feat(library/tactic): add generalize tactic, closes #34

Remark: the intros tactic has been added in a different commit: 7d0100a340

library/tools/tactic.lean

@@ -48,6 +48,7 @@ opaque definition apply   (e : expr) : tactic := builtin
 opaque definition rapply  (e : expr) : tactic := builtin
 opaque definition rename  (a b : expr) : tactic := builtin
 opaque definition intro   (e : expr) : tactic := builtin
+opaque definition generalize (e : expr) : tactic := builtin
 
 inductive expr_list : Type :=
 nil  : expr_list,

src/emacs/lean-syntax.el

@@ -119,7 +119,7 @@
      ;; tactics
      (,(rx (not (any "\.")) word-start
            (or "\\b.*_tac" "Cond" "or_else" "then" "try" "when" "assumption" "rapply" "apply" "rename" "intro" "intros"
-               "back" "beta" "done" "exact" "repeat")
+               "generalize" "back" "beta" "done" "exact" "repeat")
            word-end)
       . 'font-lock-constant-face)
      ;; Types

src/library/tactic/CMakeLists.txt

@@ -1,6 +1,6 @@
 add_library(tactic goal.cpp proof_state.cpp tactic.cpp elaborate.cpp
 apply_tactic.cpp intros_tactic.cpp rename_tactic.cpp trace_tactic.cpp
-exact_tactic.cpp unfold_tactic.cpp expr_to_tactic.cpp util.cpp
-init_module.cpp)
+exact_tactic.cpp unfold_tactic.cpp generalize_tactic.cpp
+expr_to_tactic.cpp util.cpp init_module.cpp)
 
 target_link_libraries(tactic ${LEAN_LIBS})

src/library/tactic/generalize_tactic.cpp

@@ -0,0 +1,56 @@
+/*
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#include "kernel/abstract.h"
+#include "library/reducible.h"
+#include "library/tactic/elaborate.h"
+#include "library/tactic/expr_to_tactic.h"
+
+namespace lean {
+tactic generalize_tactic(elaborate_fn const & elab, expr const & e, name const & x) {
+    return tactic01([=](environment const & env, io_state const & ios, proof_state const & s) {
+            proof_state new_s = s;
+            if (auto new_e = elaborate_with_respect_to(env, ios, elab, new_s, e)) {
+                name_generator ngen = new_s.get_ngen();
+                substitution subst  = new_s.get_subst();
+                goals const & gs    = new_s.get_goals();
+                goal const & g      = head(gs);
+                auto tc     = mk_type_checker(env, ngen.mk_child());
+                auto e_t_cs = tc->infer(*new_e);
+                if (e_t_cs.second)
+                    return none_proof_state(); // constraints were generated
+                expr e_t    = e_t_cs.first;
+                expr t      = subst.instantiate(g.get_type());
+                name n;
+                if (is_constant(e))
+                    n = const_name(e);
+                else if (is_local(e))
+                    n = local_pp_name(e);
+                else
+                    n = x;
+                expr new_t = mk_pi(n, e_t, abstract(t, *new_e));
+                expr new_m = g.mk_meta(ngen.next(), new_t);
+                expr new_v = g.abstract(mk_app(new_m, *new_e));
+                subst.assign(g.get_name(), new_v);
+                goal new_g(new_m, new_t);
+                return some(proof_state(new_s, goals(new_g, tail(gs)), subst, ngen));
+            }
+            return none_proof_state();
+        });
+}
+
+void initialize_generalize_tactic() {
+    register_tac(name({"tactic", "generalize"}),
+                 [](type_checker &, elaborate_fn const & fn, expr const & e, pos_info_provider const *) {
+                     check_tactic_expr(app_arg(e), "invalid 'generalize' tactic, invalid argument");
+                     // TODO(Leo): allow user to provide name to abstract variable
+                     return generalize_tactic(fn, get_tactic_expr_expr(app_arg(e)), "x");
+                 });
+}
+
+void finalize_generalize_tactic() {
+}
+}

src/library/tactic/generalize_tactic.h

@@ -0,0 +1,14 @@
+/*
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#pragma once
+#include "library/tactic/elaborate.h"
+
+namespace lean {
+tactic generalize_tactic(elaborate_fn const & elab, expr const & e);
+void initialize_generalize_tactic();
+void finalize_generalize_tactic();
+}

src/library/tactic/init_module.cpp

@@ -12,6 +12,7 @@ Author: Leonardo de Moura
 #include "library/tactic/trace_tactic.h"
 #include "library/tactic/exact_tactic.h"
 #include "library/tactic/unfold_tactic.h"
+#include "library/tactic/generalize_tactic.h"
 
 namespace lean {
 void initialize_tactic_module() {
@@ -23,9 +24,11 @@ void initialize_tactic_module() {
     initialize_trace_tactic();
     initialize_exact_tactic();
     initialize_unfold_tactic();
+    initialize_generalize_tactic();
 }
 
 void finalize_tactic_module() {
+    finalize_generalize_tactic();
     finalize_unfold_tactic();
     finalize_exact_tactic();
     finalize_trace_tactic();

tests/lean/run/get_tac1.lean

@@ -0,0 +1,11 @@
+import hott.path tools.tactic
+open path
+
+definition concat_pV_p {A : Type} {x y z : A} (p : x ≈ z) (q : y ≈ z) : (p ⬝ q⁻¹) ⬝ q ≈ p :=
+begin
+  generalize p,
+  apply (path.induction_on q),
+  intro p,
+  apply (path.induction_on p),
+  apply idp
+end