removed Hoare/hoare.ML, Hoare/hoareAbort.ML, ex/svc_oracle.ML (which can be mistaken as attached ML script on case-insensitive file-system);
--- a/src/HOL/Hoare/Hoare.thy Wed Aug 29 10:20:22 2007 +0200
+++ b/src/HOL/Hoare/Hoare.thy Wed Aug 29 11:10:28 2007 +0200
@@ -10,7 +10,7 @@
*)
theory Hoare imports Main
-uses ("hoare.ML") begin
+begin
types
'a bexp = "'a set"
@@ -225,7 +225,167 @@
done
-use "hoare.ML"
+subsection {* Derivation of the proof rules and, most importantly, the VCG tactic *}
+
+ML {*
+(*** The tactics ***)
+
+(*****************************************************************************)
+(** The function Mset makes the theorem **)
+(** "?Mset <= {(x1,...,xn). ?P (x1,...,xn)} ==> ?Mset <= {s. ?P s}", **)
+(** where (x1,...,xn) are the variables of the particular program we are **)
+(** working on at the moment of the call **)
+(*****************************************************************************)
+
+local open HOLogic in
+
+(** maps (%x1 ... xn. t) to [x1,...,xn] **)
+fun abs2list (Const ("split",_) $ (Abs(x,T,t))) = Free (x, T)::abs2list t
+ | abs2list (Abs(x,T,t)) = [Free (x, T)]
+ | abs2list _ = [];
+
+(** maps {(x1,...,xn). t} to [x1,...,xn] **)
+fun mk_vars (Const ("Collect",_) $ T) = abs2list T
+ | mk_vars _ = [];
+
+(** abstraction of body over a tuple formed from a list of free variables.
+Types are also built **)
+fun mk_abstupleC [] body = absfree ("x", unitT, body)
+ | mk_abstupleC (v::w) body = let val (n,T) = dest_Free v
+ in if w=[] then absfree (n, T, body)
+ else let val z = mk_abstupleC w body;
+ val T2 = case z of Abs(_,T,_) => T
+ | Const (_, Type (_,[_, Type (_,[T,_])])) $ _ => T;
+ in Const ("split", (T --> T2 --> boolT) --> mk_prodT (T,T2) --> boolT)
+ $ absfree (n, T, z) end end;
+
+(** maps [x1,...,xn] to (x1,...,xn) and types**)
+fun mk_bodyC [] = HOLogic.unit
+ | mk_bodyC (x::xs) = if xs=[] then x
+ else let val (n, T) = dest_Free x ;
+ val z = mk_bodyC xs;
+ val T2 = case z of Free(_, T) => T
+ | Const ("Pair", Type ("fun", [_, Type
+ ("fun", [_, T])])) $ _ $ _ => T;
+ in Const ("Pair", [T, T2] ---> mk_prodT (T, T2)) $ x $ z end;
+
+(** maps a goal of the form:
+ 1. [| P |] ==> VARS x1 ... xn {._.} _ {._.} or to [x1,...,xn]**)
+fun get_vars thm = let val c = Logic.unprotect (concl_of (thm));
+ val d = Logic.strip_assums_concl c;
+ val Const _ $ pre $ _ $ _ = dest_Trueprop d;
+ in mk_vars pre end;
+
+
+(** Makes Collect with type **)
+fun mk_CollectC trm = let val T as Type ("fun",[t,_]) = fastype_of trm
+ in Collect_const t $ trm end;
+
+fun inclt ty = Const (@{const_name HOL.less_eq}, [ty,ty] ---> boolT);
+
+(** Makes "Mset <= t" **)
+fun Mset_incl t = let val MsetT = fastype_of t
+ in mk_Trueprop ((inclt MsetT) $ Free ("Mset", MsetT) $ t) end;
+
+
+fun Mset thm = let val vars = get_vars(thm);
+ val varsT = fastype_of (mk_bodyC vars);
+ val big_Collect = mk_CollectC (mk_abstupleC vars
+ (Free ("P",varsT --> boolT) $ mk_bodyC vars));
+ val small_Collect = mk_CollectC (Abs("x",varsT,
+ Free ("P",varsT --> boolT) $ Bound 0));
+ val impl = implies $ (Mset_incl big_Collect) $
+ (Mset_incl small_Collect);
+ in Goal.prove (ProofContext.init (Thm.theory_of_thm thm)) ["Mset", "P"] [] impl (K (CLASET' blast_tac 1)) end;
+
+end;
+*}
+
+(*****************************************************************************)
+(** Simplifying: **)
+(** Some useful lemmata, lists and simplification tactics to control which **)
+(** theorems are used to simplify at each moment, so that the original **)
+(** input does not suffer any unexpected transformation **)
+(*****************************************************************************)
+
+lemma Compl_Collect: "-(Collect b) = {x. ~(b x)}"
+ by blast
+
+
+ML {*
+(**Simp_tacs**)
+
+val before_set2pred_simp_tac =
+ (simp_tac (HOL_basic_ss addsimps [@{thm Collect_conj_eq} RS sym, @{thm Compl_Collect}]));
+
+val split_simp_tac = (simp_tac (HOL_basic_ss addsimps [split_conv]));
+
+(*****************************************************************************)
