feat(library/tactic/rewrite_tactic): improve matcher in rewrite_tactic

closes #433

src/library/tactic/rewrite_tactic.cpp

@@ -8,6 +8,7 @@ Author: Leonardo de Moura
 #include <string>
 #include "util/interrupt.h"
 #include "util/list_fn.h"
+#include "util/rb_map.h"
 #include "util/sexpr/option_declarations.h"
 #include "kernel/instantiate.h"
 #include "kernel/abstract.h"
@@ -19,6 +20,7 @@ Author: Leonardo de Moura
 #include "library/kernel_serializer.h"
 #include "library/reducible.h"
 #include "library/util.h"
+#include "library/expr_lt.h"
 #include "library/match.h"
 #include "library/projection.h"
 #include "library/local_context.h"
@@ -730,7 +732,7 @@ class rewrite_fn {
     expr to_meta_idx(expr const & e) {
         m_lsubst.clear();
         m_esubst.clear();
-        name_map<expr>  emap;
+        rb_map<expr, expr, expr_quick_cmp>  emap;
         name_map<level> lmap;
 
         auto to_meta_idx = [&](level const & l) {
@@ -753,22 +755,27 @@ class rewrite_fn {
                 });
         };
 
+        // return true if the arguments of e are not metavar applications
+        auto no_meta_args = [&](expr const & e) {
+            buffer<expr> args;
+            get_app_args(e, args);
+            return !std::any_of(args.begin(), args.end(), [&](expr const & e) { return is_meta(e); });
+        };
+
         return replace(e, [&](expr const & e, unsigned) {
                 if (!has_metavar(e)) {
                     return some_expr(e); // done
                 } else if (is_binding(e)) {
                     throw_rewrite_exception("invalid rewrite tactic, pattern contains binders");
                 } else if (is_meta(e)) {
-                    expr const & fn = get_app_fn(e);
-                    lean_assert(is_metavar(fn));
-                    name const & n  = mlocal_name(fn);
-                    if (auto it = emap.find(n)) {
+                    if (auto it = emap.find(e)) {
                         return some_expr(*it);
                     } else {
                         unsigned next_idx = m_esubst.size();
                         expr r = mk_idx_meta(next_idx, m_tc->infer(e).first);
                         m_esubst.push_back(none_expr());
-                        emap.insert(n, r);
+                        if (no_meta_args(e))
+                            emap.insert(e, r); // cache only if arguments of e are not metavariables
                         return some_expr(r);
                     }
                 } else if (is_constant(e)) {

