Difference between pages "ADVANCE D3.2 Improvement of automated proof" and "ADVANCE D3.2 Language extension"

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== Overview ==
 
== Overview ==
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The automated prover enhancement was a continuous task since the birth of the Rodin platform. It could be achieved by core platform internal refactorings and enhancements, but also by adding some external reasoning ability such as external provers.<br>
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Mathematical extensions have been co-developed by Systerel (for the Core Rodin Platform) and Southampton (for the Theory plug-in). The main purpose of this new feature was to provide the Rodin user with a way to extend the standard Event-B mathematical language by supporting user-defined operators, basic predicates and algebraic types. Along with these additional notations, the user can also define new proof rules (proof extensions).  
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From the core platform point of view, and within the ten first month of ADVANCE, it consisted into two tasks: the addition of rewriting and inference rules, and the addition of a mechanism to allow the customization and the parametrization or combination of tactics. The user is now able to define various types of tactics called 'profiles' which could be customized and parameterized tactics to discharge some specific proof obligations. The user can furthermore share and backup these defined tactics using the provided import/export mechanism.<br>
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From an external point of view, the SMT Solvers plug-in allowing to use the SMT solvers within Rodin is an effective alternative to the Atelier-B provers, particularly when reasoning on linear arithmetic. It is maintained in the time frame of ADVANCE, and increases the rate of automatically discharged proof obligations.
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The Theory plugin provides, among other things, a user-friendly mechanism to extend the Event-B mathematical language as well as the prover. The theory component is used to hold mathematical extensions (datatypes, operators with direct definitions, operators with recursive definitions and operators with axiomatic definitions), and proof extensions (polymorphic theorems, rewrite and inference rules). Theories are developed in the workspace (akin to models), and are subject to static checking and proof obligation generation. Proof obligations generated from theories ensure any contributed extensions do not compromise the soundness of the existing infrastructure for modelling and proof. In essence, the Theory plugin provides a systematic platform for defining, validating and using extensions while exploiting the benefits brought by proof obligations.
  
 
== Motivations / Decisions ==
 
== Motivations / Decisions ==
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The integration of SMT solvers into the Rodin platform is motivated by two main reasons. On the one hand, the enhancement of its proving capability, especially in the field of arithmetics. On the other hand, the ability of extracting some useful informations from the proofs produced by these solvers, such as unsatisfiable cores, in order to significantly decrease the time necessary to prove a modified model.
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In the past 9 months, the development of the Theory plugin resulted in the following additions:
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* Support for polymorphic theorems in proofs: theorems can be used to ensure the operator and datatype definitions capture the intended understanding by the theory developer. However, requests have been made to ensure that theorems are accessible for proofs. It was decided to provide a user interface-based wizard for instantiating the type parameters in order to 'localise' the theorem based on the current sequent.
 +
* Added support of axiomatic definitions: as of version 1.3.2 of the Theory plugin, only direct and recursive definitions for operators are possible. Requests have been made to add support for axiomatic operator definitions, which can open the door for sophisticated type definitions, e.g., the definition of REALS as an ordered ring with addition and multiplication.
  
 
== Available Documentation ==
 
== Available Documentation ==
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{{TODO|Fill this paragraph.}}
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* Pre-studies (states of the art, proposals, discussions).
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** [http://deploy-eprints.ecs.soton.ac.uk/216/ ''Proposals for Mathematical Extensions for Event-B'']
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** [http://deploy-eprints.ecs.soton.ac.uk/251/ ''Mathematical Extension in Event-B through the Rodin Theory Component'']
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** [http://wiki.event-b.org/index.php/Constrained_Dynamic_Parser#Design_Alternatives ''Generic Parser's Design Alternatives'' ]
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** [http://wiki.event-b.org/index.php/Structured_Types ''Theoretical Description of Structured Types'']
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* Technical details (specifications).
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** [http://wiki.event-b.org/index.php/Mathematical_Extensions ''Mathematical_Extensions wiki page'']
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** [http://wiki.event-b.org/index.php/Constrained_Dynamic_Lexer ''Constrained Dynamic Lexer wiki page'']
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** [http://wiki.event-b.org/index.php/Constrained_Dynamic_Parser ''Constrained Dynamic Parser wiki page'']
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** [http://wiki.event-b.org/index.php/Theory_Plug-in ''Theory plug-in wiki page]
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** [http://wiki.event-b.org/index.php/Records_Extension ''Records Extension Documentation on wiki'']
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* Teaching materials (tutorials).
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* User's guides.
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** [http://wiki.event-b.org/images/Theory_UM.pdf ''Theory Plug-in User Manual'']
  
 
== Planning ==
 
== Planning ==
−
{{TODO|Fill this paragraph.}}
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The Theory plugin became part of the core distribution of Rodin since version 2.6.
 +
 
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Issam Maamria will not be part of Advance after July 31, 2012.
  
 
== References ==
 
== References ==

Revision as of 15:46, 23 June 2012

Overview

Mathematical extensions have been co-developed by Systerel (for the Core Rodin Platform) and Southampton (for the Theory plug-in). The main purpose of this new feature was to provide the Rodin user with a way to extend the standard Event-B mathematical language by supporting user-defined operators, basic predicates and algebraic types. Along with these additional notations, the user can also define new proof rules (proof extensions).

The Theory plugin provides, among other things, a user-friendly mechanism to extend the Event-B mathematical language as well as the prover. The theory component is used to hold mathematical extensions (datatypes, operators with direct definitions, operators with recursive definitions and operators with axiomatic definitions), and proof extensions (polymorphic theorems, rewrite and inference rules). Theories are developed in the workspace (akin to models), and are subject to static checking and proof obligation generation. Proof obligations generated from theories ensure any contributed extensions do not compromise the soundness of the existing infrastructure for modelling and proof. In essence, the Theory plugin provides a systematic platform for defining, validating and using extensions while exploiting the benefits brought by proof obligations.

Motivations / Decisions

In the past 9 months, the development of the Theory plugin resulted in the following additions:

  • Support for polymorphic theorems in proofs: theorems can be used to ensure the operator and datatype definitions capture the intended understanding by the theory developer. However, requests have been made to ensure that theorems are accessible for proofs. It was decided to provide a user interface-based wizard for instantiating the type parameters in order to 'localise' the theorem based on the current sequent.
  • Added support of axiomatic definitions: as of version 1.3.2 of the Theory plugin, only direct and recursive definitions for operators are possible. Requests have been made to add support for axiomatic operator definitions, which can open the door for sophisticated type definitions, e.g., the definition of REALS as an ordered ring with addition and multiplication.

Available Documentation

Planning

The Theory plugin became part of the core distribution of Rodin since version 2.6.

Issam Maamria will not be part of Advance after July 31, 2012.

References

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