+(** set2pred transforms sets inclusion into predicates implication, **)
+(** maintaining the original variable names. **)
+(** Ex. "{x. x=0} <= {x. x <= 1}" -set2pred-> "x=0 --> x <= 1" **)
+(** Subgoals containing intersections (A Int B) or complement sets (-A) **)
+(** are first simplified by "before_set2pred_simp_tac", that returns only **)
+(** subgoals of the form "{x. P x} <= {x. Q x}", which are easily **)
+(** transformed. **)
+(** This transformation may solve very easy subgoals due to a ligth **)
+(** simplification done by (split_all_tac) **)
+(*****************************************************************************)
+
+fun set2pred i thm =
+ let val var_names = map (fst o dest_Free) (get_vars thm) in
+ ((before_set2pred_simp_tac i) THEN_MAYBE
+ (EVERY [rtac subsetI i,
+ rtac CollectI i,
+ dtac CollectD i,
+ (TRY(split_all_tac i)) THEN_MAYBE
+ ((rename_params_tac var_names i) THEN
+ (full_simp_tac (HOL_basic_ss addsimps [split_conv]) i)) ])) thm
+ end;
+
+(*****************************************************************************)
+(** BasicSimpTac is called to simplify all verification conditions. It does **)
+(** a light simplification by applying "mem_Collect_eq", then it calls **)
+(** MaxSimpTac, which solves subgoals of the form "A <= A", **)
+(** and transforms any other into predicates, applying then **)
+(** the tactic chosen by the user, which may solve the subgoal completely. **)
+(*****************************************************************************)
+
+fun MaxSimpTac tac = FIRST'[rtac subset_refl, set2pred THEN_MAYBE' tac];
+
+fun BasicSimpTac tac =
+ simp_tac
+ (HOL_basic_ss addsimps [mem_Collect_eq,split_conv] addsimprocs [record_simproc])
+ THEN_MAYBE' MaxSimpTac tac;
+
+(** HoareRuleTac **)
+
+fun WlpTac Mlem tac i =
+ rtac @{thm SeqRule} i THEN HoareRuleTac Mlem tac false (i+1)
+and HoareRuleTac Mlem tac pre_cond i st = st |>
+ (*abstraction over st prevents looping*)
+ ( (WlpTac Mlem tac i THEN HoareRuleTac Mlem tac pre_cond i)
+ ORELSE
+ (FIRST[rtac @{thm SkipRule} i,
+ EVERY[rtac @{thm BasicRule} i,
+ rtac Mlem i,
+ split_simp_tac i],
+ EVERY[rtac @{thm CondRule} i,
+ HoareRuleTac Mlem tac false (i+2),
+ HoareRuleTac Mlem tac false (i+1)],
+ EVERY[rtac @{thm WhileRule} i,
+ BasicSimpTac tac (i+2),
+ HoareRuleTac Mlem tac true (i+1)] ]
+ THEN (if pre_cond then (BasicSimpTac tac i) else (rtac subset_refl i)) ));
+
+
+(** tac:(int -> tactic) is the tactic the user chooses to solve or simplify **)
+(** the final verification conditions **)
+
+fun hoare_tac tac i thm =
+ let val Mlem = Mset(thm)
+ in SELECT_GOAL(EVERY[HoareRuleTac Mlem tac true 1]) i thm end;
+*}
method_setup vcg = {*
Method.no_args (Method.SIMPLE_METHOD' (hoare_tac (K all_tac))) *}
--- a/src/HOL/Hoare/HoareAbort.thy Wed Aug 29 10:20:22 2007 +0200
+++ b/src/HOL/Hoare/HoareAbort.thy Wed Aug 29 11:10:28 2007 +0200
@@ -7,7 +7,7 @@
*)
theory HoareAbort imports Main
-uses ("hoareAbort.ML") begin
+begin
types
'a bexp = "'a set"
@@ -235,7 +235,169 @@
lemma AbortRule: "p \<subseteq> {s. False} \<Longrightarrow> Valid p Abort q"
by(auto simp:Valid_def)
-use "hoareAbort.ML"
+
+subsection {* Derivation of the proof rules and, most importantly, the VCG tactic *}
+
+ML {*
+(*** The tactics ***)
+
+(*****************************************************************************)
+(** The function Mset makes the theorem **)
+(** "?Mset <= {(x1,...,xn). ?P (x1,...,xn)} ==> ?Mset <= {s. ?P s}", **)
+(** where (x1,...,xn) are the variables of the particular program we are **)
+(** working on at the moment of the call **)
+(*****************************************************************************)
+
+local open HOLogic in
+
+(** maps (%x1 ... xn. t) to [x1,...,xn] **)
+fun abs2list (Const ("split",_) $ (Abs(x,T,t))) = Free (x, T)::abs2list t
+ | abs2list (Abs(x,T,t)) = [Free (x, T)]
+ | abs2list _ = [];
+
+(** maps {(x1,...,xn). t} to [x1,...,xn] **)
+fun mk_vars (Const ("Collect",_) $ T) = abs2list T
+ | mk_vars _ = [];
+
+(** abstraction of body over a tuple formed from a list of free variables.
