Add datalog infrastructure for min aggregation function

This patch adds an instruction to the datalog interpreter and
constructs a new AST node for min aggregation functions.

The compiler is currently still work in progress and depends on
changes made to the handling of simple joins and the preprocessor.

Signed-off-by: Alex Horn <t-alexh@microsoft.com>

src/ast/dl_decl_plugin.cpp

@@ -44,7 +44,8 @@ namespace datalog {
         m_num_sym("N"),
         m_lt_sym("<"),
         m_le_sym("<="),
-        m_rule_sym("R")
+        m_rule_sym("R"),
+        m_min_sym("min")
     {
     }
 
@@ -490,6 +491,66 @@ namespace datalog {
         return m_manager->mk_func_decl(m_clone_sym, 1, &s, s, info);
     }
 
+    /**
+      In SMT2 syntax, we can write \c ((_ min R N) v_0 v_1 ... v_k)) where 0 <= N <= k,
+      R is a relation of sort V_0 x V_1 x ... x V_k and each v_i is a zero-arity function
+      (also known as a "constant" in SMT2 parlance) whose range is of sort V_i.
+
+      Example:
+
+        (define-sort number_t () (_ BitVec 2))
+        (declare-rel numbers (number_t number_t))
+        (declare-rel is_min (number_t number_t))
+
+        (declare-var x number_t)
+        (declare-var y number_t)
+
+        (rule (numbers #b00 #b11))
+        (rule (numbers #b00 #b01))
+
+        (rule (=> (and (numbers x y) ((_ min numbers 1) x y)) (is_min x y)))
+
+      This says that we want to find the mininum y grouped by x.
+    */
+    func_decl * dl_decl_plugin::mk_min(decl_kind k, unsigned num_parameters, parameter const * parameters) {
+        if (num_parameters < 2) {
+            m_manager->raise_exception("invalid min aggregate definition due to missing parameters");
+            return 0;
+        }
+
+        parameter const & relation_parameter = parameters[0];
+        if (!relation_parameter.is_ast() || !is_func_decl(relation_parameter.get_ast())) {
+            m_manager->raise_exception("invalid min aggregate definition, first parameter is not a function declaration");
+            return 0;
+        }
+
+        func_decl* f = to_func_decl(relation_parameter.get_ast());
+        if (!m_manager->is_bool(f->get_range())) {
+            m_manager->raise_exception("invalid min aggregate definition, first paramater must be a predicate");
+            return 0;
+        }
+
+        parameter const & min_col_parameter = parameters[1];
+        if (!min_col_parameter.is_int()) {
+            m_manager->raise_exception("invalid min aggregate definition, second parameter must be an integer");
+            return 0;
+        }
+
+        if (min_col_parameter.get_int() < 0) {
+            m_manager->raise_exception("invalid min aggregate definition, second parameter must be non-negative");
+            return 0;
+        }
+
+        if ((unsigned)min_col_parameter.get_int() >= f->get_arity()) {
+            m_manager->raise_exception("invalid min aggregate definition, second parameter exceeds the arity of the relation");
+            return 0;
+        }
+
+        func_decl_info info(m_family_id, k, num_parameters, parameters);
+        SASSERT(f->get_info() == 0);
+        return m_manager->mk_func_decl(m_min_sym, f->get_arity(), f->get_domain(), f->get_range(), info);
+    }
+
     func_decl * dl_decl_plugin::mk_func_decl(
         decl_kind k, unsigned num_parameters, parameter const * parameters, 
         unsigned arity, sort * const * domain, sort * range) {
@@ -617,6 +678,9 @@ namespace datalog {
                 break;
             }
 
+            case OP_DL_MIN:
+                return mk_min(k, num_parameters, parameters);
+
             default:
                 m_manager->raise_exception("operator not recognized");
                 return 0;
@@ -627,7 +691,7 @@ namespace datalog {
     }
 
     void dl_decl_plugin::get_op_names(svector<builtin_name> & op_names, symbol const & logic) {
-
+        op_names.push_back(builtin_name(m_min_sym.bare_str(), OP_DL_MIN));
     }
 
     void dl_decl_plugin::get_sort_names(svector<builtin_name> & sort_names, symbol const & logic) {

src/ast/dl_decl_plugin.h

@@ -50,6 +50,7 @@ namespace datalog {
         OP_DL_LT,
         OP_DL_REP,
         OP_DL_ABS,
+        OP_DL_MIN,
         LAST_RA_OP
     };
     
