger { + size_t class1Id : NodeIdTraits::s_id_bits; + size_t class2Id : NodeIdTraits::s_id_bits; + }; + + +public: + + /** + * Initialize the equalty engine, given the owning class. This will initialize the notifier with + * the owner information. + */ + EqualityEngine(OwnerClass& owner, context::Context* context) + : d_notify(owner), d_assertedEqualitiesCount(context, 0) {} + + /** + * Adds a term to the term database. Returns the internal id of the term. + */ + size_t addTerm(TNode t); + + /** + * Check whether the node is already in the database. + */ + inline bool hasTerm(TNode t) const; + + /** + * Adds an equality t1 = t2 to the database. + */ + void addEquality(TNode t1, TNode t2); + + /** + * Returns the representative of the term t. + */ + inline TNode getRepresentative(TNode t) const; + + /** + * Returns true if the two nodes are in the same class. + */ + inline bool areEqual(TNode t1, TNode t2) const; + + /** + * Get an explanation of the equality t1 = t2. Returns the asserted equalities that + * imply t1 = t2. Returns TNodes as the assertion equalities should be hashed somewhere + * else. TODO: mark the phantom equalities (skolems). + */ + void getExplanation(TNode t1, TNode t2, std::vector<TNode>& equalities) const; + + /** + * Adds a notify trigger for equality t1 = t2, i.e. when t1 = t2 the notify will be called with + * (t1, t2). + */ + void addTrigger(TNode t1, TNode t2); + +}; + +template <typename OwnerClass, typename NotifyClass> +size_t EqualityEngine<OwnerClass, NotifyClass>::addTerm(TNode t) { + + Debug("equality") << "addTerm(" << t << ")" << std::endl; + + // If term already added, retrurn it's id + if (hasTerm(t)) return getNodeId(t); + + // Register the new id of the term + size_t newId = d_nodes.size(); + d_nodeIds[t] = newId; + // Add the node to it's position + d_nodes.push_back(t); + // Add it to the equality graph + d_equalityGraph.push_back(NodeIdTraits::null); + // Add the equality node to the nodes + if (d_equalityNodes.size() <= newId) { + d_equalityNodes.resize(newId + 100); + } + d_equalityNodes[newId].init(newId); + // Return the id of the term + return newId; +} + +template <typename OwnerClass, typename NotifyClass> +bool EqualityEngine<OwnerClass, NotifyClass>::hasTerm(TNode t) const { + return d_nodeIds.find(t) != d_nodeIds.end(); +} + +template <typename OwnerClass, typename NotifyClass> +size_t EqualityEngine<OwnerClass, NotifyClass>::getNodeId(TNode node) const { + Assert(hasTerm(node)); + return (*d_nodeIds.find(node)).second; +} + +template <typename OwnerClass, typename NotifyClass> +EqualityNode& EqualityEngine<OwnerClass, NotifyClass>::getEqualityNode(TNode t) { + return getEqualityNode(getNodeId(t)); +} + +template <typename OwnerClass, typename NotifyClass> +EqualityNode& EqualityEngine<OwnerClass, NotifyClass>::getEqualityNode(size_t nodeId) { + Assert(nodeId < d_equalityNodes.size()); + return d_equalityNodes[nodeId]; +} + +template <typename OwnerClass, typename NotifyClass> +void EqualityEngine<OwnerClass, NotifyClass>::addEquality(TNode t1, TNode t2) { + + Debug("equality") << "addEquality(" << t1 << "," << t2 << ")" << std::endl; + + // Backtrack if necessary + backtrack(); + + // Add the terms if they are not already in the database + size_t t1Id = getNodeId(t1); + size_t t2Id = getNodeId(t2); + + // Get the representatives + size_t t1classId = getEqualityNode(t1Id).getFind(); + size_t t2classId = getEqualityNode(t2Id).getFind(); + + // If already the same, we're done + if (t1classId == t2classId) return; + + // Get the nodes of the representatives + EqualityNode& node1 = getEqualityNode(t1classId); + EqualityNode& node2 = getEqualityNode(t2classId); + + Assert(node1.getFind() == t1classId); + Assert(node2.getFind() == t2classId); + + // Depending