+Types are also built **)
+fun mk_abstupleC [] body = absfree ("x", unitT, body)
+ | mk_abstupleC (v::w) body = let val (n,T) = dest_Free v
+ in if w=[] then absfree (n, T, body)
+ else let val z = mk_abstupleC w body;
+ val T2 = case z of Abs(_,T,_) => T
+ | Const (_, Type (_,[_, Type (_,[T,_])])) $ _ => T;
+ in Const ("split", (T --> T2 --> boolT) --> mk_prodT (T,T2) --> boolT)
+ $ absfree (n, T, z) end end;
+
+(** maps [x1,...,xn] to (x1,...,xn) and types**)
+fun mk_bodyC [] = HOLogic.unit
+ | mk_bodyC (x::xs) = if xs=[] then x
+ else let val (n, T) = dest_Free x ;
+ val z = mk_bodyC xs;
+ val T2 = case z of Free(_, T) => T
+ | Const ("Pair", Type ("fun", [_, Type
+ ("fun", [_, T])])) $ _ $ _ => T;
+ in Const ("Pair", [T, T2] ---> mk_prodT (T, T2)) $ x $ z end;
+
+(** maps a goal of the form:
+ 1. [| P |] ==> VARS x1 ... xn {._.} _ {._.} or to [x1,...,xn]**)
+fun get_vars thm = let val c = Logic.unprotect (concl_of (thm));
+ val d = Logic.strip_assums_concl c;
+ val Const _ $ pre $ _ $ _ = dest_Trueprop d;
+ in mk_vars pre end;
+
+
+(** Makes Collect with type **)
+fun mk_CollectC trm = let val T as Type ("fun",[t,_]) = fastype_of trm
+ in Collect_const t $ trm end;
+
+fun inclt ty = Const (@{const_name HOL.less_eq}, [ty,ty] ---> boolT);
+
+(** Makes "Mset <= t" **)
+fun Mset_incl t = let val MsetT = fastype_of t
+ in mk_Trueprop ((inclt MsetT) $ Free ("Mset", MsetT) $ t) end;
+
+
+fun Mset thm = let val vars = get_vars(thm);
+ val varsT = fastype_of (mk_bodyC vars);
+ val big_Collect = mk_CollectC (mk_abstupleC vars
+ (Free ("P",varsT --> boolT) $ mk_bodyC vars));
+ val small_Collect = mk_CollectC (Abs("x",varsT,
+ Free ("P",varsT --> boolT) $ Bound 0));
+ val impl = implies $ (Mset_incl big_Collect) $
+ (Mset_incl small_Collect);
+ in Goal.prove (ProofContext.init (Thm.theory_of_thm thm)) ["Mset", "P"] [] impl (K (CLASET' blast_tac 1)) end;
+
+end;
+*}
+
+(*****************************************************************************)
+(** Simplifying: **)
+(** Some useful lemmata, lists and simplification tactics to control which **)
+(** theorems are used to simplify at each moment, so that the original **)
+(** input does not suffer any unexpected transformation **)
+(*****************************************************************************)
+
+lemma Compl_Collect: "-(Collect b) = {x. ~(b x)}"
+ by blast
+
+
+ML {*
+(**Simp_tacs**)
+
+val before_set2pred_simp_tac =
+ (simp_tac (HOL_basic_ss addsimps [@{thm Collect_conj_eq} RS sym, @{thm Compl_Collect}]));
+
+val split_simp_tac = (simp_tac (HOL_basic_ss addsimps [split_conv]));
+
+(*****************************************************************************)
+(** set2pred transforms sets inclusion into predicates implication, **)
+(** maintaining the original variable names. **)
+(** Ex. "{x. x=0} <= {x. x <= 1}" -set2pred-> "x=0 --> x <= 1" **)
+(** Subgoals containing intersections (A Int B) or complement sets (-A) **)
+(** are first simplified by "before_set2pred_simp_tac", that returns only **)
+(** subgoals of the form "{x. P x} <= {x. Q x}", which are easily **)
+(** transformed. **)
+(** This transformation may solve very easy subgoals due to a ligth **)
+(** simplification done by (split_all_tac) **)
+(*****************************************************************************)
+
+fun set2pred i thm =
+ let val var_names = map (fst o dest_Free) (get_vars thm) in
+ ((before_set2pred_simp_tac i) THEN_MAYBE
+ (EVERY [rtac subsetI i,
+ rtac CollectI i,
+ dtac CollectD i,
+ (TRY(split_all_tac i)) THEN_MAYBE
+ ((rename_params_tac var_names i) THEN
+ (full_simp_tac (HOL_basic_ss addsimps [split_conv]) i)) ])) thm
+ end;
+
+(*****************************************************************************)
+(** BasicSimpTac is called to simplify all verification conditions. It does **)
+(** a light simplification by applying "mem_Collect_eq", then it calls **)
+(** MaxSimpTac, which solves subgoals of the form "A <= A", **)
+(** and transforms any other into predicates, applying then **)
+(** the tactic chosen by the user, which may solve the subgoal completely. **)
+(*****************************************************************************)
+
+fun MaxSimpTac tac = FIRST'[rtac subset_refl, set2pred THEN_MAYBE' tac];
+
+fun BasicSimpTac tac =
+ simp_tac
+ (HOL_basic_ss addsimps [mem_Collect_eq,split_conv] addsimprocs [record_simproc])
+ THEN_MAYBE' MaxSimpTac tac;
+
+(** HoareRuleTac **)
+
+fun WlpTac Mlem tac i =
+ rtac @{thm SeqRule} i THEN HoareRuleTac Mlem tac false (i+1)
+and HoareRuleTac Mlem tac pre_cond i st = st |>
+ (*abstraction over st prevents looping*)
+ ( (WlpTac Mlem tac i THEN HoareRuleTac Mlem tac pre_cond i)
+ ORELSE
+ (FIRST[rtac @{thm SkipRule} i,
+ rtac @{thm AbortRule} i,
+ EVERY[rtac @{thm BasicRule} i,
+ rtac Mlem i,
+ split_simp_tac i],
+ EVERY[rtac @{thm CondRule} i,
+ HoareRuleTac Mlem tac false (i+2),
+ HoareRuleTac Mlem tac false (i+1)],
+ EVERY[rtac @{thm WhileRule} i,
+ BasicSimpTac tac (i+2),
+ HoareRuleTac Mlem tac true (i+1)] ]
+ THEN (if pre_cond then (BasicSimpTac tac i) else rtac subset_refl i) ));
+
+
+(** tac:(int -> tactic) is the tactic the user chooses to solve or simplify **)
+(** the final verification conditions **)
+
+fun hoare_tac tac i thm =
+ let val Mlem = Mset(thm)
+ in SELECT_GOAL(EVERY[HoareRuleTac Mlem tac true 1]) i thm end;
+*}
method_setup vcg = {*
Method.no_args (Method.SIMPLE_METHOD' (hoare_tac (K all_tac))) *}
--- a/src/HOL/Hoare/hoare.ML Wed Aug 29 10:20:22 2007 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,171 +0,0 @@
-(* Title: HOL/Hoare/Hoare.ML
- ID: $Id$
- Author: Leonor Prensa Nieto & Tobias Nipkow
- Copyright 1998 TUM
-
-Derivation of the proof rules and, most importantly, the VCG tactic.