@@ -71,6 +72,7 @@ namespace datalog {
         symbol m_lt_sym;
         symbol m_le_sym;
         symbol m_rule_sym;
+        symbol m_min_sym;
 
         bool check_bounds(char const* msg, unsigned low, unsigned up, unsigned val) const;
         bool check_domain(unsigned low, unsigned up, unsigned val) const;
@@ -94,12 +96,69 @@ namespace datalog {
         func_decl * mk_compare(decl_kind k, symbol const& sym, sort*const* domain);
         func_decl * mk_clone(sort* r);
         func_decl * mk_rule(unsigned arity);
+        func_decl * mk_min(decl_kind k, unsigned num_parameters, parameter const * parameters);
                                 
         sort * mk_finite_sort(unsigned num_params, parameter const* params);
         sort * mk_relation_sort(unsigned num_params, parameter const* params);
         sort * mk_rule_sort();
 
     public:
+        /**
+        Is \c decl a min aggregation function?
+        */
+        static bool is_aggregate(const func_decl* const decl)
+        {
+            return decl->get_decl_kind() == OP_DL_MIN;
+        }
+
+        /**
+        \pre: is_aggregate(aggregate)
+
+        \returns function declaration of predicate which is subject to min aggregation function
+        */
+        static func_decl * min_func_decl(const func_decl* const aggregate)
+        {
+            SASSERT(is_aggregate(aggregate));
+            parameter const & relation_parameter = aggregate->get_parameter(0);
+            return to_func_decl(relation_parameter.get_ast());
+        }
+
+        /**
+        \pre: is_aggregate(aggregate)
+
+        \returns column identifier (starting at zero) which is minimized by aggregation function
+        */
+        static unsigned min_col(const func_decl* const aggregate)
+        {
+            SASSERT(is_aggregate(aggregate));
+            return (unsigned)aggregate->get_parameter(1).get_int();
+        }
+
+        /**
+        \pre: is_aggregate(aggregate)
+
+        \returns column identifiers for the "group by" in the given min aggregation function
+        */
+        static unsigned_vector group_by_cols(const func_decl* const aggregate)
+        {
+            SASSERT(is_aggregate(aggregate));
+            unsigned _min_col = min_col(aggregate);
+            if (aggregate->get_arity() == 0U)
+                return unsigned_vector();
+
+            unsigned col_num = 0;
+            unsigned_vector cols(aggregate->get_arity() - 1U);
+            for (unsigned i = 0; i < cols.size(); ++i, ++col_num)
+            {
+                if (col_num == _min_col)
+                    ++col_num;
+
+                cols[i] = col_num;
+            }
+
+            return cols;
+        }
+
         dl_decl_plugin();
         virtual ~dl_decl_plugin() {}
 

src/muz/base/dl_rule.h

@@ -346,6 +346,13 @@ namespace datalog {
 
         bool is_neg_tail(unsigned i) const { SASSERT(i < m_tail_size); return GET_TAG(m_tail[i]) == 1; }
 
+        /**
+           A predicate P(Xj) can be annotated by adding an interpreted predicate of the form ((_ min P N) ...)
+           where N is the column number that should be used for the min aggregation function.
+           Such an interpreted predicate is an example for which this function returns true.
+        */
+        bool is_min_tail(unsigned i) const { return dl_decl_plugin::is_aggregate(get_tail(i)->get_decl()); }
+
         /**
         Check whether predicate p is in the interpreted tail.
         

src/muz/base/dl_rule_set.h

@@ -179,6 +179,7 @@ namespace datalog {
         void compute_deps();
         void compute_tc_deps();
         bool stratified_negation();
+
     public:
         rule_set(context & ctx);
         rule_set(const rule_set & rs);

src/muz/rel/dl_base.cpp

@@ -485,4 +485,126 @@ namespace datalog {
         brw.mk_or(disjs.size(), disjs.c_ptr(), fml);        
     }
 
