# HG changeset patch
# User blanchet
# Date 1350412268 -7200
# Node ID a6ebdaf8e2679977cfee762923330849be3c09f4
# Parent  946efb120c42c488aa51e71cdc5382fd06b5243c
added missing file

diff -r 946efb120c42 -r a6ebdaf8e267 src/HOL/Tools/Sledgehammer/sledgehammer_reconstruct.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_reconstruct.ML	Tue Oct 16 20:31:08 2012 +0200
@@ -0,0 +1,414 @@
+(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_reconstruct.ML
+    Author:     Jasmin Blanchette, TU Muenchen
+    Author:     Steffen Juilf Smolka, TU Muenchen
+
+*)
+
+signature SLEDGEHAMMER_PROOF_RECONSTRUCT =
+sig
+  type isar_params = ATP_Proof_Reconstruct.isar_params
+  type one_line_params = ATP_Proof_Reconstruct.one_line_params
+  val isar_proof_text :
+    Proof.context -> bool -> isar_params -> 
+      one_line_params -> string
+  val proof_text :
+    Proof.context -> bool -> isar_params -> 
+      int -> one_line_params -> string
+end;
+
+structure Sledgehammer_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT =
+struct
+
+open ATP_Util
+open ATP_Proof
+open ATP_Problem_Generate
+open ATP_Proof_Reconstruct
+open String_Redirect
+
+(** Type annotations **)
+
+fun post_traverse_term_type' f _ (t as Const (_, T)) s = f t T s
+  | post_traverse_term_type' f _ (t as Free (_, T)) s = f t T s
+  | post_traverse_term_type' f _ (t as Var (_, T)) s = f t T s
+  | post_traverse_term_type' f env (t as Bound i) s = f t (nth env i) s
+  | post_traverse_term_type' f env (Abs (x, T1, b)) s =
+    let
+      val ((b', s'), T2) = post_traverse_term_type' f (T1 :: env) b s
+    in f (Abs (x, T1, b')) (T1 --> T2) s' end
+  | post_traverse_term_type' f env (u $ v) s =
+    let
+      val ((u', s'), Type (_, [_, T])) = post_traverse_term_type' f env u s
+      val ((v', s''), _) = post_traverse_term_type' f env v s'
+    in f (u' $ v') T s'' end
+
+fun post_traverse_term_type f s t =
+  post_traverse_term_type' (fn t => fn T => fn s => (f t T s, T)) [] t s |> fst
+fun post_fold_term_type f s t =
+  post_traverse_term_type (fn t => fn T => fn s => (t, f t T s)) s t |> snd
+
+(* Data structures, orders *)
+val cost_ord = prod_ord int_ord (prod_ord int_ord int_ord)
+
+structure Var_Set_Tab = Table(
+  type key = indexname list
+  val ord = list_ord Term_Ord.fast_indexname_ord)
+
+(* (1) Generalize Types *)
+fun generalize_types ctxt t =
+  t |> map_types (fn _ => dummyT)
+    |> Syntax.check_term
+         (Proof_Context.set_mode Proof_Context.mode_pattern ctxt)
+
+(* (2) Typing-spot Table *)
+local
+fun key_of_atype (TVar (idxn, _)) =
+    Ord_List.insert Term_Ord.fast_indexname_ord idxn
+  | key_of_atype _ = I
+fun key_of_type T = fold_atyps key_of_atype T []
+fun update_tab t T (tab, pos) =
+  (case key_of_type T of
+     [] => tab
+   | key =>
+     let val cost = (size_of_typ T, (size_of_term t, pos)) in
+       case Var_Set_Tab.lookup tab key of
+         NONE => Var_Set_Tab.update_new (key, cost) tab
+       | SOME old_cost =>
+         (case cost_ord (cost, old_cost) of
+            LESS => Var_Set_Tab.update (key, cost) tab
+          | _ => tab)
+     end,
+   pos + 1)
+in
+val typing_spot_table =
+  post_fold_term_type update_tab (Var_Set_Tab.empty, 0) #> fst
+end
+
+(* (3) Reverse-Greedy *)
+fun reverse_greedy typing_spot_tab =
+  let
+    fun update_count z =
+      fold (fn tvar => fn tab =>
+        let val c = Vartab.lookup tab tvar |> the_default 0 in
+          Vartab.update (tvar, c + z) tab
+        end)
+    fun superfluous tcount =
