feat(library/tactic/rewrite_tactic): rewrite goal

src/library/tactic/location.cpp

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 
 Author: Leonardo de Moura
 */
+#include "kernel/replace_fn.h"
 #include "library/kernel_serializer.h"
 #include "library/tactic/location.h"
 
@@ -110,4 +111,16 @@ deserializer & operator>>(deserializer & d, location & loc) {
     loc.m_hyps = to_list(tmp);
     return d;
 }
+
+expr replace_occurrences(expr const & e, expr const & t, occurrence const & occ, unsigned idx) {
+    unsigned occ_idx = 0;
+    return replace(e, [&](expr const & e, unsigned offset) {
+            if (e == t) {
+                occ_idx++;
+                if (occ.contains(occ_idx))
+                    return some_expr(mk_var(offset+idx));
+            }
+            return none_expr();
+        });
+}
 }

src/library/tactic/location.h

@@ -49,6 +49,11 @@ public:
     friend deserializer & operator>>(deserializer & d, occurrence & o);
 };
 
+/** \brief Replace occurrences of \c t in \c e with the free variable #vidx.
+    The j-th occurrence is replaced iff occ.contains(j)
+*/
+expr replace_occurrences(expr const & e, expr const & t, occurrence const & occ, unsigned vidx);
+
 class location {
 public:
     enum kind { Everywhere, GoalOnly, AllHypotheses, Hypotheses, GoalHypotheses };

src/library/tactic/rewrite_tactic.cpp

@@ -10,6 +10,7 @@ Author: Leonardo de Moura
 #include "kernel/instantiate.h"
 #include "kernel/replace_fn.h"
 #include "kernel/for_each_fn.h"
+#include "kernel/inductive/inductive.h"
 #include "library/kernel_serializer.h"
 #include "library/reducible.h"
 #include "library/util.h"
@@ -18,6 +19,7 @@ Author: Leonardo de Moura
 #include "library/local_context.h"
 #include "library/unifier.h"
 #include "library/util.h"
+#include "library/constants.h"
 #include "library/generic_exception.h"
 #include "library/tactic/rewrite_tactic.h"
 #include "library/tactic/expr_to_tactic.h"
@@ -498,6 +500,7 @@ class rewrite_fn {
     // rule, new_t
     typedef optional<pair<expr, expr>> unify_result;
 
+    // When successful, the result is the pair (H, new_t) where (H : new_t = t)
     unify_result unify_target(expr const & t, expr const & pre_elem) {
         try {
             expr rule         = get_rewrite_rule(pre_elem);
@@ -545,9 +548,9 @@ class rewrite_fn {
                 expr lhs = app_arg(app_fn(rule_type));
                 expr rhs = app_arg(rule_type);
                 if (symm) {
-                    rule = mk_symm(*m_tc, rule);
                     return unify_result(rule, lhs);
                 } else {
+                    rule = mk_symm(*m_tc, rule);
                     return unify_result(rule, rhs);
                 }
             }
@@ -555,7 +558,7 @@ class rewrite_fn {
         return unify_result();
     }
 
-    // target, rule, new_target  : represents the rewrite rule : target = new_target
+    // target, new_target, H  : represents the rewrite H : target = new_target
     typedef optional<std::tuple<expr, expr, expr>> find_result;
 
     // Search for \c pattern in \c e. If \c t is a match, then try to unify the type of the rule
@@ -575,7 +578,7 @@ class rewrite_fn {
                         reset_subst();
                     if (r) {
                         if (auto p = unify_target(t, pre_elem)) {
-                            result = std::make_tuple(t, p->first, p->second);
+                            result = std::make_tuple(t, p->second, p->first);
                             return false;
                         }
                     }
@@ -585,73 +588,112 @@ class rewrite_fn {
         return result;
     }
 
-    bool process_rewrite_hypothesis(expr const & hyp, expr const & elem, expr const & pre_elem, expr const & pattern) {
+    /** Given (a, b, P[a], Heq : b = a, occ), return (P[b], M : P[b], H : P[a])
+        where M is a metavariable application of a fresh metavariable, and H is a witness (based on M) for P[a].
+
+        \remark occ is used to select which occurrences of a in P[a] will be replaced with b
+
+        \remark the witness \c H is used using eq.rec
+    */
+    std::tuple<expr, expr, expr> apply_rewrite(expr const & a, expr const & b, expr const & Pa, expr const & Heq, occurrence const & occ) {
+        bool has_dep_elim = inductive::has_dep_elim(m_env, get_eq_name());
+        unsigned vidx = has_dep_elim ? 1 : 0;
+        expr Px  = replace_occurrences(Pa, a, occ, vidx);
+        expr Pb  = instantiate(Px, vidx, b);
+        expr A   = m_tc->infer(a).first;
+        level l1 = sort_level(m_tc->ensure_type(Pa).first);
+        level l2 = sort_level(m_tc->ensure_type(A).first);
+        expr M   = m_g.mk_meta(m_ngen.next(), Pb);
+        expr H;
+        if (has_dep_elim) {
+            expr Haeqx = mk_app(mk_constant(get_eq_name(), {l1}), A, b, mk_var(0));
+            expr P     = mk_lambda("x", A, mk_lambda("H", Haeqx, Px));
+            H          = mk_app({mk_constant(get_eq_rec_name(), {l1, l2}), A, b, P, M, a, Heq});
+        } else {
+            H          = mk_app({mk_constant(get_eq_rec_name(), {l1, l2}), A, b, mk_lambda("x", A, Px), M, a, Heq});
+        }
+        return std::make_tuple(Pb, M, H);
+    }
+
+    bool process_rewrite_hypothesis(expr const & hyp, expr const & pre_elem, expr const & pattern, occurrence const & occ) {
         // TODO(Leo)
         return false;
     }
 
