diff -r e2fcd88be55d -r ab8f39f48a6f src/HOL/UNITY/PPROD.ML
--- a/src/HOL/UNITY/PPROD.ML	Fri Jan 24 14:06:49 2003 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,281 +0,0 @@
-(*  Title:      HOL/UNITY/PPROD.ML
-    ID:         $Id$
-    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
-    Copyright   1999  University of Cambridge
-
-Abstraction over replicated components (PLam)
-General products of programs (Pi operation)
-
-Some dead wood here!
-*)
-
-(*** Basic properties ***)
-
-Goal "Init (PLam I F) = (INT i:I. lift_set i (Init (F i)))";
-by (simp_tac (simpset() addsimps [PLam_def, lift_def, lift_set_def]) 1);
-qed "Init_PLam";
-
-Addsimps [Init_PLam];
-
-Goal "PLam {} F = SKIP";
-by (simp_tac (simpset() addsimps [PLam_def]) 1);
-qed "PLam_empty";
-
-Goal "(plam i: I. SKIP) = SKIP";
-by (simp_tac (simpset() addsimps [PLam_def,lift_SKIP,JN_constant]) 1);
-qed "PLam_SKIP";
-
-Addsimps [PLam_SKIP, PLam_empty];
-
-Goalw [PLam_def] "PLam (insert i I) F = (lift i (F i)) Join (PLam I F)";
-by Auto_tac;
-qed "PLam_insert";
-
-Goal "((PLam I F) <= H) = (ALL i: I. lift i (F i) <= H)";
-by (simp_tac (simpset() addsimps [PLam_def, JN_component_iff]) 1);
-qed "PLam_component_iff";
-
-Goalw [PLam_def] "i : I ==> lift i (F i) <= (PLam I F)";
-(*blast_tac doesn't use HO unification*)
-by (fast_tac (claset() addIs [component_JN]) 1);
-qed "component_PLam";
-
-
-(** Safety & Progress: but are they used anywhere? **)
-
-Goal "[| i : I;  ALL j. F j : preserves snd |] ==>  \
-\     (PLam I F : (lift_set i (A <*> UNIV)) co \
-\                 (lift_set i (B <*> UNIV)))  =  \
-\     (F i : (A <*> UNIV) co (B <*> UNIV))";
-by (asm_simp_tac (simpset() addsimps [PLam_def, JN_constrains]) 1);
-by (stac (insert_Diff RS sym) 1 THEN assume_tac 1);
-by (asm_simp_tac (simpset() addsimps [lift_constrains]) 1);
-by (blast_tac (claset() addIs [constrains_imp_lift_constrains]) 1);
-qed "PLam_constrains";
-
-Goal "[| i : I;  ALL j. F j : preserves snd |]  \
-\     ==> (PLam I F : stable (lift_set i (A <*> UNIV))) = \
-\         (F i : stable (A <*> UNIV))";
-by (asm_simp_tac (simpset() addsimps [stable_def, PLam_constrains]) 1);
-qed "PLam_stable";
-
-Goal "i : I ==> \
-\   PLam I F : transient A = (EX i:I. lift i (F i) : transient A)";
-by (asm_simp_tac (simpset() addsimps [JN_transient, PLam_def]) 1);
-qed "PLam_transient";
-
-(*This holds because the F j cannot change (lift_set i)*)
-Goal "[| i : I;  F i : (A <*> UNIV) ensures (B <*> UNIV);  \
-\        ALL j. F j : preserves snd |] ==>  \
-\     PLam I F : lift_set i (A <*> UNIV) ensures lift_set i (B <*> UNIV)";
-by (auto_tac (claset(), 
-    simpset() addsimps [ensures_def, PLam_constrains, PLam_transient,
-	                lift_transient_eq_disj,
-			lift_set_Un_distrib RS sym,
-			lift_set_Diff_distrib RS sym,
-			Times_Un_distrib1 RS sym,
-			Times_Diff_distrib1 RS sym]));
-qed "PLam_ensures";
-
-Goal "[| i : I;  \
-\        F i : ((A <*> UNIV) - (B <*> UNIV)) co \
-\              ((A <*> UNIV) Un (B <*> UNIV));  \
-\        F i : transient ((A <*> UNIV) - (B <*> UNIV));  \
-\        ALL j. F j : preserves snd |] ==>  \
-\     PLam I F : lift_set i (A <*> UNIV) leadsTo lift_set i (B <*> UNIV)";
-by (rtac (PLam_ensures RS leadsTo_Basis) 1);
-by (rtac ensuresI 2);
-by (ALLGOALS assume_tac);
-qed "PLam_leadsTo_Basis";
-
-
-(** invariant **)
-
-Goal "[| F i : invariant (A <*> UNIV);  i : I;  \
-\        ALL j. F j : preserves snd |] \
-\     ==> PLam I F : invariant (lift_set i (A <*> UNIV))";
-by (auto_tac (claset(),
