author  haftmann 
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permissions  rwrr 
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(* Title: HOL/Imperative_HOL/Array.thy 
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Author: John Matthews, Galois Connections; Alexander Krauss, Lukas Bulwahn & Florian Haftmann, TU Muenchen 
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*) 

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header {* Monadic arrays *} 

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theory Array 

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imports Heap_Monad 
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begin 
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subsection {* Primitives *} 
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definition (*FIXME present :: "heap \<Rightarrow> 'a\<Colon>heap array \<Rightarrow> bool" where*) 
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array_present :: "'a\<Colon>heap array \<Rightarrow> heap \<Rightarrow> bool" where 
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"array_present a h \<longleftrightarrow> addr_of_array a < lim h" 
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definition (*FIXME get :: "heap \<Rightarrow> 'a\<Colon>heap array \<Rightarrow> 'a list" where*) 
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get_array :: "'a\<Colon>heap array \<Rightarrow> heap \<Rightarrow> 'a list" where 
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"get_array a h = map from_nat (arrays h (TYPEREP('a)) (addr_of_array a))" 
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definition (*FIXME set*) 
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set_array :: "'a\<Colon>heap array \<Rightarrow> 'a list \<Rightarrow> heap \<Rightarrow> heap" where 
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"set_array a x = 
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arrays_update (\<lambda>h. h(TYPEREP('a) := ((h(TYPEREP('a))) (addr_of_array a:=map to_nat x))))" 
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definition (*FIXME alloc*) 
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array :: "'a list \<Rightarrow> heap \<Rightarrow> 'a\<Colon>heap array \<times> heap" where 

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"array xs h = (let 
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l = lim h; 
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r = Array l; 
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h'' = set_array r xs (h\<lparr>lim := l + 1\<rparr>) 
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in (r, h''))" 
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definition (*FIXME length :: "heap \<Rightarrow> 'a\<Colon>heap array \<Rightarrow> nat" where*) 
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length :: "'a\<Colon>heap array \<Rightarrow> heap \<Rightarrow> nat" where 

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"length a h = List.length (get_array a h)" 
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definition (*FIXME update*) 
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change :: "'a\<Colon>heap array \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> heap \<Rightarrow> heap" where 

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"change a i x h = set_array a ((get_array a h)[i:=x]) h" 
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definition (*FIXME noteq*) 
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noteq_arrs :: "'a\<Colon>heap array \<Rightarrow> 'b\<Colon>heap array \<Rightarrow> bool" (infix "=!!=" 70) where 

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"r =!!= s \<longleftrightarrow> TYPEREP('a) \<noteq> TYPEREP('b) \<or> addr_of_array r \<noteq> addr_of_array s" 

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subsection {* Monad operations *} 

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definition new :: "nat \<Rightarrow> 'a\<Colon>heap \<Rightarrow> 'a array Heap" where 

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[code del]: "new n x = Heap_Monad.heap (array (replicate n x))" 

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definition of_list :: "'a\<Colon>heap list \<Rightarrow> 'a array Heap" where 

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[code del]: "of_list xs = Heap_Monad.heap (array xs)" 

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definition make :: "nat \<Rightarrow> (nat \<Rightarrow> 'a\<Colon>heap) \<Rightarrow> 'a array Heap" where 

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[code del]: "make n f = Heap_Monad.heap (array (map f [0 ..< n]))" 

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definition len :: "'a\<Colon>heap array \<Rightarrow> nat Heap" where 

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[code del]: "len a = Heap_Monad.tap (\<lambda>h. length a h)" 
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definition nth :: "'a\<Colon>heap array \<Rightarrow> nat \<Rightarrow> 'a Heap" where 

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[code del]: "nth a i = Heap_Monad.guard (\<lambda>h. i < length a h) 

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(\<lambda>h. (get_array a h ! i, h))" 

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definition upd :: "nat \<Rightarrow> 'a \<Rightarrow> 'a\<Colon>heap array \<Rightarrow> 'a\<Colon>heap array Heap" where 

