96 lines
3.3 KiB
Plaintext
96 lines
3.3 KiB
Plaintext
(*************************************************************************
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* Copyright (C)
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* 2019-2023 The University of Exeter
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* 2018-2023 The University of Paris-Saclay
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* 2018 The University of Sheffield
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*
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* License:
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* This program can be redistributed and/or modified under the terms
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* of the 2-clause BSD-style license.
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*************************************************************************)
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chapter\<open>Ontologys Matching\<close>
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theory Ontology_Matching_Example
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imports TestKit
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"Isabelle_DOF.Isa_DOF"
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"Isabelle_DOF_Unit_Tests_document"
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begin
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section\<open>Test Purpose.\<close>
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text\<open> This is merely an example that shows that the generated invariants
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fit nicely together; i.e. allow for sensible consistency and invariant
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preservation proofs related to ontological matchings. \<close>
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section\<open>The Scenario.\<close>
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text\<open>Using HOL, we can define a mapping between two ontologies.
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It is called ontology matching or ontology alignment.
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Here is an example which show how to map two classes.
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HOL also allows us to map the invariants (ontological rules) of the classes!\<close>
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type_synonym UTF8 = string
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definition utf8_to_string
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where "utf8_to_string xx = xx"
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doc_class A =
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first_name :: UTF8
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last_name :: UTF8
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age :: nat
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married_to :: "string option"
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invariant a :: "age \<sigma> < 18 \<longrightarrow> married_to \<sigma> = None"
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doc_class B =
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name :: string
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adult :: bool
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is_married :: bool
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invariant b :: "is_married \<sigma> \<longrightarrow> adult \<sigma>"
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text\<open>We define the mapping between the two classes,
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i.e. how to transform the class @{doc_class A} in to the class @{doc_class B}:\<close>
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definition A_to_B_morphism
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where "A_to_B_morphism X =
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\<lparr> tag_attribute = A.tag_attribute X
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, name = utf8_to_string (first_name X) @ '' '' @ utf8_to_string (last_name X)
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, adult = (age X \<ge> 18)
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, is_married = (married_to X \<noteq> None) \<rparr>"
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text\<open>Sanity check: Invariants are non-contradictory, i.e. there is a witness.\<close>
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lemma inv_a_satisfyable : " Ex (a_inv::A \<Rightarrow> bool)"
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unfolding a_inv_def
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apply(rule_tac x ="\<lparr>Ontology_Matching_Example.A.tag_attribute = xxx,
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first_name = yyy, last_name = zzz, age = 17,
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married_to = None\<rparr>" in exI)
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by auto
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text\<open>Now we check that the invariant is preserved through the morphism:\<close>
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lemma inv_a_preserved :
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"a_inv X \<Longrightarrow> b_inv (A_to_B_morphism X)"
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unfolding a_inv_def b_inv_def A_to_B_morphism_def
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by auto
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text\<open>This also implies that B invariants are non-contradictory: \<close>
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lemma inv_b_preserved : "\<exists>x. (b_inv::B \<Rightarrow> bool) x"
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apply(rule_tac x ="A_to_B_morphism \<lparr>Ontology_Matching_Example.A.tag_attribute = xxx,
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first_name = yyy, last_name = zzz, age = 17,
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married_to = None\<rparr>" in exI)
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by(rule inv_a_preserved,auto simp: a_inv_def)
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lemma A_morphism_B_total :
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"A_to_B_morphism ` ({X::A. a_inv X}) \<subseteq> ({X::B. b_inv X})"
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using inv_a_preserved
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by auto
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end
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