+      forall (fn tvar => the (Vartab.lookup tcount tvar) > 1)
+    fun drop_superfluous (tvars, (_, (_, spot))) (spots, tcount) =
+      if superfluous tcount tvars then (spots, update_count ~1 tvars tcount)
+      else (spot :: spots, tcount)
+    val (typing_spots, tvar_count_tab) =
+      Var_Set_Tab.fold
+        (fn kv as (k, _) => apfst (cons kv) #> apsnd (update_count 1 k))
+        typing_spot_tab ([], Vartab.empty)
+      |>> sort_distinct (rev_order o cost_ord o pairself snd)
+  in fold drop_superfluous typing_spots ([], tvar_count_tab) |> fst end
+
+(* (4) Introduce Annotations *)
+fun introduce_annotations thy spots t t' =
+  let
+    val get_types = post_fold_term_type (K cons) []
+    fun match_types tp =
+      fold (Sign.typ_match thy) (op ~~ (pairself get_types tp)) Vartab.empty
+    fun unica' b x [] = if b then [x] else []
+      | unica' b x (y :: ys) =
+        if x = y then unica' false x ys
+        else unica' true y ys |> b ? cons x
+    fun unica ord xs =
+      case sort ord xs of x :: ys => unica' true x ys | [] => []
+    val add_all_tfree_namesT = fold_atyps (fn TFree (x, _) => cons x | _ => I)
+    fun erase_unica_tfrees env =
+      let
+        val unica =
+          Vartab.fold (add_all_tfree_namesT o snd o snd) env []
+          |> unica fast_string_ord
+        val erase_unica = map_atyps
+          (fn T as TFree (s, _) =>
+              if Ord_List.member fast_string_ord unica s then dummyT else T
+            | T => T)
+      in Vartab.map (K (apsnd erase_unica)) env end
+    val env = match_types (t', t) |> erase_unica_tfrees
+    fun get_annot env (TFree _) = (false, (env, dummyT))
+      | get_annot env (T as TVar (v, S)) =
+        let val T' = Envir.subst_type env T in
+          if T' = dummyT then (false, (env, dummyT))
+          else (true, (Vartab.update (v, (S, dummyT)) env, T'))
+        end
+      | get_annot env (Type (S, Ts)) =
+        (case fold_rev (fn T => fn (b, (env, Ts)) =>
+                  let
+                    val (b', (env', T)) = get_annot env T
+                  in (b orelse b', (env', T :: Ts)) end)
+                Ts (false, (env, [])) of
+           (true, (env', Ts)) => (true, (env', Type (S, Ts)))
+         | (false, (env', _)) => (false, (env', dummyT)))
+    fun post1 _ T (env, cp, ps as p :: ps', annots) =
+        if p <> cp then
+          (env, cp + 1, ps, annots)
+        else
+          let val (_, (env', T')) = get_annot env T in
+            (env', cp + 1, ps', (p, T') :: annots)
+          end
+      | post1 _ _ accum = accum
+    val (_, _, _, annots) = post_fold_term_type post1 (env, 0, spots, []) t'
+    fun post2 t _ (cp, annots as (p, T) :: annots') =
+        if p <> cp then (t, (cp + 1, annots))
+        else (Type.constraint T t, (cp + 1, annots'))
+      | post2 t _ x = (t, x)
+  in post_traverse_term_type post2 (0, rev annots) t |> fst end
+
+(* (5) Annotate *)
+fun annotate_types ctxt t =
+  let
+    val thy = Proof_Context.theory_of ctxt
+    val t' = generalize_types ctxt t
+    val typing_spots =
+      t' |> typing_spot_table
+         |> reverse_greedy
+         |> sort int_ord
+  in introduce_annotations thy typing_spots t t' end
+
+fun string_for_proof ctxt type_enc lam_trans i n =
+  let
+    fun fix_print_mode f x =
+      Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
+                               (print_mode_value ())) f x
+    fun do_indent ind = replicate_string (ind * indent_size) " "
+    fun do_free (s, T) =
+      maybe_quote s ^ " :: " ^