-*)
-
-val SkipRule = thm"SkipRule";
-val BasicRule = thm"BasicRule";
-val SeqRule = thm"SeqRule";
-val CondRule = thm"CondRule";
-val WhileRule = thm"WhileRule";
-
-(*** The tactics ***)
-
-(*****************************************************************************)
-(** The function Mset makes the theorem **)
-(** "?Mset <= {(x1,...,xn). ?P (x1,...,xn)} ==> ?Mset <= {s. ?P s}", **)
-(** where (x1,...,xn) are the variables of the particular program we are **)
-(** working on at the moment of the call **)
-(*****************************************************************************)
-
-local open HOLogic in
-
-(** maps (%x1 ... xn. t) to [x1,...,xn] **)
-fun abs2list (Const ("split",_) $ (Abs(x,T,t))) = Free (x, T)::abs2list t
- | abs2list (Abs(x,T,t)) = [Free (x, T)]
- | abs2list _ = [];
-
-(** maps {(x1,...,xn). t} to [x1,...,xn] **)
-fun mk_vars (Const ("Collect",_) $ T) = abs2list T
- | mk_vars _ = [];
-
-(** abstraction of body over a tuple formed from a list of free variables.
-Types are also built **)
-fun mk_abstupleC [] body = absfree ("x", unitT, body)
- | mk_abstupleC (v::w) body = let val (n,T) = dest_Free v
- in if w=[] then absfree (n, T, body)
- else let val z = mk_abstupleC w body;
- val T2 = case z of Abs(_,T,_) => T
- | Const (_, Type (_,[_, Type (_,[T,_])])) $ _ => T;
- in Const ("split", (T --> T2 --> boolT) --> mk_prodT (T,T2) --> boolT)
- $ absfree (n, T, z) end end;
-
-(** maps [x1,...,xn] to (x1,...,xn) and types**)
-fun mk_bodyC [] = HOLogic.unit
- | mk_bodyC (x::xs) = if xs=[] then x
- else let val (n, T) = dest_Free x ;
- val z = mk_bodyC xs;
- val T2 = case z of Free(_, T) => T
- | Const ("Pair", Type ("fun", [_, Type
- ("fun", [_, T])])) $ _ $ _ => T;
- in Const ("Pair", [T, T2] ---> mk_prodT (T, T2)) $ x $ z end;
-
-(** maps a goal of the form:
- 1. [| P |] ==> VARS x1 ... xn {._.} _ {._.} or to [x1,...,xn]**)
-fun get_vars thm = let val c = Logic.unprotect (concl_of (thm));
- val d = Logic.strip_assums_concl c;
- val Const _ $ pre $ _ $ _ = dest_Trueprop d;
- in mk_vars pre end;
-
-
-(** Makes Collect with type **)
-fun mk_CollectC trm = let val T as Type ("fun",[t,_]) = fastype_of trm
- in Collect_const t $ trm end;
-
-fun inclt ty = Const (@{const_name HOL.less_eq}, [ty,ty] ---> boolT);
-
-(** Makes "Mset <= t" **)
-fun Mset_incl t = let val MsetT = fastype_of t
- in mk_Trueprop ((inclt MsetT) $ Free ("Mset", MsetT) $ t) end;
-
-
-fun Mset thm = let val vars = get_vars(thm);
- val varsT = fastype_of (mk_bodyC vars);
- val big_Collect = mk_CollectC (mk_abstupleC vars
- (Free ("P",varsT --> boolT) $ mk_bodyC vars));
- val small_Collect = mk_CollectC (Abs("x",varsT,
- Free ("P",varsT --> boolT) $ Bound 0));
- val impl = implies $ (Mset_incl big_Collect) $
- (Mset_incl small_Collect);
- in Goal.prove (ProofContext.init (Thm.theory_of_thm thm)) ["Mset", "P"] [] impl (K (CLASET' blast_tac 1)) end;
-
-end;
-
-
-(*****************************************************************************)
-(** Simplifying: **)
-(** Some useful lemmata, lists and simplification tactics to control which **)
-(** theorems are used to simplify at each moment, so that the original **)
-(** input does not suffer any unexpected transformation **)
-(*****************************************************************************)
-
-Goal "-(Collect b) = {x. ~(b x)}";
-by (Fast_tac 1);
-qed "Compl_Collect";
-
-
-(**Simp_tacs**)
-
-val before_set2pred_simp_tac =
- (simp_tac (HOL_basic_ss addsimps [Collect_conj_eq RS sym,Compl_Collect]));
-
-val split_simp_tac = (simp_tac (HOL_basic_ss addsimps [split_conv]));
-
-(*****************************************************************************)
-(** set2pred transforms sets inclusion into predicates implication, **)
-(** maintaining the original variable names. **)
-(** Ex. "{x. x=0} <= {x. x <= 1}" -set2pred-> "x=0 --> x <= 1" **)
-(** Subgoals containing intersections (A Int B) or complement sets (-A) **)
-(** are first simplified by "before_set2pred_simp_tac", that returns only **)
-(** subgoals of the form "{x. P x} <= {x. Q x}", which are easily **)
-(** transformed. **)
-(** This transformation may solve very easy subgoals due to a ligth **)
-(** simplification done by (split_all_tac) **)
-(*****************************************************************************)
-
-fun set2pred i thm =
- let val var_names = map (fst o dest_Free) (get_vars thm) in
- ((before_set2pred_simp_tac i) THEN_MAYBE
- (EVERY [rtac subsetI i,
- rtac CollectI i,
- dtac CollectD i,
- (TRY(split_all_tac i)) THEN_MAYBE
- ((rename_params_tac var_names i) THEN
- (full_simp_tac (HOL_basic_ss addsimps [split_conv]) i)) ])) thm
- end;
-
-(*****************************************************************************)
-(** BasicSimpTac is called to simplify all verification conditions. It does **)
-(** a light simplification by applying "mem_Collect_eq", then it calls **)
-(** MaxSimpTac, which solves subgoals of the form "A <= A", **)
-(** and transforms any other into predicates, applying then **)
-(** the tactic chosen by the user, which may solve the subgoal completely. **)
-(*****************************************************************************)
-
-fun MaxSimpTac tac = FIRST'[rtac subset_refl, set2pred THEN_MAYBE' tac];
-
-fun BasicSimpTac tac =
- simp_tac
- (HOL_basic_ss addsimps [mem_Collect_eq,split_conv] addsimprocs [record_simproc])
- THEN_MAYBE' MaxSimpTac tac;
-
-(** HoareRuleTac **)
-
-fun WlpTac Mlem tac i =
- rtac SeqRule i THEN HoareRuleTac Mlem tac false (i+1)
-and HoareRuleTac Mlem tac pre_cond i st = st |>
- (*abstraction over st prevents looping*)
- ( (WlpTac Mlem tac i THEN HoareRuleTac Mlem tac pre_cond i)
- ORELSE
- (FIRST[rtac SkipRule i,
- EVERY[rtac BasicRule i,
- rtac Mlem i,
- split_simp_tac i],
- EVERY[rtac CondRule i,
- HoareRuleTac Mlem tac false (i+2),
- HoareRuleTac Mlem tac false (i+1)],
- EVERY[rtac WhileRule i,
- BasicSimpTac tac (i+2),
- HoareRuleTac Mlem tac true (i+1)] ]
- THEN (if pre_cond then (BasicSimpTac tac i) else (rtac subset_refl i)) ));
-
-
-(** tac:(int -> tactic) is the tactic the user chooses to solve or simplify **)
-(** the final verification conditions **)
-
-fun hoare_tac tac i thm =
- let val Mlem = Mset(thm)
- in SELECT_GOAL(EVERY[HoareRuleTac Mlem tac true 1]) i thm end;
--- a/src/HOL/Hoare/hoareAbort.ML Wed Aug 29 10:20:22 2007 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,173 +0,0 @@
-(* Title: HOL/Hoare/Hoare.ML
- ID: $Id$
- Author: Leonor Prensa Nieto & Tobias Nipkow
- Copyright 1998 TUM
-
-Derivation of the proof rules and, most importantly, the VCG tactic.