+    class table_plugin::min_fn : public table_min_fn{
+        table_signature m_sig;
+        const unsigned_vector m_group_by_cols;
+        const unsigned m_col;
+    public:
+        min_fn(const table_signature & t_sig, const unsigned_vector& group_by_cols, const unsigned col)
+            : m_sig(t_sig),
+            m_group_by_cols(group_by_cols),
+            m_col(col) {}
+
+        virtual table_base* operator()(table_base const& t) {
+            //return reference_implementation(t);
+            return reference_implementation_with_hash(t);
+        }
+
+    private:
+
+        /**
+        Reference implementation with negation:
+
+        T1 = join(T, T) by group_cols
+        T2 = { (t1,t2) in T1 | t1[col] > t2[col] }
+        T3 = { t1 | (t1,t2) in T2 }
+        T4 = T \ T3
+
+        The point of this reference implementation is to show
+        that the minimum requires negation (set difference).
+        This is relevant for fixed point computations.
+        */
+        virtual table_base * reference_implementation(const table_base & t) {
+            relation_manager & manager = t.get_manager();
+            table_join_fn * join_fn = manager.mk_join_fn(t, t, m_group_by_cols, m_group_by_cols);
+            table_base * join_table = (*join_fn)(t, t);
+
+            table_base::iterator join_table_it = join_table->begin();
+            table_base::iterator join_table_end = join_table->end();
+            table_fact row;
+
+            table_element i, j;
+
+            for (; join_table_it != join_table_end; ++join_table_it) {
+                join_table_it->get_fact(row);
+                i = row[m_col];
+                j = row[t.num_columns() + m_col];
+
+                if (i > j) {
+                    continue;
+                }
+
+                join_table->remove_fact(row);
+            }
+
+            unsigned_vector cols(t.num_columns());
+            for (unsigned k = 0; k < cols.size(); ++k) {
+                cols[k] = cols.size() + k;
+                SASSERT(cols[k] < join_table->num_columns());
+            }
+
+            table_transformer_fn * project_fn = manager.mk_project_fn(*join_table, cols);
+            table_base * gt_table = (*project_fn)(*join_table);
+
+            for (unsigned k = 0; k < cols.size(); ++k) {
+                cols[k] = k;
+                SASSERT(cols[k] < t.num_columns());
+                SASSERT(cols[k] < gt_table->num_columns());
+            }
+
+            table_base * result = t.clone();
+            table_intersection_filter_fn * diff_fn = manager.mk_filter_by_negation_fn(*result, *gt_table, cols, cols);
+            (*diff_fn)(*result, *gt_table);
+            gt_table->deallocate();
+            return result;
+        }
+
+        typedef map < table_fact, table_element, svector_hash_proc<table_element_hash>,
+            vector_eq_proc<table_fact> > group_map;
+
+        // Thanks to Nikolaj who kindly helped with the second reference implementation!
+        virtual table_base * reference_implementation_with_hash(const table_base & t) {
+            group_map group;
+            table_base::iterator it = t.begin();
+            table_base::iterator end = t.end();
+            table_fact row, row2;
+            table_element current_value, min_value;
+            for (; it != end; ++it) {
+                it->get_fact(row);
+                current_value = row[m_col];
+                group_by(row, row2);
+                group_map::entry* entry = group.find_core(row2);
+                if (!entry) {
+                    group.insert(row2, current_value);
+                }
+                else if (entry->get_data().m_value > current_value) {
+                    entry->get_data().m_value = current_value;
+                }
+            }
+            table_base* result = t.get_plugin().mk_empty(m_sig);
+            table_base::iterator it2 = t.begin();
+            for (; it2 != end; ++it2) {
+                it2->get_fact(row);
+                current_value = row[m_col];
+                group_by(row, row2);
+                VERIFY(group.find(row2, min_value));
+                if (min_value == current_value) {
+                    result->add_fact(row);
+                }
+            }
+            return result;
+        }
+
+        void group_by(table_fact const& in, table_fact& out) {
+            out.reset();
+            for (unsigned i = 0; i < m_group_by_cols.size(); ++i) {
+                out.push_back(in[m_group_by_cols[i]]);
+            }
+        }
+    };
+
+    table_min_fn * table_plugin::mk_min_fn(const table_base & t,
+        unsigned_vector & group_by_cols, const unsigned col) {
+        return alloc(table_plugin::min_fn, t.get_signature(), group_by_cols, col);
+    }
 }

src/muz/rel/dl_base.h

@@ -192,6 +192,29 @@ namespace datalog {
             virtual base_object * operator()(const base_object & t1, const base_object & t2) = 0;
         };
 