+      maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
+    fun do_label l = if l = no_label then "" else string_for_label l ^ ": "
+    fun do_have qs =
+      (if member (op =) qs Moreover then "moreover " else "") ^
+      (if member (op =) qs Ultimately then "ultimately " else "") ^
+      (if member (op =) qs Then then
+         if member (op =) qs Show then "thus" else "hence"
+       else
+         if member (op =) qs Show then "show" else "have")
+    val do_term =
+      maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
+      o annotate_types ctxt
+    val reconstr = Metis (type_enc, lam_trans)
+    fun do_facts (ls, ss) =
+      reconstructor_command reconstr 1 1 [] 0
+          (ls |> sort_distinct (prod_ord string_ord int_ord),
+           ss |> sort_distinct string_ord)
+    and do_step ind (Fix xs) =
+        do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
+      | do_step ind (Let (t1, t2)) =
+        do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
+      | do_step ind (Assume (l, t)) =
+        do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
+      | do_step ind (Prove (qs, l, t, By_Metis facts)) =
+        do_indent ind ^ do_have qs ^ " " ^
+        do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
+      | do_step ind (Prove (qs, l, t, Case_Split (proofs, facts))) =
+        implode (map (prefix (do_indent ind ^ "moreover\n") o do_block ind)
+                     proofs) ^
+        do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
+        do_facts facts ^ "\n"
+    and do_steps prefix suffix ind steps =
+      let val s = implode (map (do_step ind) steps) in
+        replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
+        String.extract (s, ind * indent_size,
+                        SOME (size s - ind * indent_size - 1)) ^
+        suffix ^ "\n"
+      end
+    and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
+    (* One-step proofs are pointless; better use the Metis one-liner
+       directly. *)
+    and do_proof [Prove (_, _, _, By_Metis _)] = ""
+      | do_proof proof =
+        (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
+        do_indent 0 ^ "proof -\n" ^ do_steps "" "" 1 proof ^ do_indent 0 ^
+        (if n <> 1 then "next" else "qed")
+  in do_proof end
+
+fun min_local ctxt type_enc lam_trans proof =
+  let
+    (* Merging spots, greedy algorithm *)
+    fun cost (Prove (_, _ , t, _)) = Term.size_of_term t
+      | cost _ = ~1
+    fun can_merge (Prove (_, lbl, _, By_Metis _))  (Prove (_, _, _, By_Metis _)) =
+      (lbl = no_label)
+      | can_merge _ _ = false
+    val merge_spots = 
+      fold_index 
+        (fn (i, s2) => fn (s1, pile) => (s2, pile |> can_merge s1 s2 ? cons (i, cost s1)))
+        (tl proof) (hd proof, [])
+    |> snd |> sort (rev_order o int_ord o pairself snd) |> map fst
+
+    (* Enrich context with facts *)
+    val thy = Proof_Context.theory_of ctxt
+    fun sorry t = Skip_Proof.make_thm thy (HOLogic.mk_Trueprop t) (* FIXME: mk_Trueprop always ok? *)
+    fun enrich_ctxt' (Prove (_, lbl, t, _)) ctxt = 
+      if lbl = no_label then ctxt 
+      else Proof_Context.put_thms false (string_for_label lbl, SOME [sorry t]) ctxt
+      | enrich_ctxt' _ ctxt = ctxt
+    val rich_ctxt = fold enrich_ctxt' proof ctxt
+
+    (* Timing *)
+    fun take_time tac arg =
+      let
+        val t_start = Timing.start ()
+      in
+        (tac arg ; Timing.result t_start |> #cpu)
+      end
+    fun try_metis (Prove (qs, _, t, By_Metis fact_names)) s0 =
+      let