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[code del]: "upd i x a = Heap_Monad.guard (\<lambda>h. i < length a h) 

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(\<lambda>h. (a, change a i x h))" 

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definition map_entry :: "nat \<Rightarrow> ('a\<Colon>heap \<Rightarrow> 'a) \<Rightarrow> 'a array \<Rightarrow> 'a array Heap" where 

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[code del]: "map_entry i f a = Heap_Monad.guard (\<lambda>h. i < length a h) 

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(\<lambda>h. (a, change a i (f (get_array a h ! i)) h))" 

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definition swap :: "nat \<Rightarrow> 'a \<Rightarrow> 'a\<Colon>heap array \<Rightarrow> 'a Heap" where 

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[code del]: "swap i x a = Heap_Monad.guard (\<lambda>h. i < length a h) 

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(\<lambda>h. (get_array a h ! i, change a i x h))" 

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definition freeze :: "'a\<Colon>heap array \<Rightarrow> 'a list Heap" where 

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[code del]: "freeze a = Heap_Monad.tap (\<lambda>h. get_array a h)" 
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subsection {* Properties *} 

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text {* FIXME: Does there exist a "canonical" array axiomatisation in 
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the literature? *} 
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text {* Primitives *} 
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lemma noteq_arrs_sym: "a =!!= b \<Longrightarrow> b =!!= a" 
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and unequal_arrs [simp]: "a \<noteq> a' \<longleftrightarrow> a =!!= a'" 
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unfolding noteq_arrs_def by auto 
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lemma noteq_arrs_irrefl: "r =!!= r \<Longrightarrow> False" 
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unfolding noteq_arrs_def by auto 
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lemma present_new_arr: "array_present a h \<Longrightarrow> a =!!= fst (array xs h)" 
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by (simp add: array_present_def noteq_arrs_def array_def Let_def) 
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lemma array_get_set_eq [simp]: "get_array r (set_array r x h) = x" 
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by (simp add: get_array_def set_array_def o_def) 
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lemma array_get_set_neq [simp]: "r =!!= s \<Longrightarrow> get_array r (set_array s x h) = get_array r h" 
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by (simp add: noteq_arrs_def get_array_def set_array_def) 
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lemma set_array_same [simp]: 
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"set_array r x (set_array r y h) = set_array r x h" 
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by (simp add: set_array_def) 
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lemma array_set_set_swap: 
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"r =!!= r' \<Longrightarrow> set_array r x (set_array r' x' h) = set_array r' x' (set_array r x h)" 
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by (simp add: Let_def expand_fun_eq noteq_arrs_def set_array_def) 
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lemma get_array_change_eq [simp]: 
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"get_array a (change a i v h) = (get_array a h) [i := v]" 
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by (simp add: change_def) 
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lemma nth_change_array_neq_array [simp]: 
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"a =!!= b \<Longrightarrow> get_array a (change b j v h) ! i = get_array a h ! i" 
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by (simp add: change_def noteq_arrs_def) 
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lemma get_arry_array_change_elem_neqIndex [simp]: 
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"i \<noteq> j \<Longrightarrow> get_array a (change a j v h) ! i = get_array a h ! i" 
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by simp 
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lemma length_change [simp]: 
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"length a (change b i v h) = length a h" 
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by (simp add: change_def length_def set_array_def get_array_def) 
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lemma change_swap_neqArray: 
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"a =!!= a' \<Longrightarrow> 
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change a i v (change a' i' v' h) 
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= change a' i' v' (change a i v h)" 
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apply (unfold change_def) 
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apply simp 
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apply (subst array_set_set_swap, assumption) 
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apply (subst array_get_set_neq) 
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apply (erule noteq_arrs_sym) 
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apply (simp) 
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done 
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lemma change_swap_neqIndex: 
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"\<lbrakk> i \<noteq> i' \<rbrakk> \<Longrightarrow> change a i v (change a i' v' h) = change a i' v' (change a i v h)" 
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by (auto simp add: change_def array_set_set_swap list_update_swap) 
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lemma get_array_init_array_list: 
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"get_array (fst (array ls h)) (snd (array ls' h)) = ls'" 
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by (simp add: Let_def split_def array_def) 
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lemma set_array: 
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"set_array (fst (array ls h)) 
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new_ls (snd (array ls h)) 
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= snd (array new_ls h)" 
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by (simp add: Let_def split_def array_def) 
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lemma array_present_change [simp]: 
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"array_present a (change b i v h) = array_present a h" 
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by (simp add: change_def array_present_def set_array_def get_array_def) 
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lemma array_present_array [simp]: 
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"array_present (fst (array xs h)) (snd (array xs h))" 
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lemma not_array_present_array [simp]: 
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"\<not> array_present (fst (array xs h)) h" 
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by (simp add: array_present_def array_def Let_def) 
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165 

