15 structure ProofRewriteRules : PROOF_REWRITE_RULES = |
15 structure ProofRewriteRules : PROOF_REWRITE_RULES = |
16 struct |
16 struct |
17 |
17 |
18 open Proofterm; |
18 open Proofterm; |
19 |
19 |
20 fun rew _ (PThm (("ProtoPure.rev_triv_goal", _), _, _, _) %% _ % |
20 fun rew _ (PThm (("ProtoPure.rev_triv_goal", _), _, _, _) % _ %% |
21 (PThm (("ProtoPure.triv_goal", _), _, _, _) %% _ % prf)) = Some prf |
21 (PThm (("ProtoPure.triv_goal", _), _, _, _) % _ %% prf)) = Some prf |
22 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% _ %% _ % |
22 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) % _ % _ %% |
23 (PAxm ("ProtoPure.equal_intr", _, _) %% _ %% _ % prf % _)) = Some prf |
23 (PAxm ("ProtoPure.equal_intr", _, _) % _ % _ %% prf %% _)) = Some prf |
24 | rew _ (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % |
24 | rew _ (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %% |
25 (PAxm ("ProtoPure.equal_intr", _, _) %% A %% B % prf1 % prf2)) = |
25 (PAxm ("ProtoPure.equal_intr", _, _) % A % B %% prf1 %% prf2)) = |
26 Some (equal_intr_axm %% B %% A % prf2 % prf1) |
26 Some (equal_intr_axm % B % A %% prf2 %% prf1) |
27 |
27 |
28 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y % |
28 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) % Some X % Some Y %% |
29 (PAxm ("ProtoPure.combination", _, _) %% _ %% _ %% _ %% _ % |
29 (PAxm ("ProtoPure.combination", _, _) % _ % _ % _ % _ %% |
30 (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("==>", _)) %% _ %% _ %% _ % |
30 (PAxm ("ProtoPure.combination", _, _) % Some (Const ("==>", _)) % _ % _ % _ %% |
31 (PAxm ("ProtoPure.reflexive", _, _) %% _) % prf1) % prf2)) = |
31 (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf1) %% prf2)) = |
32 let |
32 let |
33 val _ $ A $ C = Envir.beta_norm X; |
33 val _ $ A $ C = Envir.beta_norm X; |
34 val _ $ B $ D = Envir.beta_norm Y |
34 val _ $ B $ D = Envir.beta_norm Y |
35 in Some (AbsP ("H1", None, AbsP ("H2", None, |
35 in Some (AbsP ("H1", None, AbsP ("H2", None, |
36 equal_elim_axm %%% C %%% D % incr_pboundvars 2 0 prf2 % |
36 equal_elim_axm %> C %> D %% incr_pboundvars 2 0 prf2 %% |
37 (PBound 1 % (equal_elim_axm %%% B %%% A % |
37 (PBound 1 %% (equal_elim_axm %> B %> A %% |
38 (symmetric_axm %% None %% None % incr_pboundvars 2 0 prf1) % PBound 0))))) |
38 (symmetric_axm % None % None %% incr_pboundvars 2 0 prf1) %% PBound 0))))) |
39 end |
39 end |
40 |
40 |
41 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y % |
41 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) % Some X % Some Y %% |
42 (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % |
42 (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %% |
43 (PAxm ("ProtoPure.combination", _, _) %% _ %% _ %% _ %% _ % |
43 (PAxm ("ProtoPure.combination", _, _) % _ % _ % _ % _ %% |
44 (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("==>", _)) %% _ %% _ %% _ % |
44 (PAxm ("ProtoPure.combination", _, _) % Some (Const ("==>", _)) % _ % _ % _ %% |
45 (PAxm ("ProtoPure.reflexive", _, _) %% _) % prf1) % prf2))) = |
45 (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf1) %% prf2))) = |
46 let |
46 let |
47 val _ $ A $ C = Envir.beta_norm Y; |
47 val _ $ A $ C = Envir.beta_norm Y; |
48 val _ $ B $ D = Envir.beta_norm X |
48 val _ $ B $ D = Envir.beta_norm X |
49 in Some (AbsP ("H1", None, AbsP ("H2", None, |
49 in Some (AbsP ("H1", None, AbsP ("H2", None, |
50 equal_elim_axm %%% D %%% C % |
50 equal_elim_axm %> D %> C %% |
51 (symmetric_axm %% None %% None % incr_pboundvars 2 0 prf2) |
51 (symmetric_axm % None % None %% incr_pboundvars 2 0 prf2) |
52 % (PBound 1 % (equal_elim_axm %%% A %%% B % incr_pboundvars 2 0 prf1 % PBound 0))))) |
52 %% (PBound 1 %% (equal_elim_axm %> A %> B %% incr_pboundvars 2 0 prf1 %% PBound 0))))) |
53 end |
53 end |
54 |
54 |
55 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y % |
55 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) % Some X % Some Y %% |
56 (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("all", _)) %% _ %% _ %% _ % |
56 (PAxm ("ProtoPure.combination", _, _) % Some (Const ("all", _)) % _ % _ % _ %% |
57 (PAxm ("ProtoPure.reflexive", _, _) %% _) % |
57 (PAxm ("ProtoPure.reflexive", _, _) % _) %% |
