Difference between revisions of "Structured Types"

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The Event-B mathematical language currently does not support a syntax for the direct definition of structured types such as records or class structures.
 
The Event-B mathematical language currently does not support a syntax for the direct definition of structured types such as records or class structures.
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Nevertheless it is possible to model structured types using projection functions to represent the fields/ attributes.  For example,
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Nevertheless it is possible to model structured types using projection functions to represent the fields/attributes.  For example,
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suppose we wish to model a structured type C with fields e and f (with type E and F respectively).
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suppose we wish to model a record structure 'C' with fields 'e' and 'f' (with type E and F respectively).
 
Let us use the following syntax for this (not part of Event-B):
 
Let us use the following syntax for this (not part of Event-B):
  
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{{SimpleHeader}}
 
{{SimpleHeader}}
 
|<math> \begin{array}{lcl}
 
|<math> \begin{array}{lcl}
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  \textbf{STRUCT}~~~~ C &::&  e\in E\\
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  \textbf{RECORD}~~~~ C &::&  e\in E\\
 
     &&  f \in F
 
     &&  f \in F
 
  \end{array}  
 
  \end{array}  
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'''Names in the proof tree:''' Predicate Prover
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Now, given an element <math>c\in C</math> representing a record, we write <math>e(c)</math> for the 'e' component of structure
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'''Names in the preferences:''' PP restricted, PP after lasso, PP unrestricted
 
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'''Input:''' In the configuration "restricted" all selected hypotheses and the goal are passed to New PP.
 
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In the configuration "after lasso" a lasso operation is applied to the selected hypotheses and the goal and the result is passed to New PP.
 
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The lasso operation selects any unselected hypothesis that has a common symbol with the goal or a hypothesis that was selected before.
 
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In the configuration "unrestricted" all the available hypotheses are passed to New PP.
 
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'''How the Prover Proceeds:''' First, all function and predicate symbols that are different from "<math>\in</math>" and not related to arithmetic are translated away. For example <math>A \subseteq B</math> is translated to <math>\forall x\cdot x \in A \limp x \in B</math>. Then New PP translates the proof obligation to CNF (conjunctive normal form) and applies a combination of unit resolution and the Davis Putnam algorithm.
 
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'''Some Strengths:'''
 
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* New PP outputs a set of "used hypotheses". If an unused hypotheses changes, the old proof can be reused.
 
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* New PP has limited support for equational reasoning.
 

Revision as of 16:03, 1 May 2009

Modelling Structured Types

The Event-B mathematical language currently does not support a syntax for the direct definition of structured types such as records or class structures. Nevertheless it is possible to model structured types using projection functions to represent the fields/attributes. For example, suppose we wish to model a record structure 'C' with fields 'e' and 'f' (with type E and F respectively). Let us use the following syntax for this (not part of Event-B):

\begin{array}{lcl} \textbf{RECORD}~~~~ C &::& e\in E\\ && f \in F \end{array}

We can model this structure in Event-B by introducing (in a context) a set C and two functions e and f as constants as follows:

\begin{array}{l} \textbf{SETS}~~ C\\ \textbf{CONSTANTS}~~ e,~ f\\ \textbf{AXIOMS}\\ ~~~~\begin{array}{l} e \in C \tfun E\\ f \in C \tfun F\\ \end{array} \end{array}


Now, given an element c\in C representing a record, we write e(c) for the 'e' component of structure

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