+        /**
+        \brief Aggregate minimum value
+
+        Informally, we want to group rows in a table \c t by \c group_by_cols and
+        return the minimum value in column \c col among each group.
+
+        Let \c t be a table with N columns.
+        Let \c group_by_cols be a set of column identifers for table \c t such that |group_by_cols| < N.
+        Let \c col be a column identifier for table \c t such that \c col is not in \c group_by_cols.
+
+        Let R_col be a set of rows in table \c t such that, for all rows r_i, r_j in R_col
+        and column identifiers k in \c group_by_cols, r_i[k] = r_j[k].
+
+        For each R_col, we want to restrict R_col to those rows whose value in column \c col is minimal.
+
+        min_fn(R, group_by_cols, col) =
+        { row in R | forall row' in R . row'[group_by_cols] = row[group_by_cols] => row'[col] >= row[col] }
+        */
+        class min_fn : public base_fn {
+        public:
+            virtual base_object * operator()(const base_object & t) = 0;
+        };
+
         class transformer_fn : public base_fn {
         public:
             virtual base_object * operator()(const base_object & t) = 0;
@@ -856,6 +879,7 @@ namespace datalog {
 
     typedef table_infrastructure::base_fn base_table_fn;
     typedef table_infrastructure::join_fn table_join_fn;
+    typedef table_infrastructure::min_fn table_min_fn;
     typedef table_infrastructure::transformer_fn table_transformer_fn;
     typedef table_infrastructure::union_fn table_union_fn;
     typedef table_infrastructure::mutator_fn table_mutator_fn;
@@ -1020,6 +1044,7 @@ namespace datalog {
 
     class table_plugin : public table_infrastructure::plugin_object {
         friend class relation_manager;
+        class min_fn;
     protected:
         table_plugin(symbol const& n, relation_manager & manager) : plugin_object(n, manager) {}
     public:
@@ -1027,6 +1052,9 @@ namespace datalog {
         virtual bool can_handle_signature(const table_signature & s) { return s.functional_columns()==0; }
 
     protected:
+        virtual  table_min_fn * mk_min_fn(const table_base & t,
+            unsigned_vector & group_by_cols, const unsigned col);
+
         /**
            If the returned value is non-zero, the returned object must take ownership of \c mapper.
            Otherwise \c mapper must remain unmodified.

src/muz/rel/dl_instruction.cpp

@@ -25,6 +25,7 @@ Revision History:
 #include"rel_context.h"
 #include"debug.h"
 #include"warning.h"
+#include"dl_table_relation.h"
 
 namespace datalog {
 
@@ -883,6 +884,59 @@ namespace datalog {
                 removed_cols, result);
     }
 
+    class instr_min : public instruction {
+        reg_idx m_source_reg;
+        reg_idx m_target_reg;
+        unsigned_vector m_group_by_cols;
+        unsigned m_min_col;
+    public:
+        instr_min(reg_idx source_reg, reg_idx target_reg, const unsigned_vector & group_by_cols, unsigned min_col)
+            : m_source_reg(source_reg),
+            m_target_reg(target_reg),
+            m_group_by_cols(group_by_cols),
+            m_min_col(min_col) {
+        }
+        virtual bool perform(execution_context & ctx) {
+            log_verbose(ctx);
+            if (!ctx.reg(m_source_reg)) {
+                ctx.make_empty(m_target_reg);
+                return true;
+            }
+
+            const relation_base & s = *ctx.reg(m_source_reg);
+            if (!s.from_table()) {
+                throw default_exception("relation is not a table %s",
+                    s.get_plugin().get_name().bare_str());
+            }
+            ++ctx.m_stats.m_min;
+            const table_relation & tr = static_cast<const table_relation &>(s);
+            const table_base & source_t = tr.get_table();
+            relation_manager & r_manager = s.get_manager();
+
+            const relation_signature & r_sig = s.get_signature();
+            table_min_fn * fn = r_manager.mk_min_fn(source_t, m_group_by_cols, m_min_col);
+            table_base * target_t = (*fn)(source_t);
+
+            TRACE("dl",
+                tout << "% ";
+                target_t->display(tout);
+                tout << "\n";);
+
+            relation_base * target_r = r_manager.mk_table_relation(r_sig, target_t);
+            ctx.set_reg(m_target_reg, target_r);
+            return true;
+        }
+        virtual void display_head_impl(execution_context const& ctx, std::ostream & out) const {
+            out << " MIN AGGR ";
+        }
+        virtual void make_annotations(execution_context & ctx) {
+        }
+    };
+
+    instruction * instruction::mk_min(reg_idx source, reg_idx target, const unsigned_vector & group_by_cols,
+        const unsigned min_col) {
+        return alloc(instr_min, source, target, group_by_cols, min_col);
+    }
 
     class instr_select_equal_and_project : public instruction {
         reg_idx m_src;