-*)
-
-val SkipRule = thm"SkipRule";
-val BasicRule = thm"BasicRule";
-val AbortRule = thm"AbortRule";
-val SeqRule = thm"SeqRule";
-val CondRule = thm"CondRule";
-val WhileRule = thm"WhileRule";
-
-(*** The tactics ***)
-
-(*****************************************************************************)
-(** The function Mset makes the theorem **)
-(** "?Mset <= {(x1,...,xn). ?P (x1,...,xn)} ==> ?Mset <= {s. ?P s}", **)
-(** where (x1,...,xn) are the variables of the particular program we are **)
-(** working on at the moment of the call **)
-(*****************************************************************************)
-
-local open HOLogic in
-
-(** maps (%x1 ... xn. t) to [x1,...,xn] **)
-fun abs2list (Const ("split",_) $ (Abs(x,T,t))) = Free (x, T)::abs2list t
- | abs2list (Abs(x,T,t)) = [Free (x, T)]
- | abs2list _ = [];
-
-(** maps {(x1,...,xn). t} to [x1,...,xn] **)
-fun mk_vars (Const ("Collect",_) $ T) = abs2list T
- | mk_vars _ = [];
-
-(** abstraction of body over a tuple formed from a list of free variables.
-Types are also built **)
-fun mk_abstupleC [] body = absfree ("x", unitT, body)
- | mk_abstupleC (v::w) body = let val (n,T) = dest_Free v
- in if w=[] then absfree (n, T, body)
- else let val z = mk_abstupleC w body;
- val T2 = case z of Abs(_,T,_) => T
- | Const (_, Type (_,[_, Type (_,[T,_])])) $ _ => T;
- in Const ("split", (T --> T2 --> boolT) --> mk_prodT (T,T2) --> boolT)
- $ absfree (n, T, z) end end;
-
-(** maps [x1,...,xn] to (x1,...,xn) and types**)
-fun mk_bodyC [] = HOLogic.unit
- | mk_bodyC (x::xs) = if xs=[] then x
- else let val (n, T) = dest_Free x ;
- val z = mk_bodyC xs;
- val T2 = case z of Free(_, T) => T
- | Const ("Pair", Type ("fun", [_, Type
- ("fun", [_, T])])) $ _ $ _ => T;
- in Const ("Pair", [T, T2] ---> mk_prodT (T, T2)) $ x $ z end;
-
-(** maps a goal of the form:
- 1. [| P |] ==> VARS x1 ... xn {._.} _ {._.} or to [x1,...,xn]**)
-fun get_vars thm = let val c = Logic.unprotect (concl_of (thm));
- val d = Logic.strip_assums_concl c;
- val Const _ $ pre $ _ $ _ = dest_Trueprop d;
- in mk_vars pre end;
-
-
-(** Makes Collect with type **)
-fun mk_CollectC trm = let val T as Type ("fun",[t,_]) = fastype_of trm
- in Collect_const t $ trm end;
-
-fun inclt ty = Const (@{const_name HOL.less_eq}, [ty,ty] ---> boolT);
-
-(** Makes "Mset <= t" **)
-fun Mset_incl t = let val MsetT = fastype_of t
- in mk_Trueprop ((inclt MsetT) $ Free ("Mset", MsetT) $ t) end;
-
-
-fun Mset thm = let val vars = get_vars(thm);
- val varsT = fastype_of (mk_bodyC vars);
- val big_Collect = mk_CollectC (mk_abstupleC vars
- (Free ("P",varsT --> boolT) $ mk_bodyC vars));
- val small_Collect = mk_CollectC (Abs("x",varsT,
- Free ("P",varsT --> boolT) $ Bound 0));
- val impl = implies $ (Mset_incl big_Collect) $
- (Mset_incl small_Collect);
- in Goal.prove (ProofContext.init (Thm.theory_of_thm thm)) ["Mset", "P"] [] impl (K (CLASET' blast_tac 1)) end;
-
-end;
-
-
-(*****************************************************************************)
-(** Simplifying: **)
-(** Some useful lemmata, lists and simplification tactics to control which **)
-(** theorems are used to simplify at each moment, so that the original **)
-(** input does not suffer any unexpected transformation **)
-(*****************************************************************************)
-
-Goal "-(Collect b) = {x. ~(b x)}";
-by (Fast_tac 1);
-qed "Compl_Collect";
-
-
-(**Simp_tacs**)
-
-val before_set2pred_simp_tac =
- (simp_tac (HOL_basic_ss addsimps [Collect_conj_eq RS sym,Compl_Collect]));
-
-val split_simp_tac = (simp_tac (HOL_basic_ss addsimps [split_conv]));
-
-(*****************************************************************************)
-(** set2pred transforms sets inclusion into predicates implication, **)
-(** maintaining the original variable names. **)
-(** Ex. "{x. x=0} <= {x. x <= 1}" -set2pred-> "x=0 --> x <= 1" **)
-(** Subgoals containing intersections (A Int B) or complement sets (-A) **)
-(** are first simplified by "before_set2pred_simp_tac", that returns only **)
-(** subgoals of the form "{x. P x} <= {x. Q x}", which are easily **)
-(** transformed. **)
-(** This transformation may solve very easy subgoals due to a ligth **)