on the size, merge them + if (node1.getSize() < node2.getSize()) { + merge(node2, node1); + d_assertedEqualities.push_back(Equality(t2classId, t1classId)); + } else { + merge(node1, node2); + d_assertedEqualities.push_back(Equality(t1classId, t2classId)); + } + + // Add the actuall equality to the equality graph + addGraphEdge(t1Id, t2Id); + + Assert(2*d_assertedEqualities.size() == d_equalityEdges.size()); + + // One more equality added + d_assertedEqualitiesCount = d_assertedEqualitiesCount + 1; +} + +template <typename OwnerClass, typename NotifyClass> +TNode EqualityEngine<OwnerClass, NotifyClass>::getRepresentative(TNode t) const { + + Debug("equality") << "getRepresentative(" << t << ")" << std::endl; + + Assert(hasTerm(t)); + + // Both following commands are semantically const + const_cast<EqualityEngine*>(this)->backtrack(); + size_t representativeId = const_cast<EqualityEngine*>(this)->getEqualityNode(t).getFind(); + + Debug("equality") << "getRepresentative(" << t << ") => " << d_nodes[representativeId] << std::endl; + + return d_nodes[representativeId]; +} + +template <typename OwnerClass, typename NotifyClass> +bool EqualityEngine<OwnerClass, NotifyClass>::areEqual(TNode t1, TNode t2) const { + Debug("equality") << "areEqual(" << t1 << "," << t2 << ")" << std::endl; + + Assert(hasTerm(t1)); + Assert(hasTerm(t2)); + + // Both following commands are semantically const + const_cast<EqualityEngine*>(this)->backtrack(); + size_t rep1 = const_cast<EqualityEngine*>(this)->getEqualityNode(t1).getFind(); + size_t rep2 = const_cast<EqualityEngine*>(this)->getEqualityNode(t2).getFind(); + + Debug("equality") << "areEqual(" << t1 << "," << t2 << ") => " << (rep1 == rep2 ? "true" : "false") << std::endl; + + return rep1 == rep2; +} + +template <typename OwnerClass, typename NotifyClass> +void EqualityEngine<OwnerClass, NotifyClass>::merge(EqualityNode& class1, EqualityNode& class2) { + + Debug("equality") << "merge(" << class1.getFind() << "," << class2.getFind() << ")" << std::endl; + + size_t class1Id = class1.getFind(); + size_t class2Id = class2.getFind(); + + // Update class2 representative information + size_t currentId = class2Id; + do { + // Get the current node + EqualityNode& currentNode = getEqualityNode(currentId); + + // Update it's find to class1 id + currentNode.setFind(class1Id); + + // Move to the next node + currentId = currentNode.getNext(); + + } while (currentId != class2Id); + + // Now merge the lists + class1.merge<true>(class2); +} + +template <typename OwnerClass, typename NotifyClass> +void EqualityEngine<OwnerClass, NotifyClass>::undoMerge(EqualityNode& class1, EqualityNode& class2, size_t class2Id) { + + Debug("equality") << "undoMerge(" << class1.getFind() << "," << class2Id << ")" << std::endl; + + // Now unmerge the lists (same as merge) + class1.merge<false>(class2); + + // Update class2 representative information + size_t currentId = class2Id; + do { + // Get the current node + EqualityNode& currentNode = getEqualityNode(currentId); + + // Update it's find to class1 id + currentNode.setFind(class2Id); + + // Move to the next node + currentId = currentNode.getNext(); + + } while (currentId != class2Id); + +} + +template <typename OwnerClass, typename NotifyClass> +void EqualityEngine<OwnerClass, NotifyClass>::backtrack() { + + // If we need to backtrack then do it + if (d_assertedEqualitiesCount < d_assertedEqualities.size()) { + + Debug("equality") << "backtrack(): nodes" << std::endl; + + for (int i = (int)d_assertedEqualities.size() - 1, i_end = (int)d_assertedEqualitiesCount; i >= i_end; --i) { + // Get the ids of the merged classes + Equality& eq = d_assertedEqualities[i]; + // Undo