src/muz/rel/dl_instruction.h

@@ -93,6 +93,7 @@ namespace datalog {
             unsigned m_filter_interp_project;
             unsigned m_filter_id;
             unsigned m_filter_eq;
+            unsigned m_min;
             stats() { reset(); }
             void reset() { memset(this, 0, sizeof(*this)); }
         };
@@ -284,6 +285,8 @@ namespace datalog {
         static instruction * mk_join_project(reg_idx rel1, reg_idx rel2, unsigned joined_col_cnt,
             const unsigned * cols1, const unsigned * cols2, unsigned removed_col_cnt, 
             const unsigned * removed_cols, reg_idx result);
+        static instruction * mk_min(reg_idx source, reg_idx target, const unsigned_vector & group_by_cols,
+            const unsigned min_col);
         static instruction * mk_rename(reg_idx src, unsigned cycle_len, const unsigned * permutation_cycle, 
             reg_idx tgt);
         static instruction * mk_filter_by_negation(reg_idx tgt, reg_idx neg_rel, unsigned col_cnt,

src/muz/rel/dl_relation_manager.cpp

@@ -1021,6 +1021,11 @@ namespace datalog {
         return res;
     }
 
+    table_min_fn * relation_manager::mk_min_fn(const table_base & t,
+        unsigned_vector & group_by_cols, const unsigned col)
+    {
+        return t.get_plugin().mk_min_fn(t, group_by_cols, col);
+    }
 
     class relation_manager::auxiliary_table_transformer_fn {
         table_fact m_row;

src/muz/rel/dl_relation_manager.h

@@ -251,6 +251,9 @@ namespace datalog {
             return mk_join_fn(t1, t2, cols1.size(), cols1.c_ptr(), cols2.c_ptr(), allow_product_relation);
         }
 
+        table_min_fn * mk_min_fn(const table_base & t,
+            unsigned_vector & group_by_cols, const unsigned col);
+
         /**
             \brief Return functor that transforms a table into one that lacks columns listed in
             \c removed_cols array.

src/test/dl_table.cpp

@@ -1,4 +1,4 @@
-#ifdef _WINDOWS
+#if defined(_WINDOWS) || defined(_CYGWIN)
 #include "dl_context.h"
 #include "dl_table.h"
 #include "dl_register_engine.h"
@@ -91,9 +91,78 @@ void test_dl_bitvector_table() {
     test_table(mk_bv_table);
 }
 
+void test_table_min() {
+    std::cout << "----- test_table_min -----\n";
+    datalog::table_signature sig;
+    sig.push_back(2);
+    sig.push_back(4);
+    sig.push_back(8);
+    smt_params params;
+    ast_manager ast_m;
+    datalog::register_engine re;
+    datalog::context ctx(ast_m, re, params);
+    datalog::relation_manager & m = ctx.get_rel_context()->get_rmanager();
+
+    m.register_plugin(alloc(datalog::bitvector_table_plugin, m));
+
+    datalog::table_base* tbl = mk_bv_table(m, sig);
+    datalog::table_base& table = *tbl;
+
+    datalog::table_fact row, row1, row2, row3;
+    row.push_back(1);
+    row.push_back(2);
+    row.push_back(5);
+
+    // Group (1,2,*)
+    row1 = row;
+    row[2] = 6;
+    row2 = row;
+    row[2] = 5;
+    row3 = row;
+
+    table.add_fact(row1);
+    table.add_fact(row2);
+    table.add_fact(row3);
+
+    // Group (1,3,*)
+    row[1] = 3;
+    row1 = row;
+    row[2] = 7;
+    row2 = row;
+    row[2] = 4;
+    row3 = row;
+
+    table.add_fact(row1);
+    table.add_fact(row2);
+    table.add_fact(row3);
+
+    table.display(std::cout);
+
+    unsigned_vector group_by(2);
+    group_by[0] = 0;
+    group_by[1] = 1;
+
+    datalog::table_min_fn * min_fn = m.mk_min_fn(table, group_by, 2);
+    datalog::table_base * min_tbl = (*min_fn)(table);
+
+    min_tbl->display(std::cout);
+
+    row[1] = 2;
+    row[2] = 5;
+    SASSERT(min_tbl->contains_fact(row));
+
+    row[1] = 3;
+    row[2] = 4;
+    SASSERT(min_tbl->contains_fact(row));
+
+    dealloc(min_fn);
+    min_tbl->deallocate();
+    tbl->deallocate();
+}
 
 void tst_dl_table() {
     test_dl_bitvector_table();
+    test_table_min();
 }
 #else
 void tst_dl_table() {