-(** simplification done by (split_all_tac) **)
-(*****************************************************************************)
-
-fun set2pred i thm =
- let val var_names = map (fst o dest_Free) (get_vars thm) in
- ((before_set2pred_simp_tac i) THEN_MAYBE
- (EVERY [rtac subsetI i,
- rtac CollectI i,
- dtac CollectD i,
- (TRY(split_all_tac i)) THEN_MAYBE
- ((rename_params_tac var_names i) THEN
- (full_simp_tac (HOL_basic_ss addsimps [split_conv]) i)) ])) thm
- end;
-
-(*****************************************************************************)
-(** BasicSimpTac is called to simplify all verification conditions. It does **)
-(** a light simplification by applying "mem_Collect_eq", then it calls **)
-(** MaxSimpTac, which solves subgoals of the form "A <= A", **)
-(** and transforms any other into predicates, applying then **)
-(** the tactic chosen by the user, which may solve the subgoal completely. **)
-(*****************************************************************************)
-
-fun MaxSimpTac tac = FIRST'[rtac subset_refl, set2pred THEN_MAYBE' tac];
-
-fun BasicSimpTac tac =
- simp_tac
- (HOL_basic_ss addsimps [mem_Collect_eq,split_conv] addsimprocs [record_simproc])
- THEN_MAYBE' MaxSimpTac tac;
-
-(** HoareRuleTac **)
-
-fun WlpTac Mlem tac i =
- rtac SeqRule i THEN HoareRuleTac Mlem tac false (i+1)
-and HoareRuleTac Mlem tac pre_cond i st = st |>
- (*abstraction over st prevents looping*)
- ( (WlpTac Mlem tac i THEN HoareRuleTac Mlem tac pre_cond i)
- ORELSE
- (FIRST[rtac SkipRule i,
- rtac AbortRule i,
- EVERY[rtac BasicRule i,
- rtac Mlem i,
- split_simp_tac i],
- EVERY[rtac CondRule i,
- HoareRuleTac Mlem tac false (i+2),
- HoareRuleTac Mlem tac false (i+1)],
- EVERY[rtac WhileRule i,
- BasicSimpTac tac (i+2),
- HoareRuleTac Mlem tac true (i+1)] ]
- THEN (if pre_cond then (BasicSimpTac tac i) else rtac subset_refl i) ));
-
-
-(** tac:(int -> tactic) is the tactic the user chooses to solve or simplify **)
-(** the final verification conditions **)
-
-fun hoare_tac tac i thm =
- let val Mlem = Mset(thm)
- in SELECT_GOAL(EVERY[HoareRuleTac Mlem tac true 1]) i thm end;
--- a/src/HOL/IsaMakefile Wed Aug 29 10:20:22 2007 +0200
+++ b/src/HOL/IsaMakefile Wed Aug 29 11:10:28 2007 +0200
@@ -369,10 +369,10 @@
HOL-Hoare: HOL $(LOG)/HOL-Hoare.gz
$(LOG)/HOL-Hoare.gz: $(OUT)/HOL Hoare/Arith2.thy \
- Hoare/Examples.thy Hoare/hoare.ML Hoare/Hoare.thy \
+ Hoare/Examples.thy Hoare/Hoare.thy \
Hoare/Heap.thy Hoare/HeapSyntax.thy Hoare/Pointer_Examples.thy \
Hoare/ROOT.ML Hoare/ExamplesAbort.thy Hoare/HeapSyntaxAbort.thy \
- Hoare/hoareAbort.ML Hoare/HoareAbort.thy Hoare/SchorrWaite.thy \
+ Hoare/HoareAbort.thy Hoare/SchorrWaite.thy \
Hoare/Separation.thy Hoare/SepLogHeap.thy \
Hoare/document/root.tex Hoare/document/root.bib
@$(ISATOOL) usedir $(OUT)/HOL Hoare
@@ -667,7 +667,7 @@
ex/Puzzle.thy ex/Qsort.thy ex/Quickcheck_Examples.thy \
ex/Reflection.thy ex/reflection_data.ML ex/ReflectionEx.thy ex/ROOT.ML ex/Recdefs.thy \
ex/Records.thy ex/Reflected_Presburger.thy ex/coopertac.ML ex/coopereif.ML \
- ex/Refute_Examples.thy ex/SAT_Examples.thy ex/svc_oracle.ML ex/SVC_Oracle.thy \
+ ex/Refute_Examples.thy ex/SAT_Examples.thy ex/SVC_Oracle.thy \
ex/Sudoku.thy ex/Tarski.thy ex/Unification.thy ex/document/root.bib \
ex/document/root.tex ex/Meson_Test.thy ex/reflection.ML \
ex/set.thy ex/svc_funcs.ML ex/svc_test.thy Library/Parity.thy Library/GCD.thy
--- a/src/HOL/ex/SVC_Oracle.thy Wed Aug 29 10:20:22 2007 +0200
+++ b/src/HOL/ex/SVC_Oracle.thy Wed Aug 29 11:10:28 2007 +0200
@@ -10,7 +10,7 @@
theory SVC_Oracle
imports Main
-uses "svc_funcs.ML" ("svc_oracle.ML")
+uses "svc_funcs.ML"
begin
consts
@@ -22,6 +22,108 @@
oracle
svc_oracle ("term") = Svc.oracle
-use "svc_oracle.ML"
+ML {*
+(*
+Installing the oracle for SVC (Stanford Validity Checker)
+
+The following code merely CALLS the oracle;
+ the soundness-critical functions are at svc_funcs.ML
+
+Based upon the work of Søren T. Heilmann
+*)
+
+
+(*Generalize an Isabelle formula, replacing by Vars
+ all subterms not intelligible to SVC.*)
+fun svc_abstract t =
+ let
+ (*The oracle's result is given to the subgoal using compose_tac because
+ its premises are matched against the assumptions rather than used
