--- a/src/Pure/Proof/proof_rewrite_rules.ML Wed Jan 30 14:05:29 2002 +0100
+++ b/src/Pure/Proof/proof_rewrite_rules.ML Sat Feb 02 13:26:51 2002 +0100
@@ -9,7 +9,8 @@
signature PROOF_REWRITE_RULES =
sig
- val rprocs : (string * (typ list -> Proofterm.proof -> Proofterm.proof option)) list
+ val rew : bool -> typ list -> Proofterm.proof -> Proofterm.proof option
+ val rprocs : bool -> (string * (typ list -> Proofterm.proof -> Proofterm.proof option)) list
val setup : (theory -> theory) list
end;
@@ -18,100 +19,159 @@
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)
+fun rew b =
+ let
+ fun ? x = if b then Some x else None;
+ fun ax (prf as PAxm (s, prop, _)) Ts =
+ if b then PAxm (s, prop, Some Ts) else prf;
+ fun ty T = if b then
+ let val Type (_, [Type (_, [U, _]), _]) = T
+ in Some T end
+ else None;
+ val equal_intr_axm = ax equal_intr_axm [];
+ val equal_elim_axm = ax equal_elim_axm [];
+ val symmetric_axm = ax symmetric_axm [propT];
- | rew _ (PAxm ("ProtoPure.equal_elim", _, _) % Some (_ $ A) % Some (_ $ B) %%
- (PAxm ("ProtoPure.combination", _, _) % Some (Const ("Goal", _)) %
- _ % _ % _ %% (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf1) %%
- ((tg as PThm (("ProtoPure.triv_goal", _), _, _, _)) % _ %% prf2)) =
- Some (tg %> B %% (equal_elim_axm %> A %> B %% prf1 %% prf2))
+ 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 (_ $ A) % Some (_ $ B) %%
- (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %%
+ | rew' _ (PAxm ("ProtoPure.equal_elim", _, _) % Some (_ $ A) % Some (_ $ B) %%
(PAxm ("ProtoPure.combination", _, _) % Some (Const ("Goal", _)) %
- _ % _ % _ %% (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf1)) %%
- ((tg as PThm (("ProtoPure.triv_goal", _), _, _, _)) % _ %% prf2)) =
- Some (tg %> B %% (equal_elim_axm %> A %> B %%
- (symmetric_axm % None % None %% prf1) %% prf2))
+ _ % _ % _ %% (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf1) %%
+ ((tg as PThm (("ProtoPure.triv_goal", _), _, _, _)) % _ %% prf2)) =
+ Some (tg %> B %% (equal_elim_axm %> A %> B %% prf1 %% prf2))
- | 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 (_ $ A) % Some (_ $ B) %%
+ (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %%
+ (PAxm ("ProtoPure.combination", _, _) % Some (Const ("Goal", _)) %
+ _ % _ % _ %% (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf1)) %%
+ ((tg as PThm (("ProtoPure.triv_goal", _), _, _, _)) % _ %% prf2)) =
+ Some (tg %> B %% (equal_elim_axm %> A %> B %%
+ (symmetric_axm % ? B % ? A %% prf1) %% prf2))
- | rew _ (PAxm ("ProtoPure.equal_elim", _, _) % Some X % Some Y %%
- (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %%
+ | 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 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
+ (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf1) %% prf2)) =
+ let
+ val _ $ A $ C = Envir.beta_norm X;
+ val _ $ B $ D = Envir.beta_norm Y
+ in Some (AbsP ("H1", ? X, AbsP ("H2", ? B,
+ equal_elim_axm %> C %> D %% incr_pboundvars 2 0 prf2 %%
+ (PBound 1 %% (equal_elim_axm %> B %> A %%
+ (symmetric_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", _, _) % _ % _ % _ % _ %%
+ (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", ? X, AbsP ("H2", ? A,
+ equal_elim_axm %> D %> C %%
+ (symmetric_axm % ? C % ? D %% 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.symmetric", _, _) % _ % _ %%
+ | 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 %%
- (symmetric_axm % None % None %% (incr_pboundvars 1 1 prf %> Bound 0))
- %% (PBound 0 %> Bound 0))))
- end
