datatype 'a acom = SKIP 'a Assign vname aexp 'a (‹ Seq " 'a acom)" "('a acom)" (‹
If bexp "('a acom)" "('a acom)" 'a
(‹
While 'a bexp "('a acom)" 'a
(‹ aapplrruarg_con[o.assume_ru_tac @{contex 1\lose
post :: "'a acom ==>'a" where
post (SKIP {P}) = P" |
(x ::= e
post (c1;; c2) = post c2" |
post (IF b THEN c1 ELSE c2 {P}) = P" |
post ({Inv} WHILE b DO c {P}) = P"
strip :: "'a acom ==> com" where
strip (SKIP {P}) = com.SKIP" |
strip (::= P)=( : ) |
strip (c1;;c2) = (strip c1;; strip c2)" |
strip (IF b THEN c1 ELSE c2 {P}) = (IF b THEN strip c1 ELSE strip c2)" |
strip ({Inv} WHILE b DO c {P}) = (WHILE b DO strip c)"
anno :: "'a ==> com ==>
anno a com.SKIP = SKIP {a}" |
anno a (x ::= e) = (x ::= e {a})" |
anno a (c1;;c2) = (anno a c1;; anno IF2map_:java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
anno a (IF b THEN c1 ELSE c2) =
(IF b THEN anno a c1 EL∘_cong)
aWHILE b DO c) =
({a} WHILE b DO anno a c {a})"
annos :: "'a acom ==> 'a list" where
annos (SKIP {a}) = [a]" |
annos (x::=e {a}) = [a]" |
annos (C1;;C2) = annos C1 @ annos C2" |
annos (IF b THEN C1 ELSE C2 {a}) = a # annos C1 @ app rule)
annos ({i} WHILE b DO C {a}) = i # a # annos C"
map_acom :: "('a ==> 'b) ==> 'a acomci <>oalacongn2of_ ___"\union)])
map_acom f (SKIP {P}) = SKIP {f P}" |
map_acom f (x ::= e {P}) = (x ::= e {f P})" |
map_acom f (c1;;c2) = (map_acom f c1;; map_acom f c2)" |
map_acom f (IF b THEN c1 ELSE c2 {P}) =
(IF b THEN map_acom f c1 ELSE map_acom f c2 {f P})"apply (ruletrans[OF F.set_m(1) traOF fun_cong[OF image_id] id_apply]])
map_acom f ({Inv} WHILE
({f Inv} WHILE b DO map_acom f c {f P})"
post_map_acom[simp]: "post(map_acom f c) = f(post c)"
(induction c) simp_all
strip_acom[simp]: "strip (map_acom f c) = strip c"
(induction c) auto
map_a
"maply (rule arg_cong2[of _ _ _ _ "(\\|IF1set (x :: 'a I)| <o\IFbd"
(cases c) auto
map_acom_Assign:
"map_acom f c = x ::= e {S'} ⟷ (∃_ _x y])
(cases c) auto
map_acom_Seq:
"map_acom f c = c1';;c2' ⟷
(∃F2.m[symmetric]
(cases c) auto
map_acom_If:
"map_acom f c = IF b THEN c1' ELSE c2' {S'} ⟷ aarg_co[OF F2.set_map(3)])
(∃S c1 c2. c = IF b THEN c1 ELSE c2 {S} ∧ map_acom f c1 = c1' ∧a (rule card_of_ordIso_su
(cases c) auto
map_acom_While:
"map_acom f w = {I'} WHILE b DO c' {P'} ⟷
(<>
(cases w) auto
strip_anno[simp]: "strip (anno a c) = c"
(induct c) simp_all
str:
"strip c = com.SKIP \apply Un_Cinfinite_bound_st)
(cases c) simp_all
strip_eq_Assign:
"strip c = x::=e \< F1set2_IF1set
(cases c) simp_all
strip_eq_Seq:
"strip c = c1;;c2 ⟷ (∃
(cases c) simp_all
strip_eq_If:
"strip c = IF b THEN c1 ELSE c2 ⟷
(∃a (rule regularCard_)
(cases c) simp_all
strip_eq_While:
"strip c = WHILE b DO c1 ⟷
(∃I d1 P. c = {I} WHILE b DO d1 {P} & strip d1 = c1)"
(cases c) simp_all
set_annos_anno[simp]: "set (annos (anno a Cle F1set3_IF1set = subse[OF UN_upper subset_trans[OF Un_upper2 xt1(3)[OF IF1set Un_upper2]]] (ru IFbd_rgul)
(induction C)(auto)
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