37758  166 

167 
text {* Monad operations *} 

168 

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lemma execute_new [execute_simps]: 
37758  170 
"execute (new n x) h = Some (array (replicate n x) h)" 
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by (simp add: new_def execute_simps) 
37758  172 

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lemma success_newI [success_intros]: 
37758  174 
"success (new n x) h" 
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by (auto intro: success_intros simp add: new_def) 
26170  176 

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177 
lemma crel_newI [crel_intros]: 
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178 
assumes "(a, h') = array (replicate n x) h" 
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179 
shows "crel (new n x) h h' a" 
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by (rule crelI) (simp add: assms execute_simps) 
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181 

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lemma crel_newE [crel_elims]: 
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183 
assumes "crel (new n x) h h' r" 
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184 
obtains "r = fst (array (replicate n x) h)" "h' = snd (array (replicate n x) h)" 
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185 
"get_array r h' = replicate n x" "array_present r h'" "\<not> array_present r h" 
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186 
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187 

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lemma execute_of_list [execute_simps]: 
37758  189 
"execute (of_list xs) h = Some (array xs h)" 
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190 
by (simp add: of_list_def execute_simps) 
37758  191 

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lemma success_of_listI [success_intros]: 
37758  193 
"success (of_list xs) h" 
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194 
by (auto intro: success_intros simp add: of_list_def) 
26170  195 

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196 
lemma crel_of_listI [crel_intros]: 
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197 
assumes "(a, h') = array xs h" 
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198 
shows "crel (of_list xs) h h' a" 
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199 
by (rule crelI) (simp add: assms execute_simps) 
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200 

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201 
lemma crel_of_listE [crel_elims]: 
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202 
assumes "crel (of_list xs) h h' r" 
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203 
obtains "r = fst (array xs h)" "h' = snd (array xs h)" 
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204 
"get_array r h' = xs" "array_present r h'" "\<not> array_present r h" 
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205 
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206 

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207 
lemma execute_make [execute_simps]: 
37758  208 
"execute (make n f) h = Some (array (map f [0 ..< n]) h)" 
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209 
by (simp add: make_def execute_simps) 
26170  210 

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lemma success_makeI [success_intros]: 
37758  212 
"success (make n f) h" 
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by (auto intro: success_intros simp add: make_def) 
37758  214 

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215 
lemma crel_makeI [crel_intros]: 
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216 
assumes "(a, h') = array (map f [0 ..< n]) h" 
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217 
shows "crel (make n f) h h' a" 
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218 
by (rule crelI) (simp add: assms execute_simps) 
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219 

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220 
lemma crel_makeE [crel_elims]: 
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221 
assumes "crel (make n f) h h' r" 
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222 
obtains "r = fst (array (map f [0 ..< n]) h)" "h' = snd (array (map f [0 ..< n]) h)" 
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223 
"get_array r h' = map f [0 ..< n]" "array_present r h'" "\<not> array_present r h" 
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224 
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225 

