/usr/share/hol88-2.02.19940316/contrib/CSP/mu.ml is in hol88-contrib-source 2.02.19940316-35.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 | % Trace Semantics for the recursive process MU. %
% %
% FILE : mu.ml %
% %
% READS FILES : process_fix.th, rules_and_tacs.ml %
% LOADS LIBRARIES : sets, string %
% WRITES FILES : mu.th %
% %
% AUTHOR : Albert J Camilleri %
% AFFILIATION : Hewlett-Packard Laboratories, Bristol %
% DATE : 89.03.15 %
% REVISED : 91.10.01 %
load_library `sets`;;
load_library `string`;;
loadf `rules_and_tacs`;;
new_theory `mu`;;
new_parent `process_fix`;;
load_definition `process_ty` `IS_PROCESS`;;
map (load_theorem `process_ty`)
[`PROCESS_LEMMA6`; `ALPHA_FST`; `TRACES_SND`;
`NIL_IN_TRACES`; `APPEND_IN_TRACES`; `TRACES_IN_STAR`];;
load_theorem `stop` `ALPHA_STOP`;;
map (load_definition `process_fix`)
[`ITER`; `LIM_PROC`; `IT_UNION`; `CONTINUOUS`];;
map (load_theorem `process_fix`) [`LIM_PROC_THM`; `IS_PROCESS_LIMIT`];;
let EXISTS_MU =
prove_thm
(`EXISTS_MU`,
"?f. !A G.
(CONTINUOUS G) ==> (f A G = (LIM_PROC (\n. ITER n G (STOP A))))",
EXISTS_TAC "\ A G. LIM_PROC (\n. ITER n G (STOP A))" THEN
BETA_TAC THEN
REWRITE_TAC []);;
let MU = new_specification `MU` [(`constant`,`MU`)] EXISTS_MU;;
%
|- !G A.
CHAIN(\n. ITER n G(STOP A)) ==>
IS_PROCESS(A,IT_UNION(\n. TRACES(ITER n G(STOP A))))
%
let IS_PROCESS_MU =
save_thm
(`IS_PROCESS_MU`,
GEN_ALL
(REWRITE_RULE
[ITER; ALPHA_STOP]
(BETA_RULE (SPEC "\n. ITER n G (STOP A)" IS_PROCESS_LIMIT))));;
%
|- !G A.
CHAIN(\n. ITER n G(STOP A)) ==>
CONTINUOUS G ==>
IS_PROCESS(A,IT_UNION(\n. TRACES(ITER n G(STOP A))))
%
let IS_PROCESS_MU' =
prove_thm
(`IS_PROCESS_MU'`,
"!G A.
CHAIN(\n. ITER n G(STOP A)) ==>
(CONTINUOUS G) ==>
IS_PROCESS(A,IT_UNION(\n. TRACES(ITER n G(STOP A))))",
REPEAT STRIP_TAC THEN
IMP_RES_TAC IS_PROCESS_MU THEN
ASM_REWRITE_TAC []);;
%
|- CHAIN(\n. ITER n G(STOP A)) ==>
CONTINUOUS G ==>
(MU A G = ABS_process(A,IT_UNION(\n. TRACES(ITER n G(STOP A)))))
%
let MU_THM =
DISCH_ALL
(SUBS
[UNDISCH
(REWRITE_RULE
[ITER; ALPHA_STOP]
(BETA_RULE (SPEC "\n. ITER n G (STOP A)" LIM_PROC_THM)))]
(SPEC_ALL MU));;
let ALPHA_MU =
save_thm
(`ALPHA_MU`,
DISCH_ALL
(DISCH "CONTINUOUS G"
(REWRITE_RULE
[SYM (UNDISCH_ALL (SPEC_ALL MU_THM))]
(MP (SPECL ["A:alphabet"; "IT_UNION(\n. TRACES(ITER n G(STOP A)))"]
ALPHA_FST)
(UNDISCH (SPEC_ALL IS_PROCESS_MU))))));;
let TRACES_MU =
save_thm
(`TRACES_MU`,
DISCH_ALL
(DISCH "CONTINUOUS G"
(REWRITE_RULE
[SYM (UNDISCH_ALL (SPEC_ALL MU_THM))]
(MP (SPECL ["A:alphabet"; "IT_UNION(\n. TRACES(ITER n G(STOP A)))"]
TRACES_SND)
(UNDISCH (SPEC_ALL IS_PROCESS_MU))))));;
close_theory();;
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