the merge + undoMerge(d_equalityNodes[eq.lhs], d_equalityNodes[eq.rhs], eq.rhs); + } + + d_assertedEqualities.resize(d_assertedEqualitiesCount); + + Debug("equality") << "backtrack(): edges" << std::endl; + + for (int i = (int)d_equalityEdges.size() - 2, i_end = (int)(2*d_assertedEqualitiesCount); i >= i_end; i -= 2) { + EqualityEdge& edge1 = d_equalityEdges[i]; + EqualityEdge& edge2 = d_equalityEdges[i | 1]; + d_equalityGraph[edge2.getNodeId()] = edge1.getNext(); + d_equalityGraph[edge1.getNodeId()] = edge2.getNext(); + } + + d_equalityEdges.resize(2 * d_assertedEqualitiesCount); + } + +} + +template <typename OwnerClass, typename NotifyClass> +void EqualityEngine<OwnerClass, NotifyClass>::addGraphEdge(size_t t1, size_t t2) { + size_t edge = d_equalityEdges.size(); + d_equalityEdges.push_back(EqualityEdge(t2, d_equalityGraph[t1])); + d_equalityEdges.push_back(EqualityEdge(t1, d_equalityGraph[t2])); + d_equalityGraph[t1] = edge; + d_equalityGraph[t2] = edge | 1; +} + +template <typename OwnerClass, typename NotifyClass> +void EqualityEngine<OwnerClass, NotifyClass>::getExplanation(TNode t1, TNode t2, std::vector<TNode>& equalities) const { + Assert(equalities.empty()); + Assert(t1 != t2); + Assert(getRepresentative(t1) == getRepresentative(t2)); + + Debug("equality") << "getExplanation(" << t1 << "," << t2 << ")" << std::endl; + + const_cast<EqualityEngine*>(this)->backtrack(); + + // Queue for the BFS containing nodes + std::vector<BfsData> bfsQueue; + + // The id's of the nodes + size_t t1Id = getNodeId(t1); + size_t t2Id = getNodeId(t2); + + // Find a path from t1 to t2 in the graph (BFS) + bfsQueue.push_back(BfsData(t1Id, NodeIdTraits::null, 0)); + size_t currentIndex = 0; + while (true) { + // There should always be a path, and every node can be visited only once (tree) + Assert(currentIndex < bfsQueue.size()); + + // The next node to visit + BfsData& current = bfsQueue[currentIndex]; + size_t currentNode = current.nodeId; + + Debug("equality") << "getExplanation(): currentNode: " << currentNode << std::endl; + + // Go through the equality edges of this node + size_t currentEdge = d_equalityGraph[currentNode]; + + while (currentEdge != NodeIdTraits::null) { + Debug("equality") << "getExplanation(): currentEdge: " << currentEdge << std::endl; + + // Get the edge + const EqualityEdge& edge = d_equalityEdges[currentEdge]; + + // Did we find the path + if (edge.getNodeId() == t2Id) { + + Debug("equality") << "getExplanation(): path found: " << std::endl; + + // Reconstruct the path + do { + // Get the left and right hand side from the edge + size_t firstEdge = (currentEdge >> 1) << 1; + size_t secondEdge = (currentEdge | 1); + TNode lhs = d_nodes[d_equalityEdges[secondEdge].getNodeId()]; + TNode rhs = d_nodes[d_equalityEdges[firstEdge].getNodeId()]; + // Add the actual equality to the vector + equalities.push_back(lhs.eqNode(rhs)); + + Debug("equality") << "getExplanation(): adding: " << lhs.eqNode(rhs) << std::endl; + + // Go to the previous + currentEdge = bfsQueue[currentIndex].edgeId; + currentIndex = bfsQueue[currentIndex].previousIndex; + } while (currentEdge != NodeIdTraits::null); + + // Done + return; + } + + // Push to the visitation queue if it's not the backward edge + if ((currentEdge | 1) != (current.edgeId | 1)) { + bfsQueue.push_back(BfsData(edge.getNodeId(), currentEdge, currentIndex)); + } + + // Go to the next edge + currentEdge = edge.getNext(); + } + + // Go to the next node to visit + ++ currentIndex; + } +} + +template <typename OwnerClass, typename NotifyClass> +void EqualityEngine<OwnerClass, NotifyClass>::addTrigger(TNode t1, TNode t2) { + + + +} + + + +} // Namespace bv +} // Namespace theory +} // Namespace CVC4 + |