+ (PAxm ("ProtoPure.abstract_rule", _, _) % _ % _ %% prf))) =
+ let
+ val Const (_, T) $ P = Envir.beta_norm X;
+ val _ $ Q = Envir.beta_norm Y;
+ in Some (AbsP ("H", ? X, Abst ("x", ty T,
+ 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 Const (_, T) $ P = Envir.beta_norm X;
+ val _ $ Q = Envir.beta_norm Y;
+ val t = incr_boundvars 1 P $ Bound 0;
+ val u = incr_boundvars 1 Q $ Bound 0
+ in Some (AbsP ("H", ? X, Abst ("x", ty T,
+ equal_elim_axm %> t %> u %%
+ (symmetric_axm % ? u % ? t %% (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 % ? C % ? B %% prf1) %%
+ (equal_elim_axm %> A %> B %% (symmetric_axm % ? B % ? A %% 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' _ (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %%
+ (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %% prf)) = Some prf
- | 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.equal_elim", _, _) % Some (_ $ A $ C) % Some (_ $ B $ D) %%
+ (PAxm ("ProtoPure.combination", _, _) % _ % _ % _ % _ %%
+ (PAxm ("ProtoPure.combination", _, _) % Some (Const ("==", _)) % _ % _ % _ %%
+ (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf1) %% prf2) %% prf3) %% prf4) =
+ Some (equal_elim_axm %> C %> D %% prf2 %%
+ (equal_elim_axm %> A %> C %% prf3 %%
+ (equal_elim_axm %> B %> A %% (symmetric_axm % ? A % ? B %% prf1) %% prf4)))
+
+ | rew' _ (PAxm ("ProtoPure.equal_elim", _, _) % _ % _ %%
+ (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %%
+ (PAxm ("ProtoPure.equal_elim", _, _) % Some (_ $ A $ C) % Some (_ $ B $ D) %%
+ (PAxm ("ProtoPure.combination", _, _) % _ % _ % _ % _ %%
+ (PAxm ("ProtoPure.combination", _, _) % Some (Const ("==", _)) % _ % _ % _ %%
+ (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf1) %% prf2) %% prf3)) %% prf4) =
+ Some (equal_elim_axm %> A %> B %% prf1 %%
+ (equal_elim_axm %> C %> A %% (symmetric_axm % ? A % ? C %% prf3) %%
+ (equal_elim_axm %> D %> C %% (symmetric_axm % ? C % ? D %% prf2) %% prf4)))
- | 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' _ (PAxm ("ProtoPure.equal_elim", _, _) % _ % _ %%
+ (PAxm ("ProtoPure.equal_elim", _, _) % Some (_ $ B $ D) % Some (_ $ A $ C) %%
+ (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %%
+ (PAxm ("ProtoPure.combination", _, _) % _ % _ % _ % _ %%
+ (PAxm ("ProtoPure.combination", _, _) % Some (Const ("==", _)) % _ % _ % _ %%
+ (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf1) %% prf2)) %% prf3) %% prf4) =
+ Some (equal_elim_axm %> D %> C %% (symmetric_axm % ? C % ? D %% prf2) %%
+ (equal_elim_axm %> B %> D %% prf3 %%
+ (equal_elim_axm %> A %> B %% prf1 %% prf4)))
- | rew _ _ = None;
+ | rew' _ (PAxm ("ProtoPure.equal_elim", _, _) % _ % _ %%
+ (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %%
+ (PAxm ("ProtoPure.equal_elim", _, _) % Some (_ $ B $ D) % Some (_ $ A $ C) %%
+ (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %%
+ (PAxm ("ProtoPure.combination", _, _) % _ % _ % _ % _ %%
+ (PAxm ("ProtoPure.combination", _, _) % Some (Const ("==", _)) % _ % _ % _ %%
+ (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf1) %% prf2)) %% prf3)) %% prf4) =
+ Some (equal_elim_axm %> B %> A %% (symmetric_axm % ? A % ? B %% prf1) %%
+ (equal_elim_axm %> D %> B %% (symmetric_axm % ? B % ? D %% prf3) %%
+ (equal_elim_axm %> C %> D %% prf2 %% prf4)))
-val rprocs = [("Pure/meta_equality", rew)];
-val setup = [Proofterm.add_prf_rprocs rprocs];
+ | rew' _ _ = None;
+ in rew' end;
+
+fun rprocs b = [("Pure/meta_equality", rew b)];
+val setup = [Proofterm.add_prf_rprocs (rprocs false)];
end;