Update Morphisms section
- Add ontology in document - Add antiquations to reference classes, etc.
This commit is contained in:
Nicolas Méric
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1a23140534
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@ -790,6 +790,108 @@ text\<open>
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section*["morphisms"::technical,main_author="Some(@{docitem ''idir''}::author)"] \<open>Proving Morphisms on Ontologies\<close>
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(*<*)
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(* Mapped_PILIB_Ontology example *)
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term\<open>fold (+) S 0\<close>
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definition sum
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where "sum S = (fold (+) S 0)"
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datatype Hardware_Type =
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Motherboard |
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Expansion_Card |
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Storage_Device |
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Fixed_Media |
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Removable_Media |
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Input_Device |
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Output_Device
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(* Reference Ontology *)
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onto_class Resource =
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name :: string
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onto_class Electronic = Resource +
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provider :: string
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manufacturer :: string
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onto_class Component = Electronic +
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mass :: int
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dimensions :: "int list"
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onto_class Simulation_Model = Electronic +
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type :: string
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onto_class Informatic = Resource +
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description :: string
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onto_class Hardware = Informatic +
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type :: Hardware_Type
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mass :: int
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composed_of :: "Component list"
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invariant c1 :: "mass \<sigma> = sum(map Component.mass (composed_of \<sigma>))"
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onto_class R_Software = Informatic +
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version :: int
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(* Local Ontology *)
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onto_class Item =
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name :: string
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onto_class Product = Item +
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serial_number :: int
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provider :: string
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mass :: int
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onto_class Computer_Software = Item +
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version :: int
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onto_class Electronic_Component = Product +
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dimensions :: "int set"
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onto_class Computer_Hardware = Product +
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type :: Hardware_Type
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composed_of :: "Product list"
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invariant c2 :: "Product.mass \<sigma> = sum(map Product.mass (composed_of \<sigma>))"
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definition Item_to_Resource_morphism :: "'a Item_scheme \<Rightarrow> Resource"
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("_ \<langle>Resource\<rangle>\<^sub>I\<^sub>t\<^sub>e\<^sub>m" [1000]999)
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where "\<sigma> \<langle>Resource\<rangle>\<^sub>I\<^sub>t\<^sub>e\<^sub>m = \<lparr> Resource.tag_attribute = 0::int ,
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Resource.name = name \<sigma> \<rparr>"
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definition Product_to_Component_morphism :: "'a Product_scheme \<Rightarrow> Component"
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("_ \<langle>Component\<rangle>\<^sub>P\<^sub>r\<^sub>o\<^sub>d\<^sub>u\<^sub>c\<^sub>t" [1000]999)
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where " \<sigma> \<langle>Component\<rangle>\<^sub>P\<^sub>r\<^sub>o\<^sub>d\<^sub>u\<^sub>c\<^sub>t = \<lparr> Resource.tag_attribute = 1::int ,
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Resource.name = name \<sigma> ,
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Electronic.provider = Product.provider \<sigma> ,
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Electronic.manufacturer = ''no manufacturer'' ,
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Component.mass = Product.mass \<sigma> ,
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Component.dimensions = [] \<rparr>"
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definition Computer_Hardware_to_Hardware_morphism :: "'a Computer_Hardware_scheme \<Rightarrow> Hardware"
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("_ \<langle>Hardware\<rangle>\<^sub>C\<^sub>o\<^sub>m\<^sub>p\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>H\<^sub>a\<^sub>r\<^sub>d\<^sub>w\<^sub>a\<^sub>r\<^sub>e" [1000]999)
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where "\<sigma> \<langle>Hardware\<rangle>\<^sub>C\<^sub>o\<^sub>m\<^sub>p\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>H\<^sub>a\<^sub>r\<^sub>d\<^sub>w\<^sub>a\<^sub>r\<^sub>e =
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\<lparr> Resource.tag_attribute = 2::int ,
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Resource.name = name \<sigma> ,
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Informatic.description = ''no description'',
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Hardware.type = Computer_Hardware.type \<sigma> ,
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Hardware.mass = mass \<sigma> ,
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Hardware.composed_of = map Product_to_Component_morphism
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(Computer_Hardware.composed_of \<sigma>)
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\<rparr>"
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lemma inv_c2_preserved :
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"c2_inv \<sigma> \<Longrightarrow> c1_inv (\<sigma> \<langle>Hardware\<rangle>\<^sub>C\<^sub>o\<^sub>m\<^sub>p\<^sub>u\<^sub>t\<^sub>e\<^sub>r\<^sub>H\<^sub>a\<^sub>r\<^sub>d\<^sub>w\<^sub>a\<^sub>r\<^sub>e)"
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unfolding c1_inv_def c2_inv_def
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Computer_Hardware_to_Hardware_morphism_def Product_to_Component_morphism_def
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by (auto simp: comp_def)
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lemma Computer_Hardware_to_Hardware_morphism_total :
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"Computer_Hardware_to_Hardware_morphism ` ({X::Computer_Hardware. c2_inv X}) \<subseteq> ({X::Hardware. c1_inv X})"
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using inv_c2_preserved
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by auto
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(*>*)
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text\<open>
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\<^dof> framework does not assume that all documents reference the same ontology.
