handle case where the same Skolem name is given different types in different subgoals in the new Skolemizer (this can happen if several type-instances of the same fact are needed by Metis, cf. example in "Clausify.thy") -- the solution reintroduces old code removed in a6725f293377

--- a/src/HOL/Metis_Examples/Clausify.thy	Thu Apr 14 11:24:04 2011 +0200
+++ b/src/HOL/Metis_Examples/Clausify.thy	Thu Apr 14 11:24:05 2011 +0200
@@ -8,15 +8,6 @@
 imports Complex_Main
 begin
 
-text {* Outstanding issues *}
-
-lemma ex_tl: "EX ys. tl ys = xs"
-using tl.simps(2) by fast
-
-lemma "(\<exists>ys\<Colon>nat list. tl ys = xs) \<and> (\<exists>bs\<Colon>int list. tl bs = as)"
-using [[metis_new_skolemizer = false]] (* FAILS with "= true" *)
-by (metis ex_tl)
-
 text {* Definitional CNF for goal *}
 
 (* FIXME: shouldn't need this *)
@@ -52,7 +43,7 @@
 
 lemma
   fixes x :: real
-  assumes fn_le: "!!n. f n \<le> x" and 1: "f----> lim f"
+  assumes fn_le: "!!n. f n \<le> x" and 1: "f ----> lim f"
   shows "lim f \<le> x"
 by (metis 1 LIMSEQ_le_const2 fn_le)
 
@@ -71,7 +62,13 @@
 
 lemma
   "(\<exists>x \<in> set xs. P x) \<longleftrightarrow>
-   (\<exists>ys x zs. xs = ys@x#zs \<and> P x \<and> (\<forall>z \<in> set zs. \<not> P z))"
+   (\<exists>ys x zs. xs = ys @ x # zs \<and> P x \<and> (\<forall>z \<in> set zs. \<not> P z))"
 by (metis split_list_last_prop [where P = P] in_set_conv_decomp)
 
+lemma ex_tl: "EX ys. tl ys = xs"
+using tl.simps(2) by fast
+
+lemma "(\<exists>ys\<Colon>nat list. tl ys = xs) \<and> (\<exists>bs\<Colon>int list. tl bs = as)"
+by (metis ex_tl)
+
 end

--- a/src/HOL/Tools/Metis/metis_reconstruct.ML	Thu Apr 14 11:24:04 2011 +0200
+++ b/src/HOL/Tools/Metis/metis_reconstruct.ML	Thu Apr 14 11:24:05 2011 +0200
@@ -611,7 +611,50 @@
                   (fn () => "=============================================")
     in (fol_th, th) :: thpairs end
 
-fun term_instantiate thy = cterm_instantiate o map (pairself (cterm_of thy))
+(* It is normally sufficient to apply "assume_tac" to unify the conclusion with
+   one of the premises. Unfortunately, this sometimes yields "Variable
+   ?SK_a_b_c_x has two distinct types" errors. To avoid this, we instantiate the
+   variables before applying "assume_tac". Typical constraints are of the form
+     ?SK_a_b_c_x SK_d_e_f_y ... SK_a_b_c_x ... SK_g_h_i_z =?= SK_a_b_c_x,
+   where the nonvariables are goal parameters. *)
+fun unify_first_prem_with_concl thy i th =
+  let
+    val goal = Logic.get_goal (prop_of th) i |> Envir.beta_eta_contract
+    val prem = goal |> Logic.strip_assums_hyp |> hd
+    val concl = goal |> Logic.strip_assums_concl
+    fun pair_untyped_aconv (t1, t2) (u1, u2) =
+      untyped_aconv t1 u1 andalso untyped_aconv t2 u2
+    fun add_terms tp inst =
+      if exists (pair_untyped_aconv tp) inst then inst
+      else tp :: map (apsnd (subst_atomic [tp])) inst
+    fun is_flex t =
+      case strip_comb t of
+        (Var _, args) => forall is_Bound args
+      | _ => false
+    fun unify_flex flex rigid =
+      case strip_comb flex of
+        (Var (z as (_, T)), args) =>
+        add_terms (Var z,
+          fold_rev (curry absdummy) (take (length args) (binder_types T)) rigid)
+      | _ => I
+    fun unify_potential_flex comb atom =
+      if is_flex comb then unify_flex comb atom
+      else if is_Var atom then add_terms (atom, comb)
+      else I
+    fun unify_terms (t, u) =
+      case (t, u) of
+        (t1 $ t2, u1 $ u2) =>
+        if is_flex t then unify_flex t u
+        else if is_flex u then unify_flex u t
+        else fold unify_terms [(t1, u1), (t2, u2)]
+      | (_ $ _, _) => unify_potential_flex t u
+      | (_, _ $ _) => unify_potential_flex u t
+      | (Var _, _) => add_terms (t, u)
+      | (_, Var _) => add_terms (u, t)
+      | _ => I
+    val t_inst = [] |> unify_terms (prem, concl)
+                    |> map (pairself (cterm_of thy))
+  in th |> cterm_instantiate t_inst end
 
 val copy_prem = @{lemma "P ==> (P ==> P ==> Q) ==> Q" by fast}
 
@@ -663,9 +706,7 @@
                         tyenv []
           val t_inst =
             [pairself (cterm_of thy o Envir.norm_term env) (Var var, t')]
-        in
-          th |> instantiate (ty_inst, t_inst)
-        end
+        in th |> instantiate (ty_inst, t_inst) end
       | _ => raise Fail "expected a single non-zapped, non-Metis Var"
   in
     (DETERM (etac @{thm allE} i THEN rotate_tac ~1 i)
@@ -841,6 +882,7 @@
               THEN ALLGOALS (fn i =>
                        rtac @{thm Meson.skolem_COMBK_I} i
                        THEN rotate_tac (rotation_for_subgoal i) i
+                       THEN PRIMITIVE (unify_first_prem_with_concl thy i)
                        THEN assume_tac i
                        THEN flexflex_tac)))
       handle ERROR _ =>