+        fun thmify (Prove (_, _, t, _)) = sorry t
+        val facts = fact_names |>> map string_for_label
+                               |> op@
+                               |> map (Proof_Context.get_thm rich_ctxt)
+                               |> (if member op= qs Then 
+                                   then cons (the s0 |> thmify)
+                                   else I)
+        val goal = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop t) (* FIXME: mk_Trueprop always ok? *)
+        fun tac {context = ctxt, prems = _} =
+          Metis_Tactic.metis_tac [type_enc] lam_trans ctxt facts 1
+      in
+        take_time (fn () => goal tac)
+      end
+  
+    (* Merging *)
+    fun merge (Prove (qs1, _, _, By_Metis (ls1, ss1))) 
+              (Prove (qs2, lbl , t, By_Metis (ls2, ss2))) =
+      let
+        val qs = (inter op= qs1 qs2) (* FIXME: Is this correct? *)
+          |> member op= (union op= qs1 qs2) Ultimately ? cons Ultimately
+          |> member op= qs2 Show ? cons Show
+      in Prove (qs, lbl, t, By_Metis (ls1@ls2, ss1@ss2)) end
+    fun try_merge proof i =
+      let
+        val (front, s0, s1, s2, tail) = 
+          case (proof, i) of
+            ((s1::s2::proof), 0) => ([], NONE, s1, s2, proof)
+          | _ => let val (front, s0::s1::s2::tail) = chop (i-1) proof
+                 in (front, SOME s0, s1, s2, tail) end
+        val s12 = merge s1 s2
+        val t1 = try_metis s1 s0 ()
+        val t2 = try_metis s2 (SOME s1) ()
+        val tlimit = t1 + t2 |> Time.toReal |> curry Real.* 1.2 |> Time.fromReal
+      in
+        (TimeLimit.timeLimit tlimit (try_metis s12 s0) ();
+          SOME (front @ (case s0 of NONE => s12::tail | SOME s => s::s12::tail)))
+        handle _ => NONE
+      end
+    fun merge_steps proof [] = proof
+      | merge_steps proof (i::is) = 
+        case try_merge proof i of 
+          NONE => merge_steps proof is
+        | SOME proof' => merge_steps proof' (map (fn j => if j>i then j-1 else j) is)
+  in merge_steps proof merge_spots end
+
+fun isar_proof_text ctxt isar_proof_requested
+        (debug, isar_shrink_factor, pool, fact_names, sym_tab, atp_proof, goal)
+        (one_line_params as (_, _, _, _, subgoal, subgoal_count)) =
+  let
+    val isar_shrink_factor =
+      (if isar_proof_requested then 1 else 2) * isar_shrink_factor
+    val (params, hyp_ts, concl_t) = strip_subgoal ctxt goal subgoal
+    val frees = fold Term.add_frees (concl_t :: hyp_ts) []
+    val one_line_proof = one_line_proof_text 0 one_line_params
+    val type_enc =
+      if is_typed_helper_used_in_atp_proof atp_proof then full_typesN
+      else partial_typesN
+    val lam_trans = lam_trans_from_atp_proof atp_proof metis_default_lam_trans
+
+    fun isar_proof_of () =
+      let
+        val atp_proof =
+          atp_proof
+          |> clean_up_atp_proof_dependencies
+          |> nasty_atp_proof pool
+          |> map_term_names_in_atp_proof repair_name
+          |> decode_lines ctxt sym_tab
+          |> rpair [] |-> fold_rev (add_line fact_names)
+          |> repair_waldmeister_endgame
+          |> rpair [] |-> fold_rev add_nontrivial_line
+          |> rpair (0, [])
+          |-> fold_rev (add_desired_line isar_shrink_factor fact_names frees)
+          |> snd
+        val conj_name = conjecture_prefix ^ string_of_int (length hyp_ts)
+        val conjs =
+          atp_proof
+          |> map_filter (fn Inference_Step (name as (_, ss), _, _, []) =>
+                            if member (op =) ss conj_name then SOME name else NONE
