# HG changeset patch # User wenzelm # Date 1188388680 -7200 # Node ID 943ef707396c7dfda4313489f8d6aeeb7a6b31ee # Parent d7cf53c1085ff9724292fb19c19e22e966fe8cc8 added Hoare/hoare_tac.ML (code from Hoare/Hoare.thy, also required in Isar_examples/Hoare.thy); diff -r d7cf53c1085f -r 943ef707396c src/HOL/Hoare/Hoare.thy --- a/src/HOL/Hoare/Hoare.thy Wed Aug 29 11:10:59 2007 +0200 +++ b/src/HOL/Hoare/Hoare.thy Wed Aug 29 13:58:00 2007 +0200 @@ -10,6 +10,7 @@ *) theory Hoare imports Main +uses ("hoare_tac.ML") begin types @@ -225,167 +226,10 @@ done -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; -*} +use "hoare_tac.ML" method_setup vcg = {* Method.no_args (Method.SIMPLE_METHOD' (hoare_tac (K all_tac))) *} diff -r d7cf53c1085f -r 943ef707396c src/HOL/IsaMakefile --- a/src/HOL/IsaMakefile Wed Aug 29 11:10:59 2007 +0200 +++ b/src/HOL/IsaMakefile Wed Aug 29 13:58:00 2007 +0200 @@ -369,7 +369,7 @@ HOL-Hoare: HOL $(LOG)/HOL-Hoare.gz $(LOG)/HOL-Hoare.gz: $(OUT)/HOL Hoare/Arith2.thy \ - Hoare/Examples.thy Hoare/Hoare.thy \ + Hoare/Examples.thy Hoare/Hoare.thy Hoare/hoare_tac.ML \ Hoare/Heap.thy Hoare/HeapSyntax.thy Hoare/Pointer_Examples.thy \ Hoare/ROOT.ML Hoare/ExamplesAbort.thy Hoare/HeapSyntaxAbort.thy \ Hoare/HoareAbort.thy Hoare/SchorrWaite.thy \ @@ -687,7 +687,7 @@ Isar_examples/Puzzle.thy Isar_examples/Summation.thy \ Isar_examples/ROOT.ML Isar_examples/document/proof.sty \ Isar_examples/document/root.bib Isar_examples/document/root.tex \ - Isar_examples/document/style.tex Hoare/hoare.ML + Isar_examples/document/style.tex Hoare/hoare_tac.ML @$(ISATOOL) usedir $(OUT)/HOL Isar_examples diff -r d7cf53c1085f -r 943ef707396c src/HOL/Isar_examples/Hoare.thy --- a/src/HOL/Isar_examples/Hoare.thy Wed Aug 29 11:10:59 2007 +0200 +++ b/src/HOL/Isar_examples/Hoare.thy Wed Aug 29 13:58:00 2007 +0200 @@ -8,7 +8,7 @@ header {* Hoare Logic *} theory Hoare imports Main -uses ("~~/src/HOL/Hoare/hoare.ML") begin +uses ("~~/src/HOL/Hoare/hoare_tac.ML") begin subsection {* Abstract syntax and semantics *} @@ -442,8 +442,7 @@ apply blast done -ML {* val Valid_def = thm "Valid_def" *} -use "~~/src/HOL/Hoare/hoare.ML" +use "~~/src/HOL/Hoare/hoare_tac.ML" method_setup hoare = {* Method.no_args