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226 
lemma execute_len [execute_simps]: 
37758  227 
"execute (len a) h = Some (length a h, h)" 
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228 
by (simp add: len_def execute_simps) 
37758  229 

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230 
lemma success_lenI [success_intros]: 
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"success (len a) h" 
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232 
by (auto intro: success_intros simp add: len_def) 
37752  233 

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234 
lemma crel_lengthI [crel_intros]: 
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235 
assumes "h' = h" "r = length a h" 
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236 
shows "crel (len a) h h' r" 
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237 
by (rule crelI) (simp add: assms execute_simps) 
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238 

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239 
lemma crel_lengthE [crel_elims]: 
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240 
assumes "crel (len a) h h' r" 
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241 
obtains "r = length a h'" "h' = h" 
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242 
using assms by (rule crelE) (simp add: execute_simps) 
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243 

37758  244 
lemma execute_nth [execute_simps]: 
37752  245 
"i < length a h \<Longrightarrow> 
37758  246 
execute (nth a i) h = Some (get_array a h ! i, h)" 
247 
"i \<ge> length a h \<Longrightarrow> execute (nth a i) h = None" 

248 
by (simp_all add: nth_def execute_simps) 

249 

250 
lemma success_nthI [success_intros]: 

251 
"i < length a h \<Longrightarrow> success (nth a i) h" 

252 
by (auto intro: success_intros simp add: nth_def) 

26170  253 

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254 
lemma crel_nthI [crel_intros]: 
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255 
assumes "i < length a h" "h' = h" "r = get_array a h ! i" 
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256 
shows "crel (nth a i) h h' r" 
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257 
by (rule crelI) (insert assms, simp add: execute_simps) 
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258 

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259 
lemma crel_nthE [crel_elims]: 
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260 
assumes "crel (nth a i) h h' r" 
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261 
obtains "i < length a h" "r = get_array a h ! i" "h' = h" 
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262 
using assms by (rule crelE) 
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263 
(erule successE, cases "i < length a h", simp_all add: execute_simps) 
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264 

37758  265 
lemma execute_upd [execute_simps]: 
37752  266 
"i < length a h \<Longrightarrow> 
37758  267 
execute (upd i x a) h = Some (a, change a i x h)" 
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268 
"i \<ge> length a h \<Longrightarrow> execute (upd i x a) h = None" 
37758  269 
by (simp_all add: upd_def execute_simps) 
26170  270 

37758  271 
lemma success_updI [success_intros]: 
272 
"i < length a h \<Longrightarrow> success (upd i x a) h" 

273 
by (auto intro: success_intros simp add: upd_def) 

274 

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275 
lemma crel_updI [crel_intros]: 
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276 
assumes "i < length a h" "h' = change a i v h" 
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277 
shows "crel (upd i v a) h h' a" 
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278 
by (rule crelI) (insert assms, simp add: execute_simps) 
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279 

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280 
lemma crel_updE [crel_elims]: 
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281 
assumes "crel (upd i v a) h h' r" 
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282 
obtains "r = a" "h' = change a i v h" "i < length a h" 
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283 
using assms by (rule crelE) 
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284 
(erule successE, cases "i < length a h", simp_all add: execute_simps) 
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285 

37758  286 
lemma execute_map_entry [execute_simps]: 
37752  287 
"i < length a h \<Longrightarrow> 
37758  288 
execute (map_entry i f a) h = 
37752  289 
Some (a, change a i (f (get_array a h ! i)) h)" 
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290 
"i \<ge> length a h \<Longrightarrow> execute (map_entry i f a) h = None" 
37758  291 
by (simp_all add: map_entry_def execute_simps) 
37752  292 

37758  293 
lemma success_map_entryI [success_intros]: 
294 
"i < length a h \<Longrightarrow> success (map_entry i f a) h" 

295 
by (auto intro: success_intros simp add: map_entry_def) 

