79 lines
3.1 KiB
Plaintext
79 lines
3.1 KiB
Plaintext
-- Copyright (c) 2003-2007 ETH Zurich, Switzerland
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-- 2016 The University of Sheffield, UK
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--
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-- All rights reserved.
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--
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-- Redistribution and use in source and binary forms, with or without
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-- modification, are permitted provided that the following conditions are met:
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--
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-- * Redistributions of source code must retain the above copyright notice, this
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-- list of conditions and the following disclaimer.
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--
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-- * Redistributions in binary form must reproduce the above copyright notice,
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-- this list of conditions and the following disclaimer in the documentation
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-- and/or other materials provided with the distribution.
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--
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-- THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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-- AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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-- IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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-- DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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-- FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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-- DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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-- SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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-- CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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-- OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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-- OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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--
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-- SPDX-License-Identifier: BSD-2-Clause
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--
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package rbt
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context RBTree
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inv wff: not left.oclIsInvalid() and not right.oclIsInvalid()
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inv redinv: color implies
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((left = null or not left.color)
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and (right = null or not right.color))
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inv ordinv: (left = null or left.max() < key)
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inv balinv: black_depth(left) = black_depth(right)
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context RBTree::min(tree: RBTree):Integer
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pre: tree<>null
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post: isMember(tree, result) and
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Integer::allInstances()->forAll(m:Integer |
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isMember(tree, m) implies result<=m)
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context RBTree::max(tree: RBTree):Integer
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pre: tree<>null
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post: isMember(tree, result) and
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Integer::allInstances()->forAll(m:Integer |
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isMember(tree, m) implies m<=result)
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context RBTree::black_depth(tree: RBTree):Integer
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pre: true
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post: (tree = null and result = 0)
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or (tree.left.color and result = black_depth(tree.left))
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or (not tree.left.color and result = black_depth(tree.left) + 1)
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context RBTree::isMember(tree: RBTree, a:Integer):Boolean
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pre: true
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post: result = tree <> null and (a = tree.key or isMember(tree.left, a) or isMember(tree.right, a))
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context RBTree::insert(tree: RBTree, k : Integer):
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pre: tree <> null
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post: isMember(tree, k) and
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Integer::allInstances()->forAll(m:Integer | m = k
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or (isMember(tree, m) = isMember@pre(tree, m)))
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context RBTree::insertFail(tree: RBTree, k : Integer):
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pre: tree <> null
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post: isMember(tree, k) and
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Integer::allInstances()->forAll(m:Integer | m = k
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or (isMember(tree, m) = isMember@pre(tree, m)))
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endpackage
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