+ to make subgoals. Therefore , abstraction must copy the parameters
+ precisely and make them available to all generated Vars.*)
+ val params = Term.strip_all_vars t
+ and body = Term.strip_all_body t
+ val Us = map #2 params
+ val nPar = length params
+ val vname = ref "V_a"
+ val pairs = ref ([] : (term*term) list)
+ fun insert t =
+ let val T = fastype_of t
+ val v = Logic.combound (Var ((!vname,0), Us--->T), 0, nPar)
+ in vname := Symbol.bump_string (!vname);
+ pairs := (t, v) :: !pairs;
+ v
+ end;
+ fun replace t =
+ case t of
+ Free _ => t (*but not existing Vars, lest the names clash*)
+ | Bound _ => t
+ | _ => (case AList.lookup Pattern.aeconv (!pairs) t of
+ SOME v => v
+ | NONE => insert t)
+ (*abstraction of a numeric literal*)
+ fun lit (t as Const(@{const_name HOL.zero}, _)) = t
+ | lit (t as Const(@{const_name HOL.one}, _)) = t
+ | lit (t as Const(@{const_name Numeral.number_of}, _) $ w) = t
+ | lit t = replace t
+ (*abstraction of a real/rational expression*)
+ fun rat ((c as Const(@{const_name HOL.plus}, _)) $ x $ y) = c $ (rat x) $ (rat y)
+ | rat ((c as Const(@{const_name HOL.minus}, _)) $ x $ y) = c $ (rat x) $ (rat y)
+ | rat ((c as Const(@{const_name HOL.divide}, _)) $ x $ y) = c $ (rat x) $ (rat y)
+ | rat ((c as Const(@{const_name HOL.times}, _)) $ x $ y) = c $ (rat x) $ (rat y)
+ | rat ((c as Const(@{const_name HOL.uminus}, _)) $ x) = c $ (rat x)
+ | rat t = lit t
+ (*abstraction of an integer expression: no div, mod*)
+ fun int ((c as Const(@{const_name HOL.plus}, _)) $ x $ y) = c $ (int x) $ (int y)
+ | int ((c as Const(@{const_name HOL.minus}, _)) $ x $ y) = c $ (int x) $ (int y)
+ | int ((c as Const(@{const_name HOL.times}, _)) $ x $ y) = c $ (int x) $ (int y)
+ | int ((c as Const(@{const_name HOL.uminus}, _)) $ x) = c $ (int x)
+ | int t = lit t
+ (*abstraction of a natural number expression: no minus*)
+ fun nat ((c as Const(@{const_name HOL.plus}, _)) $ x $ y) = c $ (nat x) $ (nat y)
+ | nat ((c as Const(@{const_name HOL.times}, _)) $ x $ y) = c $ (nat x) $ (nat y)
+ | nat ((c as Const(@{const_name Suc}, _)) $ x) = c $ (nat x)
+ | nat t = lit t
+ (*abstraction of a relation: =, <, <=*)
+ fun rel (T, c $ x $ y) =
+ if T = HOLogic.realT then c $ (rat x) $ (rat y)
+ else if T = HOLogic.intT then c $ (int x) $ (int y)
+ else if T = HOLogic.natT then c $ (nat x) $ (nat y)
+ else if T = HOLogic.boolT then c $ (fm x) $ (fm y)
+ else replace (c $ x $ y) (*non-numeric comparison*)
+ (*abstraction of a formula*)
+ and fm ((c as Const("op &", _)) $ p $ q) = c $ (fm p) $ (fm q)
+ | fm ((c as Const("op |", _)) $ p $ q) = c $ (fm p) $ (fm q)
+ | fm ((c as Const("op -->", _)) $ p $ q) = c $ (fm p) $ (fm q)
+ | fm ((c as Const("Not", _)) $ p) = c $ (fm p)
+ | fm ((c as Const("True", _))) = c
+ | fm ((c as Const("False", _))) = c
+ | fm (t as Const("op =", Type ("fun", [T,_])) $ _ $ _) = rel (T, t)
+ | fm (t as Const(@{const_name HOL.less}, Type ("fun", [T,_])) $ _ $ _) = rel (T, t)
+ | fm (t as Const(@{const_name HOL.less_eq}, Type ("fun", [T,_])) $ _ $ _) = rel (T, t)
+ | fm t = replace t
+ (*entry point, and abstraction of a meta-formula*)
+ fun mt ((c as Const("Trueprop", _)) $ p) = c $ (fm p)
+ | mt ((c as Const("==>", _)) $ p $ q) = c $ (mt p) $ (mt q)
+ | mt t = fm t (*it might be a formula*)
+ in (list_all (params, mt body), !pairs) end;
+
+
+(*Present the entire subgoal to the oracle, assumptions and all, but possibly
+ abstracted. Use via compose_tac, which performs no lifting but will
+ instantiate variables.*)
+
+fun svc_tac i st =
+ let
+ val (abs_goal, _) = svc_abstract (Logic.get_goal (Thm.prop_of st) i)
+ val th = svc_oracle (Thm.theory_of_thm st) abs_goal
+ in compose_tac (false, th, 0) i st end
+ handle TERM _ => no_tac st;
+
+
+(*check if user has SVC installed*)
+fun svc_enabled () = getenv "SVC_HOME" <> "";
+fun if_svc_enabled f x = if svc_enabled () then f x else ();
+*}
end
--- a/src/HOL/ex/svc_oracle.ML Wed Aug 29 10:20:22 2007 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,105 +0,0 @@
-(* Title: HOL/SVC_Oracle.ML
- ID: $Id$
- Author: Lawrence C Paulson
- Copyright 1999 University of Cambridge
-
-Installing the oracle for SVC (Stanford Validity Checker)
-
-The following code merely CALLS the oracle;
