59 lines
1.7 KiB
Plaintext
59 lines
1.7 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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theory DataMap
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imports Main
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begin
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type_synonym ('k, 'a) map = "'k \<rightharpoonup> 'a"
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definition
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data_map_empty :: "('k, 'a) map"
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where
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data_map_empty_def[simp]: "data_map_empty \<equiv> Map.empty"
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definition
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data_map_insert :: "'k \<Rightarrow> 'a \<Rightarrow> ('k, 'a) map \<Rightarrow> ('k, 'a) map"
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where
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data_map_insert_def[simp]: "data_map_insert x y m \<equiv> (m (x \<mapsto> y))"
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definition
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lookupBefore :: "('k :: {linorder, finite}) \<Rightarrow> ('k, 'a) map \<Rightarrow> ('k \<times> 'a) option"
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where
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"lookupBefore x m \<equiv>
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let Ks = {k \<in> dom m. k \<le> x}
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in if Ks = {} then None
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else Some (Max Ks, the (m (Max Ks)))"
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definition
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lookupAround :: "('k :: {linorder, finite}) \<Rightarrow> ('k, 'a) map
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\<Rightarrow> (('k \<times> 'a) option \<times> 'a option \<times> ('k \<times> 'a) option)"
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where
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"lookupAround x m \<equiv>
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let Bs = {k \<in> dom m. k < x};
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As = {k \<in> dom m. k > x}
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in (if Bs = {} then None else Some (Max Bs, the (m (Max Bs))),
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m x,
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if As = {} then None else Some (Min As, the (m (Min Bs))))"
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definition
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data_map_filterWithKey :: "('k \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('k, 'a) map \<Rightarrow> ('k, 'a) map"
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where
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"data_map_filterWithKey f m \<equiv> \<lambda>x. case m x of
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None \<Rightarrow> None
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| Some y \<Rightarrow> if f x y then Some y else None"
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abbreviation(input)
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"data_set_empty \<equiv> {}"
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abbreviation(input)
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"data_set_insert \<equiv> insert"
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abbreviation(input)
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"data_set_delete x S \<equiv> S - {x}"
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end
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