src/Pure/Proof/proof_rewrite_rules.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/Proof/proof_rewrite_rules.ML	Fri Aug 31 16:17:05 2001 +0200
@@ -0,0 +1,103 @@
+(*  Title:      Pure/Proof/proof_rewrite_rules.ML
+    ID:         $Id$
+    Author:     Stefan Berghofer
+    Copyright   2000  TU Muenchen
+
+Simplification function for partial proof terms involving
+meta level rules.
+*)
+
+signature PROOF_REWRITE_RULES =
+sig
+  val rprocs : (string * (typ list -> Proofterm.proof -> Proofterm.proof option)) list
+end;
+
+structure ProofRewriteRules : PROOF_REWRITE_RULES =
+struct
+
+open Proofterm;
+
+fun rew _ (PThm (("ProtoPure.rev_triv_goal", _), _, _, _) %% _ %
+      (PThm (("ProtoPure.triv_goal", _), _, _, _) %% _ % prf)) = Some prf
+  | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% _ %% _ %
+      (PAxm ("ProtoPure.equal_intr", _, _) %% _ %% _ % prf % _)) = Some prf
+  | rew _ (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ %
+      (PAxm ("ProtoPure.equal_intr", _, _) %% A %% B % prf1 % prf2)) =
+          Some (equal_intr_axm %% B %% A % prf2 % prf1)
+
+  | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y %
+      (PAxm ("ProtoPure.combination", _, _) %% _ %% _ %% _ %% _ %
+        (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("==>", _)) %% _ %% _ %% _ %
+           (PAxm ("ProtoPure.reflexive", _, _) %% _) % prf1) % prf2)) =
+      let
+        val _ $ A $ C = Envir.beta_norm X;
+        val _ $ B $ D = Envir.beta_norm Y
+      in Some (AbsP ("H1", None, AbsP ("H2", None,
+        equal_elim_axm %%% C %%% D % incr_pboundvars 2 0 prf2 %
+          (PBound 1 % (equal_elim_axm %%% B %%% A %
+            (symmetric_axm %% None %% None % incr_pboundvars 2 0 prf1) % PBound 0)))))
+      end
+
+  | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y %
+      (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ %
+        (PAxm ("ProtoPure.combination", _, _) %% _ %% _ %% _ %% _ %
+          (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("==>", _)) %% _ %% _ %% _ %
+             (PAxm ("ProtoPure.reflexive", _, _) %% _) % prf1) % prf2))) =
+      let
+        val _ $ A $ C = Envir.beta_norm Y;
+        val _ $ B $ D = Envir.beta_norm X
+      in Some (AbsP ("H1", None, AbsP ("H2", None,
+        equal_elim_axm %%% D %%% C %
+          (symmetric_axm %% None %% None % incr_pboundvars 2 0 prf2)
+            % (PBound 1 % (equal_elim_axm %%% A %%% B % incr_pboundvars 2 0 prf1 % PBound 0)))))
+      end
+
+  | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y %
+      (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("all", _)) %% _ %% _ %% _ %
+        (PAxm ("ProtoPure.reflexive", _, _) %% _) %
+          (PAxm ("ProtoPure.abstract_rule", _, _) %% _ %% _ % prf))) =
+      let
+        val _ $ P = Envir.beta_norm X;
+        val _ $ Q = Envir.beta_norm Y;
+      in Some (AbsP ("H", None, Abst ("x", None,
+          equal_elim_axm %%% incr_boundvars 1 P $ Bound 0 %%% incr_boundvars 1 Q $ Bound 0 %
+            (incr_pboundvars 1 1 prf %%% Bound 0) % (PBound 0 %%% Bound 0))))
+      end
+
+  | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y %
+      (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ %        
+        (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("all", _)) %% _ %% _ %% _ %
+          (PAxm ("ProtoPure.reflexive", _, _) %% _) %
+            (PAxm ("ProtoPure.abstract_rule", _, _) %% _ %% _ % prf)))) =
+      let
+        val _ $ P = Envir.beta_norm X;
+        val _ $ Q = Envir.beta_norm Y;
+      in Some (AbsP ("H", None, Abst ("x", None,
+        equal_elim_axm %%% incr_boundvars 1 P $ Bound 0 %%% incr_boundvars 1 Q $ Bound 0 %
+          (symmetric_axm %% None %% None % (incr_pboundvars 1 1 prf %%% Bound 0))
+            % (PBound 0 %%% Bound 0))))
+      end
+
+  | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some A %% Some C %
+      (PAxm ("ProtoPure.transitive", _, _) %% _ %% Some B %% _ % prf1 % prf2) % prf3) =
+         Some (equal_elim_axm %%% B %%% C % prf2 %
+           (equal_elim_axm %%% A %%% B % prf1 % prf3))
+  | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some A %% Some C %
+      (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ %
+        (PAxm ("ProtoPure.transitive", _, _) %% _ %% Some B %% _ % prf1 % prf2)) % prf3) =
+         Some (equal_elim_axm %%% B %%% C % (symmetric_axm %% None %% None % prf1) %
+           (equal_elim_axm %%% A %%% B % (symmetric_axm %% None %% None % prf2) % prf3))
+
+  | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% _ %% _ %
+      (PAxm ("ProtoPure.reflexive", _, _) %% _) % prf) = Some prf
+  | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% _ %% _ %
+      (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ %
+        (PAxm ("ProtoPure.reflexive", _, _) %% _)) % prf) = Some prf
+
+  | rew _ _ = None;
+
+val rprocs = [("Pure/meta_equality", rew)];
+
+end;
+
+Proofterm.add_prf_rprocs ProtoPure.thy ProofRewriteRules.rprocs;