- the soundness-critical functions are at HOL/Tools/svc_funcs.ML
-
-Based upon the work of Soren T. Heilmann
-*)
-
-
-(*Generalize an Isabelle formula, replacing by Vars
- all subterms not intelligible to SVC.*)
-fun svc_abstract t =
- let
- (*The oracle's result is given to the subgoal using compose_tac because
- its premises are matched against the assumptions rather than used
- to make subgoals. Therefore , abstraction must copy the parameters
- precisely and make them available to all generated Vars.*)
- val params = Term.strip_all_vars t
- and body = Term.strip_all_body t
- val Us = map #2 params
- val nPar = length params
- val vname = ref "V_a"
- val pairs = ref ([] : (term*term) list)
- fun insert t =
- let val T = fastype_of t
- val v = Logic.combound (Var ((!vname,0), Us--->T), 0, nPar)
- in vname := Symbol.bump_string (!vname);
- pairs := (t, v) :: !pairs;
- v
- end;
- fun replace t =
- case t of
- Free _ => t (*but not existing Vars, lest the names clash*)
- | Bound _ => t
- | _ => (case AList.lookup Pattern.aeconv (!pairs) t of
- SOME v => v
- | NONE => insert t)
- (*abstraction of a numeric literal*)
- fun lit (t as Const(@{const_name HOL.zero}, _)) = t
- | lit (t as Const(@{const_name HOL.one}, _)) = t
- | lit (t as Const(@{const_name Numeral.number_of}, _) $ w) = t
- | lit t = replace t
- (*abstraction of a real/rational expression*)
- fun rat ((c as Const(@{const_name HOL.plus}, _)) $ x $ y) = c $ (rat x) $ (rat y)
- | rat ((c as Const(@{const_name HOL.minus}, _)) $ x $ y) = c $ (rat x) $ (rat y)
- | rat ((c as Const(@{const_name HOL.divide}, _)) $ x $ y) = c $ (rat x) $ (rat y)
- | rat ((c as Const(@{const_name HOL.times}, _)) $ x $ y) = c $ (rat x) $ (rat y)
- | rat ((c as Const(@{const_name HOL.uminus}, _)) $ x) = c $ (rat x)
- | rat t = lit t
- (*abstraction of an integer expression: no div, mod*)
- fun int ((c as Const(@{const_name HOL.plus}, _)) $ x $ y) = c $ (int x) $ (int y)
- | int ((c as Const(@{const_name HOL.minus}, _)) $ x $ y) = c $ (int x) $ (int y)
- | int ((c as Const(@{const_name HOL.times}, _)) $ x $ y) = c $ (int x) $ (int y)
- | int ((c as Const(@{const_name HOL.uminus}, _)) $ x) = c $ (int x)
- | int t = lit t
- (*abstraction of a natural number expression: no minus*)
- fun nat ((c as Const(@{const_name HOL.plus}, _)) $ x $ y) = c $ (nat x) $ (nat y)
- | nat ((c as Const(@{const_name HOL.times}, _)) $ x $ y) = c $ (nat x) $ (nat y)
- | nat ((c as Const(@{const_name Suc}, _)) $ x) = c $ (nat x)
- | nat t = lit t
- (*abstraction of a relation: =, <, <=*)
- fun rel (T, c $ x $ y) =
- if T = HOLogic.realT then c $ (rat x) $ (rat y)
- else if T = HOLogic.intT then c $ (int x) $ (int y)
- else if T = HOLogic.natT then c $ (nat x) $ (nat y)
- else if T = HOLogic.boolT then c $ (fm x) $ (fm y)
- else replace (c $ x $ y) (*non-numeric comparison*)
- (*abstraction of a formula*)
- and fm ((c as Const("op &", _)) $ p $ q) = c $ (fm p) $ (fm q)
- | fm ((c as Const("op |", _)) $ p $ q) = c $ (fm p) $ (fm q)
- | fm ((c as Const("op -->", _)) $ p $ q) = c $ (fm p) $ (fm q)
- | fm ((c as Const("Not", _)) $ p) = c $ (fm p)
- | fm ((c as Const("True", _))) = c
- | fm ((c as Const("False", _))) = c
- | fm (t as Const("op =", Type ("fun", [T,_])) $ _ $ _) = rel (T, t)
- | fm (t as Const(@{const_name HOL.less}, Type ("fun", [T,_])) $ _ $ _) = rel (T, t)
- | fm (t as Const(@{const_name HOL.less_eq}, Type ("fun", [T,_])) $ _ $ _) = rel (T, t)
- | fm t = replace t
- (*entry point, and abstraction of a meta-formula*)
- fun mt ((c as Const("Trueprop", _)) $ p) = c $ (fm p)
- | mt ((c as Const("==>", _)) $ p $ q) = c $ (mt p) $ (mt q)
- | mt t = fm t (*it might be a formula*)
- in (list_all (params, mt body), !pairs) end;
-
-
-(*Present the entire subgoal to the oracle, assumptions and all, but possibly
- abstracted. Use via compose_tac, which performs no lifting but will
- instantiate variables.*)
-
-fun svc_tac i st =
- let
- val (abs_goal, _) = svc_abstract (Logic.get_goal (Thm.prop_of st) i)
- val th = svc_oracle (Thm.theory_of_thm st) abs_goal
- in compose_tac (false, th, 0) i st end
- handle TERM _ => no_tac st;
-
-
-(*check if user has SVC installed*)
-fun svc_enabled () = getenv "SVC_HOME" <> "";
-fun if_svc_enabled f x = if svc_enabled () then f x else ();