-	      simpset() addsimps [PLam_stable, invariant_def]));
-qed "invariant_imp_PLam_invariant";
-
-
-Goal "ALL j. F j : preserves snd \
-\     ==> (PLam I F : preserves (v o sub j o fst)) = \
-\         (if j: I then F j : preserves (v o fst) else True)";
-by (asm_simp_tac (simpset() addsimps [PLam_def, lift_preserves_sub]) 1);
-qed "PLam_preserves_fst";
-Addsimps [PLam_preserves_fst];
-
-Goal "ALL j. F j : preserves snd ==> PLam I F : preserves snd";
-by (asm_simp_tac (simpset() addsimps [PLam_def, lift_preserves_snd_I]) 1);
-qed "PLam_preserves_snd";
-Addsimps [PLam_preserves_snd];
-AddIs [PLam_preserves_snd];
-
-
-(*** guarantees properties ***)
-
-(*This rule looks unsatisfactory because it refers to "lift".  One must use
-  lift_guarantees_eq_lift_inv to rewrite the first subgoal and
-  something like lift_preserves_sub to rewrite the third.  However there's
-  no obvious way to alternative for the third premise.*)
-Goalw [PLam_def]
-    "[| lift i (F i): X guarantees Y;  i : I;  \
-\       OK I (%i. lift i (F i)) |]  \
-\    ==> (PLam I F) : X guarantees Y"; 
-by (asm_simp_tac (simpset() addsimps [guarantees_JN_I]) 1);
-qed "guarantees_PLam_I";
-
-Goal "Allowed (PLam I F) = (INT i:I. lift i ` Allowed(F i))";
-by (simp_tac (simpset() addsimps [PLam_def]) 1); 
-qed "Allowed_PLam";
-Addsimps [Allowed_PLam];
-
-Goal "(PLam I F) : preserves v = (ALL i:I. F i : preserves (v o lift_map i))";
-by (simp_tac (simpset() addsimps [PLam_def, lift_def, rename_preserves]) 1); 
-qed "PLam_preserves";
-Addsimps [PLam_preserves];
-
-(**UNUSED
-    (*The f0 premise ensures that the product is well-defined.*)
-    Goal "[| PLam I F : invariant (lift_set i A);  i : I;  \
-    \        f0: Init (PLam I F) |] ==> F i : invariant A";
-    by (auto_tac (claset(),
-		  simpset() addsimps [invariant_def]));
-    by (dres_inst_tac [("c", "f0(i:=x)")] subsetD 1);
-    by Auto_tac;
-    qed "PLam_invariant_imp_invariant";
-
-    Goal "[| i : I;  f0: Init (PLam I F) |] \
-    \     ==> (PLam I F : invariant (lift_set i A)) = (F i : invariant A)";
-    by (blast_tac (claset() addIs [invariant_imp_PLam_invariant, 
-				   PLam_invariant_imp_invariant]) 1);
-    qed "PLam_invariant";
-
-    (*The f0 premise isn't needed if F is a constant program because then
-      we get an initial state by replicating that of F*)
-    Goal "i : I \
-    \     ==> ((plam x:I. F) : invariant (lift_set i A)) = (F : invariant A)";
-    by (auto_tac (claset(),
-		  simpset() addsimps [invariant_def]));
-    qed "const_PLam_invariant";
-**)
-
-
-(**UNUSED
-    (** Reachability **)
-
-    Goal "[| f : reachable (PLam I F);  i : I |] ==> f i : reachable (F i)";
-    by (etac reachable.induct 1);
-    by (auto_tac (claset() addIs reachable.intrs, simpset()));
-    qed "reachable_PLam";
-
-    (*Result to justify a re-organization of this file*)
-    Goal "{f. ALL i:I. f i : R i} = (INT i:I. lift_set i (R i))";
-    by Auto_tac;
-    result();
-
-    Goal "reachable (PLam I F) <= (INT i:I. lift_set i (reachable (F i)))";
-    by (force_tac (claset() addSDs [reachable_PLam], simpset()) 1);
-    qed "reachable_PLam_subset1";
-
-    (*simplify using reachable_lift??*)
-    Goal "[| i ~: I;  A : reachable (F i) |]     \
-    \  ==> ALL f. f : reachable (PLam I F)      \
-    \             --> f(i:=A) : reachable (lift i (F i) Join PLam I F)";
-    by (etac reachable.induct 1);
-    by (ALLGOALS Clarify_tac);
-    by (etac reachable.induct 1);
-    (*Init, Init case*)
-    by (force_tac (claset() addIs reachable.intrs, simpset()) 1);
-    (*Init of F, action of PLam F case*)