296 

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297 
lemma crel_map_entryI [crel_intros]: 
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298 
assumes "i < length a h" "h' = change a i (f (get_array a h ! i)) h" "r = a" 
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299 
shows "crel (map_entry i f a) h h' r" 
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300 
by (rule crelI) (insert assms, simp add: execute_simps) 
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301 

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302 
lemma crel_map_entryE [crel_elims]: 
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303 
assumes "crel (map_entry i f a) h h' r" 
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304 
obtains "r = a" "h' = change a i (f (get_array a h ! i)) h" "i < length a h" 
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305 
using assms by (rule crelE) 
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306 
(erule successE, cases "i < length a h", simp_all add: execute_simps) 
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307 

37758  308 
lemma execute_swap [execute_simps]: 
37752  309 
"i < length a h \<Longrightarrow> 
37758  310 
execute (swap i x a) h = 
37752  311 
Some (get_array a h ! i, change a i x h)" 
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312 
"i \<ge> length a h \<Longrightarrow> execute (swap i x a) h = None" 
37758  313 
by (simp_all add: swap_def execute_simps) 
314 

315 
lemma success_swapI [success_intros]: 

316 
"i < length a h \<Longrightarrow> success (swap i x a) h" 

317 
by (auto intro: success_intros simp add: swap_def) 

37752  318 

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319 
lemma crel_swapI [crel_intros]: 
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320 
assumes "i < length a h" "h' = change a i x h" "r = get_array a h ! i" 
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321 
shows "crel (swap i x a) h h' r" 
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322 
by (rule crelI) (insert assms, simp add: execute_simps) 
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323 

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324 
lemma crel_swapE [crel_elims]: 
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325 
assumes "crel (swap i x a) h h' r" 
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326 
obtains "r = get_array a h ! i" "h' = change a i x h" "i < length a h" 
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327 
using assms by (rule crelE) 
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328 
(erule successE, cases "i < length a h", simp_all add: execute_simps) 
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329 

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330 
lemma execute_freeze [execute_simps]: 
37758  331 
"execute (freeze a) h = Some (get_array a h, h)" 
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332 
by (simp add: freeze_def execute_simps) 
37758  333 

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334 
lemma success_freezeI [success_intros]: 
37758  335 
"success (freeze a) h" 
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336 
by (auto intro: success_intros simp add: freeze_def) 
26170  337 

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338 
lemma crel_freezeI [crel_intros]: 
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339 
assumes "h' = h" "r = get_array a h" 
1bec64044b5e
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changeset

340 
shows "crel (freeze a) h h' r" 
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341 
by (rule crelI) (insert assms, simp add: execute_simps) 
1bec64044b5e
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changeset

342 

1bec64044b5e
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343 
lemma crel_freezeE [crel_elims]: 
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344 
assumes "crel (freeze a) h h' r" 
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changeset

345 
obtains "h' = h" "r = get_array a h" 
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parents:
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changeset

346 
using assms by (rule crelE) (simp add: execute_simps) 
37771
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changeset

347 

26170  348 
lemma upd_return: 
349 
"upd i x a \<guillemotright> return a = upd i x a" 

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changeset

350 
by (rule Heap_eqI) (simp add: bind_def guard_def upd_def execute_simps) 
26170  351 

37752  352 
lemma array_make: 
353 
"new n x = make n (\<lambda>_. x)" 

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354 
by (rule Heap_eqI) (simp add: map_replicate_trivial execute_simps) 
26170  355 

37752  356 
lemma array_of_list_make: 
357 
"of_list xs = make (List.length xs) (\<lambda>n. xs ! n)" 

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changeset

358 
by (rule Heap_eqI) (simp add: map_nth execute_simps) 
26170  359 

37771
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diff
changeset

360 
hide_const (open) new 
26170  361 

26182  362 

363 
subsection {* Code generator setup *} 

364 

365 
subsubsection {* Logical intermediate layer *} 

366 

367 
definition new' where 

31205
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String.literal replaces message_string, code_numeral replaces (code_)index
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368 
[code del]: "new' = Array.new o Code_Numeral.nat_of" 
37752  369 