tests/lean/hott/433.hlean

@@ -0,0 +1,122 @@
+/-
+Copyright (c) 2014 Floris van Doorn. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Author: Floris van Doorn
+Ported from Coq HoTT
+
+Theorems about pi-types (dependent function spaces)
+-/
+import types.sigma
+
+open eq equiv is_equiv funext
+
+namespace pi
+  universe variables l k
+  variables {A A' : Type.{l}} {B : A → Type.{k}} {B' : A' → Type.{k}} {C : Πa, B a → Type}
+            {D : Πa b, C a b → Type}
+            {a a' a'' : A} {b b₁ b₂ : B a} {b' : B a'} {b'' : B a''} {f g : Πa, B a}
+
+  /- Paths -/
+
+  /- Paths [p : f ≈ g] in a function type [Πx:X, P x] are equivalent to functions taking values in path types, [H : Πx:X, f x ≈ g x], or concisely, [H : f ∼ g].
+
+  This equivalence, however, is just the combination of [apD10] and function extensionality [funext], and as such, [path_forall], et seq. are given in axioms.funext and path:  -/
+
+  /- Now we show how these things compute. -/
+
+  definition apD10_path_pi [H : funext] (h : f ∼ g) : apD10 (path_pi h) ∼ h :=
+  apD10 (retr apD10 h)
+
+  definition path_pi_eta [H : funext] (p : f = g) : path_pi (apD10 p) = p :=
+  sect apD10 p
+
+  definition path_pi_idp [H : funext] : path_pi (λx : A, refl (f x)) = refl f :=
+  !path_pi_eta
+
+  /- The identification of the path space of a dependent function space, up to equivalence, is of course just funext. -/
+
+  definition path_equiv_homotopy [H : funext] (f g : Πx, B x) : (f = g) ≃ (f ∼ g) :=
+  equiv.mk _ !funext.ap
+
+  definition is_equiv_path_pi [instance] [H : funext] (f g : Πx, B x)
+      : is_equiv (@path_pi _ _ _ f g) :=
+  inv_closed apD10
+
+  definition homotopy_equiv_path [H : funext] (f g : Πx, B x) : (f ∼ g) ≃ (f = g) :=
+  equiv.mk _ !is_equiv_path_pi
+
+
+  /- Transport -/
+
+  protected definition transport (p : a = a') (f : Π(b : B a), C a b)
+    : (transport (λa, Π(b : B a), C a b) p f)
+      ∼ (λb, transport (C a') !transport_pV (transportD _ _ p _ (f (p⁻¹ ▹ b)))) :=
+  eq.rec_on p (λx, idp)
+
+  /- A special case of [transport_pi] where the type [B] does not depend on [A],
+      and so it is just a fixed type [B]. -/
+  definition transport_constant {C : A → A' → Type} (p : a = a') (f : Π(b : A'), C a b)
+    : (eq.transport (λa, Π(b : A'), C a b) p f) ∼ (λb, eq.transport (λa, C a b) p (f b)) :=
+  eq.rec_on p (λx, idp)
+
+  /- Maps on paths -/
+
+  /- The action of maps given by lambda. -/
+  definition ap_lambdaD [H : funext] {C : A' → Type} (p : a = a') (f : Πa b, C b) :
+    ap (λa b, f a b) p = path_pi (λb, ap (λa, f a b) p) :=
+  begin
+    apply (eq.rec_on p),
+    apply inverse,
+    apply path_pi_idp
+  end
+
+  /- Dependent paths -/
+
+  /- with more implicit arguments the conclusion of the following theorem is
+     (Π(b : B a), transportD B C p b (f b) = g (eq.transport B p b)) ≃
+     (eq.transport (λa, Π(b : B a), C a b) p f = g) -/
+  definition dpath_pi [H : funext] (p : a = a') (f : Π(b : B a), C a b) (g : Π(b' : B a'), C a' b')
+    : (Π(b : B a), p ▹D (f b) = g (p ▹ b)) ≃ (p ▹ f = g) :=
+  eq.rec_on p (λg, !homotopy_equiv_path) g
+
+  section open sigma sigma.ops
+  /- more implicit arguments:
+  (Π(b : B a), eq.transport C (sigma.path p idp) (f b) = g (p ▹ b)) ≃
+  (Π(b : B a), transportD B (λ(a : A) (b : B a), C ⟨a, b⟩) p b (f b) = g (eq.transport B p b)) -/
+  definition dpath_pi_sigma {C : (Σa, B a) → Type} (p : a = a')
+    (f : Π(b : B a), C ⟨a, b⟩) (g : Π(b' : B a'), C ⟨a', b'⟩) :
+    (Π(b : B a), (sigma.path p idp) ▹ (f b) = g (p ▹ b)) ≃ (Π(b : B a), p ▹D (f b) = g (p ▹ b)) :=
+  eq.rec_on p (λg, !equiv.refl) g
+  end
+
+  variables (f0 : A' → A) (f1 : Π(a':A'), B (f0 a') → B' a')
+
+  definition transport_V [reducible] (P : A → Type) {x y : A} (p : x = y) (u : P y) : P x :=
+  p⁻¹ ▹ u
+
+  protected definition functor_pi : (Π(a:A), B a) → (Π(a':A'), B' a') := (λg a', f1 a' (g (f0 a')))
+  /- Equivalences -/
+  definition isequiv_functor_pi [instance] (f0 : A' → A) (f1 : Π(a':A'), B (f0 a') → B' a')
+    [H0 : is_equiv f0] [H1 : Πa', @is_equiv (B (f0 a')) (B' a') (f1 a')]
+      : is_equiv (functor_pi f0 f1) :=
+  begin
+  apply (adjointify (functor_pi f0 f1) (functor_pi (f0⁻¹)
+        (λ(a : A) (b' : B' (f0⁻¹ a)), transport B (retr f0 a) ((f1 (f0⁻¹ a))⁻¹ b')))),
+  intro h, apply path_pi,
+  esimp {functor_pi, function.compose}, -- simplify (and unfold function_pi and function.compose)
+  --first subgoal
+  intro a', esimp,
+  rewrite adj,
+  rewrite -transport_compose,
+  rewrite {f1 a' _}(ap_transport _ f1 _),
+  apply (transport_V (λx, sect f0 a' ▹ x = h a') (retr (f1 _) _)),
+  -- retr cannot be used as rewrite rule, the resulting type is not an equality
+  apply apD,
+  intro h, beta,
+  apply path_pi, intro a, esimp,
+  apply (transport_V (λx, retr f0 a ▹ x = h a) (sect (f1 _) _)),
+  esimp {function.id},
+  apply apD
+  end
+
+end pi