-    bool process_rewrite_goal(expr const & elem, expr const & pre_elem, expr const & pattern) {
+    bool process_rewrite_goal(expr const & pre_elem, expr const & pattern, occurrence const & occ) {
-        expr goal_type = m_g.get_type();
+        expr Pa = m_g.get_type();
-        if (auto it = find_target(goal_type, pattern, pre_elem)) {
+        if (auto it = find_target(Pa, pattern, pre_elem)) {
-            regular(m_env, m_ios) << "FOUND\n" << std::get<0>(*it) << "\n==\n" << std::get<1>(*it) << "\n==>\n" << std::get<2>(*it) << "\n";
+            expr a, Heq, b;
-            // TODO(Leo)
+            std::tie(a, b, Heq) = *it;
+            expr Pb, M, H;
+            std::tie(Pb, M, H) = apply_rewrite(a, b, Pa, Heq, occ);
+            goal new_g(M, Pb);
+            expr val = m_g.abstract(H);
+            m_subst.assign(m_g.get_name(), val);
+            update_goal(new_g);
+            // regular(m_env, m_ios) << "FOUND\n" << a << "\n==>\n" << b << "\nWITH\n" << Heq << "\n";
+            // regular(m_env, m_ios) << H << "\n";
+            return true;
         }
         return false;
     }
 
-    bool process_rewrite_single_step(expr const & elem, expr const & pre_elem, expr const & pattern) {
+    bool process_rewrite_single_step(expr const & pre_elem, expr const & pattern) {
         check_system("rewrite tactic");
-        rewrite_info const & info = get_rewrite_info(elem);
+        rewrite_info const & info = get_rewrite_info(pre_elem);
         location const & loc      = info.get_location();
         if (loc.is_goal_only())
-            return process_rewrite_goal(elem, pre_elem, pattern);
+            return process_rewrite_goal(pre_elem, pattern, *loc.includes_goal());
         bool progress = false;
         buffer<expr> hyps;
         m_g.get_hyps(hyps);
         for (expr const & h : hyps) {
-            if (!loc.includes_hypothesis(local_pp_name(h)))
+            auto occ = loc.includes_hypothesis(local_pp_name(h));
+            if (!occ)
                 continue;
-            if (process_rewrite_hypothesis(h, elem, pre_elem, pattern))
+            if (process_rewrite_hypothesis(h, pre_elem, pattern, *occ))
+                progress = true;
+        }
+        if (auto occ = loc.includes_goal()) {
+            if (process_rewrite_goal(pre_elem, pattern, *occ))
                 progress = true;
         }
-        if (loc.includes_goal() && process_rewrite_goal(elem, pre_elem, pattern))
-            progress = true;
         return progress;
     }
 
     bool process_rewrite_step(expr const & elem, expr const & pre_elem) {
         lean_assert(is_rewrite_step(elem));
         expr pattern              = get_pattern(elem);
-        regular(m_env, m_ios) << "pattern: " << pattern << "\n";
+        // regular(m_env, m_ios) << "pattern: " << pattern << "\n";
         rewrite_info const & info = get_rewrite_info(elem);
         unsigned num;
         switch (info.get_multiplicity()) {
         case rewrite_info::Once:
-            return process_rewrite_single_step(elem, pre_elem, pattern);
+            return process_rewrite_single_step(pre_elem, pattern);
         case rewrite_info::AtMostN:
             num = info.num();
             for (unsigned i = 0; i < num; i++) {
-                if (!process_rewrite_single_step(elem, pre_elem, pattern))
+                if (!process_rewrite_single_step(pre_elem, pattern))
                     return true;
             }
             return true;
         case rewrite_info::ExactlyN:
             num = info.num();
             for (unsigned i = 0; i < num; i++) {
-                if (!process_rewrite_single_step(elem, pre_elem, pattern))
+                if (!process_rewrite_single_step(pre_elem, pattern))
                     return false;
             }
             return true;
         case rewrite_info::ZeroOrMore:
             while (true) {
-                if (!process_rewrite_single_step(elem, pre_elem, pattern))
+                if (!process_rewrite_single_step(pre_elem, pattern))
                     return true;
             }
         case rewrite_info::OneOrMore:
-            if (!process_rewrite_single_step(elem, pre_elem, pattern))
+            if (!process_rewrite_single_step(pre_elem, pattern))
                 return false;
             while (true) {
-                if (!process_rewrite_single_step(elem, pre_elem, pattern))
+                if (!process_rewrite_single_step(pre_elem, pattern))
                     return true;
             }
         }
@@ -680,7 +722,6 @@ public:
     }
 
     proof_state_seq operator()(buffer<expr> const & elems) {
-        std::cout << "rewrite_tactic\n";
         buffer<expr> new_elems;
         elaborate_elems(elems, new_elems);
 
@@ -692,7 +733,9 @@ public:
             }
         }
 
-        return proof_state_seq(m_ps);
+        goals new_gs = cons(m_g, tail(m_ps.get_goals()));
+        proof_state new_ps(m_ps, new_gs, m_subst, m_ngen);
+        return proof_state_seq(new_ps);
     }
 };