67 lines
2.4 KiB
Plaintext
67 lines
2.4 KiB
Plaintext
(*
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* Copyright 2020, Data61, CSIRO (ABN 41 687 119 230)
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*)
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chapter "List Manipulation Functions"
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theory List_Lib
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imports Main
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begin
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definition list_replace :: "'a list \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> 'a list" where
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"list_replace list a b \<equiv> map (\<lambda>x. if x = a then b else x) list"
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primrec list_replace_list :: "'a list \<Rightarrow> 'a \<Rightarrow> 'a list \<Rightarrow> 'a list" where
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"list_replace_list [] a list' = []" |
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"list_replace_list (x # xs) a list' = (if x = a then list' @ xs
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else x # list_replace_list xs a list')"
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definition list_swap :: "'a list \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> 'a list" where
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"list_swap list a b \<equiv> map (\<lambda>x. if x = a then b else if x = b then a else x) list"
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primrec list_insert_after :: "'a list \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> 'a list" where
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"list_insert_after [] a b = []" |
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"list_insert_after (x # xs) a b = (if x = a then x # b # xs
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else x # list_insert_after xs a b)"
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\<comment> \<open>Inserts the value new immediately before the first occurence of a (if any) in the list\<close>
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primrec list_insert_before :: "'a list \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> 'a list" where
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"list_insert_before [] a new = []" |
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"list_insert_before (x # xs) a new = (if x = a then new # x # xs
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else x # list_insert_before xs a new)"
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primrec list_remove :: "'a list \<Rightarrow> 'a \<Rightarrow> 'a list" where
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"list_remove [] a = []" |
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"list_remove (x # xs) a = (if x = a then (list_remove xs a)
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else x # (list_remove xs a))"
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fun after_in_list :: "'a list \<Rightarrow> 'a \<Rightarrow> 'a option" where
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"after_in_list [] a = None" |
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"after_in_list [x] a = None" |
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"after_in_list (x # y # xs) a = (if a = x then Some y else after_in_list (y # xs) a)"
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lemma zip_take1:
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"zip (take n xs) ys = take n (zip xs ys)"
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apply (induct xs arbitrary: n ys)
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apply simp_all
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apply (case_tac n, simp_all)
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apply (case_tac ys, simp_all)
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done
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lemma zip_take2:
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"zip xs (take n ys) = take n (zip xs ys)"
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apply (induct xs arbitrary: n ys)
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apply simp_all
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apply (case_tac n, simp_all)
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apply (case_tac ys, simp_all)
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done
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lemmas zip_take = zip_take1 zip_take2
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lemma replicate_append: "replicate n x @ (x # xs) = replicate (n + 1) x @ xs"
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by (induct n, simp+)
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end
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