--- a/src/HOLCF/IOA/meta_theory/Simulations.thy Sat Nov 27 14:34:54 2010 -0800
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,85 +0,0 @@
-(* Title: HOLCF/IOA/meta_theory/Simulations.thy
- Author: Olaf Müller
-*)
-
-header {* Simulations in HOLCF/IOA *}
-
-theory Simulations
-imports RefCorrectness
-begin
-
-default_sort type
-
-definition
- is_simulation :: "[('s1 * 's2)set,('a,'s1)ioa,('a,'s2)ioa] => bool" where
- "is_simulation R C A =
- ((!s:starts_of C. R``{s} Int starts_of A ~= {}) &
- (!s s' t a. reachable C s &
- s -a--C-> t &
- (s,s') : R
- --> (? t' ex. (t,t'):R & move A ex s' a t')))"
-
-definition
- is_backward_simulation :: "[('s1 * 's2)set,('a,'s1)ioa,('a,'s2)ioa] => bool" where
- "is_backward_simulation R C A =
- ((!s:starts_of C. R``{s} <= starts_of A) &
- (!s t t' a. reachable C s &
- s -a--C-> t &
- (t,t') : R
- --> (? ex s'. (s,s'):R & move A ex s' a t')))"
-
-definition
- is_forw_back_simulation :: "[('s1 * 's2 set)set,('a,'s1)ioa,('a,'s2)ioa] => bool" where
- "is_forw_back_simulation R C A =
- ((!s:starts_of C. ? S'. (s,S'):R & S'<= starts_of A) &
- (!s S' t a. reachable C s &
- s -a--C-> t &
- (s,S') : R
- --> (? T'. (t,T'):R & (! t':T'. ? s':S'. ? ex. move A ex s' a t'))))"
-
-definition
- is_back_forw_simulation :: "[('s1 * 's2 set)set,('a,'s1)ioa,('a,'s2)ioa] => bool" where
- "is_back_forw_simulation R C A =
- ((!s:starts_of C. ! S'. (s,S'):R --> S' Int starts_of A ~={}) &
- (!s t T' a. reachable C s &
- s -a--C-> t &
- (t,T') : R
- --> (? S'. (s,S'):R & (! s':S'. ? t':T'. ? ex. move A ex s' a t'))))"
-
-definition
- is_history_relation :: "[('s1 * 's2)set,('a,'s1)ioa,('a,'s2)ioa] => bool" where
- "is_history_relation R C A = (is_simulation R C A &
- is_ref_map (%x.(@y. (x,y):(R^-1))) A C)"
-
-definition
- is_prophecy_relation :: "[('s1 * 's2)set,('a,'s1)ioa,('a,'s2)ioa] => bool" where
- "is_prophecy_relation R C A = (is_backward_simulation R C A &
- is_ref_map (%x.(@y. (x,y):(R^-1))) A C)"
-
-
-lemma set_non_empty: "(A~={}) = (? x. x:A)"
-apply auto
-done
-
-lemma Int_non_empty: "(A Int B ~= {}) = (? x. x: A & x:B)"
-apply (simp add: set_non_empty)
-done
-
-
-lemma Sim_start_convert:
-"(R``{x} Int S ~= {}) = (? y. (x,y):R & y:S)"
-apply (unfold Image_def)
-apply (simp add: Int_non_empty)
-done
-
-declare Sim_start_convert [simp]
-
-
-lemma ref_map_is_simulation:
-"!! f. is_ref_map f C A ==> is_simulation {p. (snd p) = f (fst p)} C A"
-
-apply (unfold is_ref_map_def is_simulation_def)
-apply simp
-done
-
-end