28562  370 
lemma [code]: 
37752  371 
"Array.new = new' o Code_Numeral.of_nat" 
26182  372 
by (simp add: new'_def o_def) 
373 

374 
definition of_list' where 

31205
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String.literal replaces message_string, code_numeral replaces (code_)index
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parents:
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diff
changeset

375 
[code del]: "of_list' i xs = Array.of_list (take (Code_Numeral.nat_of i) xs)" 
37752  376 

28562  377 
lemma [code]: 
37752  378 
"Array.of_list xs = of_list' (Code_Numeral.of_nat (List.length xs)) xs" 
26182  379 
by (simp add: of_list'_def) 
380 

381 
definition make' where 

31205
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parents:
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diff
changeset

382 
[code del]: "make' i f = Array.make (Code_Numeral.nat_of i) (f o Code_Numeral.of_nat)" 
37752  383 

28562  384 
lemma [code]: 
37752  385 
"Array.make n f = make' (Code_Numeral.of_nat n) (f o Code_Numeral.nat_of)" 
26182  386 
by (simp add: make'_def o_def) 
387 

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388 
definition len' where 
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diff
changeset

389 
[code del]: "len' a = Array.len a \<guillemotright>= (\<lambda>n. return (Code_Numeral.of_nat n))" 
37752  390 

28562  391 
lemma [code]: 
37752  392 
"Array.len a = len' a \<guillemotright>= (\<lambda>i. return (Code_Numeral.nat_of i))" 
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diff
changeset

393 
by (simp add: len'_def) 
26182  394 

395 
definition nth' where 

31205
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parents:
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diff
changeset

396 
[code del]: "nth' a = Array.nth a o Code_Numeral.nat_of" 
37752  397 

28562  398 
lemma [code]: 
37752  399 
"Array.nth a n = nth' a (Code_Numeral.of_nat n)" 
26182  400 
by (simp add: nth'_def) 
401 

402 
definition upd' where 

31205
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String.literal replaces message_string, code_numeral replaces (code_)index
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parents:
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diff
changeset

403 
[code del]: "upd' a i x = Array.upd (Code_Numeral.nat_of i) x a \<guillemotright> return ()" 
37752  404 

28562  405 
lemma [code]: 
37752  406 
"Array.upd i x a = upd' a (Code_Numeral.of_nat i) x \<guillemotright> return a" 
37709  407 
by (simp add: upd'_def upd_return) 
26182  408 

37752  409 
lemma [code]: 
410 
"map_entry i f a = (do 

411 
x \<leftarrow> nth a i; 

412 
upd i (f x) a 

413 
done)" 

37758  414 
by (rule Heap_eqI) (simp add: bind_def guard_def map_entry_def execute_simps) 
26182  415 

37752  416 
lemma [code]: 
417 
"swap i x a = (do 

418 
y \<leftarrow> nth a i; 

419 
upd i x a; 

420 
return y 

421 
done)" 

37758  422 
by (rule Heap_eqI) (simp add: bind_def guard_def swap_def execute_simps) 
37752  423 

424 
lemma [code]: 

425 
"freeze a = (do 

426 
n \<leftarrow> len a; 

37756
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haftmann
parents:
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diff
changeset

427 
Heap_Monad.fold_map (\<lambda>i. nth a i) [0..<n] 
37752  428 
done)" 
429 
proof (rule Heap_eqI) 

430 
fix h 

431 
have *: "List.map 

432 
(\<lambda>x. fst (the (if x < length a h 

433 
then Some (get_array a h ! x, h) else None))) 

434 
[0..<length a h] = 

435 
List.map (List.nth (get_array a h)) [0..<length a h]" 

436 
by simp 

37758  437 
have "execute (Heap_Monad.fold_map (Array.nth a) [0..<length a h]) h = 
37752  438 
Some (get_array a h, h)" 
37756
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haftmann
parents:
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diff
changeset

