Initial revision of tools for proof terms.
(* 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;