-    by (res_inst_tac [("act","act")] reachable.Acts 1);
-    by (Force_tac 1);
-    by (assume_tac 1);
-    by (force_tac (claset() addIs [ext], simpset()) 1);
-    (*induction over the 2nd "reachable" assumption*)
-    by (eres_inst_tac [("xa","f")] reachable.induct 1);
-    (*Init of PLam F, action of F case*)
-    by (res_inst_tac [("act","lift_act i act")] reachable.Acts 1);
-    by (Force_tac 1);
-    by (force_tac (claset() addIs [reachable.Init], simpset()) 1);
-    by (force_tac (claset() addIs [ext], simpset() addsimps [lift_act_def]) 1);
-    (*last case: an action of PLam I F*)
-    by (res_inst_tac [("act","acta")] reachable.Acts 1);
-    by (Force_tac 1);
-    by (assume_tac 1);
-    by (force_tac (claset() addIs [ext], simpset()) 1);
-    qed_spec_mp "reachable_lift_Join_PLam";
-
-
-    (*The index set must be finite: otherwise infinitely many copies of F can
-      perform actions, and PLam can never catch up in finite time.*)
-    Goal "finite I \
-    \     ==> (INT i:I. lift_set i (reachable (F i))) <= reachable (PLam I F)";
-    by (etac finite_induct 1);
-    by (Simp_tac 1);
-    by (force_tac (claset() addDs [reachable_lift_Join_PLam], 
-		   simpset() addsimps [PLam_insert]) 1);
-    qed "reachable_PLam_subset2";
-
-    Goal "finite I ==> \
-    \     reachable (PLam I F) = (INT i:I. lift_set i (reachable (F i)))";
-    by (REPEAT_FIRST (ares_tac [equalityI,
-				reachable_PLam_subset1, 
-				reachable_PLam_subset2]));
-    qed "reachable_PLam_eq";
-
-
-    (** Co **)
-
-    Goal "[| F i : A Co B;  i: I;  finite I |]  \
-    \     ==> PLam I F : (lift_set i A) Co (lift_set i B)";
-    by (auto_tac
-	(claset(),
-	 simpset() addsimps [Constrains_def, Collect_conj_eq RS sym,
-			     reachable_PLam_eq]));
-    by (auto_tac (claset(), 
-		  simpset() addsimps [constrains_def, PLam_def]));
-    by (REPEAT (blast_tac (claset() addIs reachable.intrs) 1));
-    qed "Constrains_imp_PLam_Constrains";
-
-
-
-    Goal "[| i: I;  finite I;  f0: Init (PLam I F) |]  \
-    \     ==> (PLam I F : (lift_set i A) Co (lift_set i B)) =  \
-    \         (F i : A Co B)";
-    by (blast_tac (claset() addIs [Constrains_imp_PLam_Constrains, 
-				   PLam_Constrains_imp_Constrains]) 1);
-    qed "PLam_Constrains";
-
-    Goal "[| i: I;  finite I;  f0: Init (PLam I F) |]  \
-    \     ==> (PLam I F : Stable (lift_set i A)) = (F i : Stable A)";
-    by (asm_simp_tac (simpset() delsimps [Init_PLam]
-				addsimps [Stable_def, PLam_Constrains]) 1);
-    qed "PLam_Stable";
-
-
-    (** const_PLam (no dependence on i) doesn't require the f0 premise **)
-
-    Goal "[| i: I;  finite I |]  \
-    \     ==> ((plam x:I. F) : (lift_set i A) Co (lift_set i B)) =  \
-    \         (F : A Co B)";
-    by (blast_tac (claset() addIs [Constrains_imp_PLam_Constrains, 
-				   const_PLam_Constrains_imp_Constrains]) 1);
-    qed "const_PLam_Constrains";
-
-    Goal "[| i: I;  finite I |]  \
-    \     ==> ((plam x:I. F) : Stable (lift_set i A)) = (F : Stable A)";
-    by (asm_simp_tac (simpset() addsimps [Stable_def, const_PLam_Constrains]) 1);
-    qed "const_PLam_Stable";
-
-    Goalw [Increasing_def]
-	 "[| i: I;  finite I |]  \
-    \     ==> ((plam x:I. F) : Increasing (f o sub i)) = (F : Increasing f)";
-    by (subgoal_tac "ALL z. {s. z <= (f o sub i) s} = lift_set i {s. z <= f s}" 1);
-    by (asm_simp_tac (simpset() addsimps [lift_set_sub]) 2);
-    by (asm_full_simp_tac
-	(simpset() addsimps [finite_lessThan, const_PLam_Stable]) 1);
-    qed "const_PLam_Increasing";
-**)
-