src/Provers/splitter.ML
changeset 0 a5a9c433f639
child 4 2695ba9b40f7
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Provers/splitter.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,112 @@
+(*** case splitting ***)
+(*
+Use:
+
+val split_tac = mk_case_split_tac iffD;
+
+by(case_split_tac splits i);
+
+where splits = [P(elim(...)) == rhs, ...]
+      iffD  = [| P <-> Q; Q |] ==> P (* is called iffD2 in HOL *)
+
+*)
+
+fun mk_case_split_tac iffD =
+let
+
+val lift = prove_goal Pure.thy
+  "[| !!x::'b::logic. Q(x) == R(x) |] ==> P(%x.Q(x)) == P(%x.R(x))::'a::logic"
+  (fn [prem] => [rewtac prem, rtac reflexive_thm 1]);
+(*
+val iffD = prove_goal Pure.thy "[| PROP P == PROP Q; PROP Q |] ==> PROP P"
+  (fn [p1,p2] => [rtac (equal_elim (symmetric p1) p2) 1]);
+*)
+val trlift = lift RS transitive_thm;
+val _ $ (Var(P,PT)$_) $ _ = concl_of trlift;
+
+fun contains cmap =
+  let fun isin i (Abs(_,_,b)) = isin 0 b
+        | isin i (s$t) = isin (i+1) s orelse isin 0 t
+        | isin i (Const(c,_)) = (case assoc(cmap,c) of
+                                   Some(n,_) => n <= i
+                                 | None => false)
+        | isin _ _ = false
+  in isin 0 end;
+
+fun mk_context cmap Ts maxi t =
+  let fun var (t,i) = Var(("X",i),type_of1(Ts,t))
+
+      fun mka((None,i,ts),t) = if contains cmap t
+            then let val (u,T,j) = mk(t,i) in (Some(T),j,ts@[u]) end
+            else (None,i+1,ts@[var(t,i)])
+        | mka((some,i,ts),t) = (some,i+1,ts@[var(t,i)])
+      and mk(t as Abs _, i) = (Bound 0,type_of1(Ts,t),i)
+        | mk(t,i) =
+            let val (f,ts) = strip_comb t
+                val (Some(T),j,us) = foldl mka ((None,i,[]),ts)
+            in (list_comb(f,us),T,j) end
+
+      val (u,T,_) = mk(t,maxi+1)
+  in Abs("",T,u) end;
+
+fun nth_subgoal i thm = nth_elem(i-1,prems_of thm);
+
+fun goal_concl i thm = Logic.strip_assums_concl(nth_subgoal i thm);
+
+fun inst_lift cmap state lift i =
+  let val sg = #sign(rep_thm state)
+      val tsig = #tsig(Sign.rep_sg sg)
+      val goali = nth_subgoal i state
+      val Ts = map #2 (Logic.strip_params goali)
+      val _ $ t $ _ = Logic.strip_assums_concl goali;
+      val cntxt = mk_context cmap (rev Ts) (#maxidx(rep_thm lift)) t
+      val cu = Sign.cterm_of sg cntxt
+      val uT = #T(Sign.rep_cterm cu)
+      val cP' = Sign.cterm_of sg (Var(P,uT))
+      val ixnTs = Type.typ_match tsig ([],(PT,uT));
+      val ixncTs = map (fn (x,y) => (x,Sign.ctyp_of sg y)) ixnTs;
+  in instantiate (ixncTs, [(cP',cu)]) lift end;
+
+fun splittable al i thm =
+  let val tm = goal_concl i thm
+      fun nobound j k (Abs(_,_,t)) = nobound j (k+1) t
+        | nobound j k (s$t) = nobound j k s andalso nobound j k t
+        | nobound j k (Bound n) = n < k orelse k+j <= n
+        | nobound _ _ _ = true;
+      fun find j (None,t) = (case t of
+            Abs(_,_,t) => find (j+1) (None,t)
+          | _ => let val (h,args) = strip_comb t
+                     fun no() = foldl (find j) (None,args)
+                 in case h of
+                      Const(c,_) =>
+                        (case assoc(al,c) of
+                           Some(n,thm) =>
+                             if length args < n then no()
+                             else if forall (nobound j 0) (take(n,args))
+                                  then Some(thm)
+                                  else no()
+                         | None => no())
+                    | _ => no()
+                 end)
+        | find _ (some,_) = some
+  in find 0 (None,tm) end;
+
+fun split_tac [] i = no_tac
+  | split_tac splits i =
+  let fun const(thm) = let val _$(_$lhs)$_ = concl_of thm
+                           val (Const(a,_),args) = strip_comb lhs
+                       in (a,(length args,thm)) end
+      val cmap = map const splits;
+      fun lift thm = rtac (inst_lift cmap thm trlift i) i
+      fun lift_split thm =
+            case splittable cmap i thm of
+              Some(split) => rtac split i
+            | None => EVERY[STATE lift, rtac reflexive_thm (i+1),
+                            STATE lift_split]
+  in STATE(fn thm =>
+       if (i <= nprems_of thm)  andalso  contains cmap (goal_concl i thm)
+       then EVERY[rtac iffD i, STATE lift_split]
+       else no_tac)
+  end;
+
+in split_tac end;