+                          | _ => NONE)
+        fun dep_of_step (Definition_Step _) = NONE
+          | dep_of_step (Inference_Step (name, _, _, from)) = SOME (from, name)
+        val ref_graph = atp_proof |> map_filter dep_of_step |> make_ref_graph
+        val axioms = axioms_of_ref_graph ref_graph conjs
+        val tainted = tainted_atoms_of_ref_graph ref_graph conjs
+        val props =
+          Symtab.empty
+          |> fold (fn Definition_Step _ => I (* FIXME *)
+                    | Inference_Step ((s, _), t, _, _) =>
+                      Symtab.update_new (s,
+                          t |> fold forall_of (map Var (Term.add_vars t []))
+                            |> member (op = o apsnd fst) tainted s ? s_not))
+                  atp_proof
+        fun prop_of_clause c =
+          fold (curry s_disj) (map_filter (Symtab.lookup props o fst) c)
+               @{term False}
+        fun label_of_clause [name] = raw_label_for_name name
+          | label_of_clause c = (space_implode "___" (map fst c), 0)
+        fun maybe_show outer c =
+          (outer andalso length c = 1 andalso subset (op =) (c, conjs))
+          ? cons Show
+        fun do_have outer qs (gamma, c) =
+          Prove (maybe_show outer c qs, label_of_clause c, prop_of_clause c,
+                 By_Metis (fold (add_fact_from_dependency fact_names
+                                 o the_single) gamma ([], [])))
+        fun do_inf outer (Have z) = do_have outer [] z
+          | do_inf outer (Hence z) = do_have outer [Then] z
+          | do_inf outer (Cases cases) =
+            let val c = succedent_of_cases cases in
+              Prove (maybe_show outer c [Ultimately], label_of_clause c,
+                     prop_of_clause c,
+                     Case_Split (map (do_case false) cases, ([], [])))
+            end
+        and do_case outer (c, infs) =
+          Assume (label_of_clause c, prop_of_clause c) ::
+          map (do_inf outer) infs
+        val isar_proof =
+          (if null params then [] else [Fix params]) @
+           (ref_graph
+           |> redirect_graph axioms tainted
+           |> chain_direct_proof
+           |> map (do_inf true)
+           |> kill_duplicate_assumptions_in_proof
+           |> kill_useless_labels_in_proof
+           |> relabel_proof
+           |> min_local ctxt type_enc lam_trans)
+          |> string_for_proof ctxt type_enc lam_trans subgoal subgoal_count
+      in
+        case isar_proof of
+          "" =>
+          if isar_proof_requested then
+            "\nNo structured proof available (proof too short)."
+          else
+            ""
+        | _ =>
+          "\n\n" ^ (if isar_proof_requested then "Structured proof"
+                    else "Perhaps this will work") ^
+          ":\n" ^ Markup.markup Isabelle_Markup.sendback isar_proof
+      end
+    val isar_proof =
+      if debug then
+        isar_proof_of ()
+      else case try isar_proof_of () of
+        SOME s => s
+      | NONE => if isar_proof_requested then
+                  "\nWarning: The Isar proof construction failed."
+                else
+                  ""
+  in one_line_proof ^ isar_proof end
+
+fun proof_text ctxt isar_proof isar_params num_chained
+               (one_line_params as (preplay, _, _, _, _, _)) =
+  (if case preplay of Failed_to_Play _ => true | _ => isar_proof then
+     isar_proof_text ctxt isar_proof isar_params
+   else
+     one_line_proof_text num_chained) one_line_params
+
+end;