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Each document may build its local ontology without any external reference.
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@ -851,14 +953,17 @@ onto_class R_Software = Informatic +
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\end{figure}
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To illustrate this process, we use the reference ontology (considered as a standard) described
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in the listing \autoref{fig-Reference-Ontology-example}, defining the \<open>Resource\<close>, \<open>Electronic\<close>,
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\<open>Component\<close>, \<open>Informatic\<close>, \<open>Hardware\<close> and \<open>Software\<close> concepts (or classes).
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in the listing \autoref{fig-Reference-Ontology-example}, defining the \<^typ>\<open>Resource\<close>,
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\<^typ>\<open>Electronic\<close>, \<^typ>\<open>Component\<close>,\<^typ>\<open>Informatic\<close>, \<^typ>\<open>Hardware\<close> and \<^typ>\<open>R_Software\<close>
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concepts (or classes).
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Each class contains a set of attributes or properties and some local invariants.
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In our example, we focus on the \<open>Hardware\<close> class containing a \<open>mass\<close> attribute and composed of a list
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of components with a \<open>mass\<close> attribute formalising the mass value of each component. The \<open>Hardware\<close>
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class also contains a local invariant \<open>c1\<close> to define a constraint linking the global mass of
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a \<open>Hardware\<close> object with the masses of its own components.
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In our example, we focus on the \<^typ>\<open>Hardware\<close> class containing a \<^const>\<open>mass\<close> attribute
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and composed of a list of components with a \<^const>\<open>mass\<close> attribute formalising
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the mass value of each component.
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The \<^typ>\<open>Hardware\<close> class also contains a local \<^theory_text>\<open>invariant c1\<close>
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to define a constraint linking the global mass of a \<^typ>\<open>Hardware\<close> object
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with the masses of its own components.
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\<close>
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text\<open>
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@ -889,12 +994,13 @@ onto_class Computer_Hardware = Product +
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For the needs of our document, we have defined a simple ontology to classify Software and Hardware
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objects. This ontology is described in the figure \autoref{fig-Local-Ontology-example} and
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defines the \<open>Item\<close>, \<open>Product\<close>, \<open>Computer_Software\<close>
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and \<open>Computer_Hardware\<close> concepts. As for the reference ontology, we focus on the \<open>Computer_Hardware\<close>
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class defined as a list of products characterised by their mass value. This class contains a local
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invariant \<open>c2\<close> to guarantee that its own mass value equals the sum of all the masses of the products
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composing the object.
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objects. This ontology is described in \autoref{fig-Local-Ontology-example} and
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defines the \<^typ>\<open>Item\<close>, \<^typ>\<open>Product\<close>, \<^typ>\<open>Computer_Software\<close>
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and \<^typ>\<open>Computer_Hardware\<close> concepts.
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As for the reference ontology, we focus on the \<^typ>\<open>Computer_Hardware\<close>
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class defined as a list of products characterised by their mass value.
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This class contains a local \<^theory_text>\<open>invariant c2\<close> to guarantee that its own mass value
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equals the sum of all the masses of the products composing the object.
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\<close>
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@ -937,11 +1043,12 @@ and the reference ontology using morphism functions (or mapping rules). These ru
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define the relationship between one class of the local ontology to one or several other class(es)
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described in the reference ontology.
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For example,\<open>Product_to_Component_morphism\<close> and \<open>Computer_Hardware_to_Hardware_morphism\<close> definitions,
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detailed in the figure \autoref{fig-mapping-example}, specify how \<open>Product\<close> or \<open>Computer_Hardware\<close>
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objects are mapped to \<open>Component\<close>
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or \<open>Hardware\<close> objects defined in the reference ontology. This mapping shows that the structure
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of a (user) ontology may be quite different from the one of a standard ontology she references.
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For example, \<^const>\<open>Product_to_Component_morphism\<close> and \<^const>\<open>Computer_Hardware_to_Hardware_morphism\<close>
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definitions, detailed in \autoref{fig-mapping-example},
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specify how \<^typ>\<open>Product\<close> or \<^typ>\<open>Computer_Hardware\<close> objects are mapped to \<^typ>\<open>Component\<close>
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or \<^typ>\<open>Hardware\<close> objects defined in the reference ontology.
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This mapping shows that the structure of a (user) ontology may be quite different
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from the one of a standard ontology it references.
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\<close>
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