58 (PAxm ("ProtoPure.abstract_rule", _, _) %% _ %% _ % prf))) = |
58 (PAxm ("ProtoPure.abstract_rule", _, _) % _ % _ %% prf))) = |
59 let |
59 let |
60 val _ $ P = Envir.beta_norm X; |
60 val _ $ P = Envir.beta_norm X; |
61 val _ $ Q = Envir.beta_norm Y; |
61 val _ $ Q = Envir.beta_norm Y; |
62 in Some (AbsP ("H", None, Abst ("x", None, |
62 in Some (AbsP ("H", None, Abst ("x", None, |
63 equal_elim_axm %%% incr_boundvars 1 P $ Bound 0 %%% incr_boundvars 1 Q $ Bound 0 % |
63 equal_elim_axm %> incr_boundvars 1 P $ Bound 0 %> incr_boundvars 1 Q $ Bound 0 %% |
64 (incr_pboundvars 1 1 prf %%% Bound 0) % (PBound 0 %%% Bound 0)))) |
64 (incr_pboundvars 1 1 prf %> Bound 0) %% (PBound 0 %> Bound 0)))) |
65 end |
65 end |
66 |
66 |
67 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some X %% Some Y % |
67 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) % Some X % Some Y %% |
68 (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % |
68 (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %% |
69 (PAxm ("ProtoPure.combination", _, _) %% Some (Const ("all", _)) %% _ %% _ %% _ % |
69 (PAxm ("ProtoPure.combination", _, _) % Some (Const ("all", _)) % _ % _ % _ %% |
70 (PAxm ("ProtoPure.reflexive", _, _) %% _) % |
70 (PAxm ("ProtoPure.reflexive", _, _) % _) %% |
71 (PAxm ("ProtoPure.abstract_rule", _, _) %% _ %% _ % prf)))) = |
71 (PAxm ("ProtoPure.abstract_rule", _, _) % _ % _ %% prf)))) = |
72 let |
72 let |
73 val _ $ P = Envir.beta_norm X; |
73 val _ $ P = Envir.beta_norm X; |
74 val _ $ Q = Envir.beta_norm Y; |
74 val _ $ Q = Envir.beta_norm Y; |
75 in Some (AbsP ("H", None, Abst ("x", None, |
75 in Some (AbsP ("H", None, Abst ("x", None, |
76 equal_elim_axm %%% incr_boundvars 1 P $ Bound 0 %%% incr_boundvars 1 Q $ Bound 0 % |
76 equal_elim_axm %> incr_boundvars 1 P $ Bound 0 %> incr_boundvars 1 Q $ Bound 0 %% |
77 (symmetric_axm %% None %% None % (incr_pboundvars 1 1 prf %%% Bound 0)) |
77 (symmetric_axm % None % None %% (incr_pboundvars 1 1 prf %> Bound 0)) |
78 % (PBound 0 %%% Bound 0)))) |
78 %% (PBound 0 %> Bound 0)))) |
79 end |
79 end |
80 |
80 |
81 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some A %% Some C % |
81 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) % Some A % Some C %% |
82 (PAxm ("ProtoPure.transitive", _, _) %% _ %% Some B %% _ % prf1 % prf2) % prf3) = |
82 (PAxm ("ProtoPure.transitive", _, _) % _ % Some B % _ %% prf1 %% prf2) %% prf3) = |
83 Some (equal_elim_axm %%% B %%% C % prf2 % |
83 Some (equal_elim_axm %> B %> C %% prf2 %% |
84 (equal_elim_axm %%% A %%% B % prf1 % prf3)) |
84 (equal_elim_axm %> A %> B %% prf1 %% prf3)) |
85 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% Some A %% Some C % |
85 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) % Some A % Some C %% |
86 (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % |
86 (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %% |
87 (PAxm ("ProtoPure.transitive", _, _) %% _ %% Some B %% _ % prf1 % prf2)) % prf3) = |
87 (PAxm ("ProtoPure.transitive", _, _) % _ % Some B % _ %% prf1 %% prf2)) %% prf3) = |
88 Some (equal_elim_axm %%% B %%% C % (symmetric_axm %% None %% None % prf1) % |
88 Some (equal_elim_axm %> B %> C %% (symmetric_axm % None % None %% prf1) %% |
89 (equal_elim_axm %%% A %%% B % (symmetric_axm %% None %% None % prf2) % prf3)) |
89 (equal_elim_axm %> A %> B %% (symmetric_axm % None % None %% prf2) %% prf3)) |
90 |
90 |
91 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% _ %% _ % |
91 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) % _ % _ %% |
92 (PAxm ("ProtoPure.reflexive", _, _) %% _) % prf) = Some prf |
92 (PAxm ("ProtoPure.reflexive", _, _) % _) %% prf) = Some prf |
93 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) %% _ %% _ % |
93 | rew _ (PAxm ("ProtoPure.equal_elim", _, _) % _ % _ %% |
94 (PAxm ("ProtoPure.symmetric", _, _) %% _ %% _ % |
94 (PAxm ("ProtoPure.symmetric", _, _) % _ % _ %% |
95 (PAxm ("ProtoPure.reflexive", _, _) %% _)) % prf) = Some prf |
95 (PAxm ("ProtoPure.reflexive", _, _) % _)) %% prf) = Some prf |
96 |
96 |
97 | rew _ _ = None; |
97 | rew _ _ = None; |
98 |
98 |
99 val rprocs = [("Pure/meta_equality", rew)]; |
99 val rprocs = [("Pure/meta_equality", rew)]; |
100 |
100 |