src/Pure/Proof/proof_rewrite_rules.ML

updated;

(*  Title:      Pure/Proof/proof_rewrite_rules.ML
    ID:         $Id$
    Author:     Stefan Berghofer, TU Muenchen
    License:    GPL (GNU GENERAL PUBLIC LICENSE)

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 (_ $ 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))

  | 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 % None % None %% 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 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;