439 
apply (subst execute_fold_map_unchanged_heap) 
37752  440 
apply (simp_all add: nth_def guard_def *) 
441 
apply (simp add: length_def map_nth) 

442 
done 

37758  443 
then have "execute (do 
37752  444 
n \<leftarrow> len a; 
37756
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haftmann
parents:
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diff
changeset

445 
Heap_Monad.fold_map (Array.nth a) [0..<n] 
37752  446 
done) h = Some (get_array a h, h)" 
37787
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parents:
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diff
changeset

447 
by (auto intro: execute_bind_eq_SomeI simp add: execute_simps) 
37758  448 
then show "execute (freeze a) h = execute (do 
37752  449 
n \<leftarrow> len a; 
37756
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haftmann
parents:
37752
diff
changeset

450 
Heap_Monad.fold_map (Array.nth a) [0..<n] 
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parents:
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diff
changeset

451 
done) h" by (simp add: execute_simps) 
37752  452 
qed 
453 

454 
hide_const (open) new' of_list' make' len' nth' upd' 

455 

456 

457 
text {* SML *} 

26182  458 

459 
code_type array (SML "_/ array") 

460 
code_const Array (SML "raise/ (Fail/ \"bare Array\")") 

26752  461 
code_const Array.new' (SML "(fn/ ()/ =>/ Array.array/ ((_),/ (_)))") 
35846  462 
code_const Array.of_list' (SML "(fn/ ()/ =>/ Array.fromList/ _)") 
26752  463 
code_const Array.make' (SML "(fn/ ()/ =>/ Array.tabulate/ ((_),/ (_)))") 
37719
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haftmann
parents:
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diff
changeset

464 
code_const Array.len' (SML "(fn/ ()/ =>/ Array.length/ _)") 
26752  465 
code_const Array.nth' (SML "(fn/ ()/ =>/ Array.sub/ ((_),/ (_)))") 
466 
code_const Array.upd' (SML "(fn/ ()/ =>/ Array.update/ ((_),/ (_),/ (_)))") 

26182  467 

468 
code_reserved SML Array 

469 

470 

37752  471 
text {* OCaml *} 
26182  472 

473 
code_type array (OCaml "_/ array") 

474 
code_const Array (OCaml "failwith/ \"bare Array\"") 

32580  475 
code_const Array.new' (OCaml "(fun/ ()/ >/ Array.make/ (Big'_int.int'_of'_big'_int/ _)/ _)") 
35846  476 
code_const Array.of_list' (OCaml "(fun/ ()/ >/ Array.of'_list/ _)") 
37719
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haftmann
parents:
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diff
changeset

477 
code_const Array.len' (OCaml "(fun/ ()/ >/ Big'_int.big'_int'_of'_int/ (Array.length/ _))") 
32580  478 
code_const Array.nth' (OCaml "(fun/ ()/ >/ Array.get/ _/ (Big'_int.int'_of'_big'_int/ _))") 
479 
code_const Array.upd' (OCaml "(fun/ ()/ >/ Array.set/ _/ (Big'_int.int'_of'_big'_int/ _)/ _)") 

26182  480 

481 
code_reserved OCaml Array 

482 

483 

37752  484 
text {* Haskell *} 
26182  485 

29793  486 
code_type array (Haskell "Heap.STArray/ Heap.RealWorld/ _") 
26182  487 
code_const Array (Haskell "error/ \"bare Array\"") 
29793  488 
code_const Array.new' (Haskell "Heap.newArray/ (0,/ _)") 
489 
code_const Array.of_list' (Haskell "Heap.newListArray/ (0,/ _)") 

37719
271ecd4fb9f9
moved "open" operations from Heap.thy to Array.thy and Ref.thy
haftmann
parents:
37716
diff
changeset

490 
code_const Array.len' (Haskell "Heap.lengthArray") 
29793  491 
code_const Array.nth' (Haskell "Heap.readArray") 
492 
code_const Array.upd' (Haskell "Heap.writeArray") 

26182  493 

26170  494 
end 