Plugging external provers into the Rodin platform Laurent Voisin - - PowerPoint PPT Presentation

Plugging external provers into the Rodin platform

Laurent Voisin (Systerel)

Rodin and Event-B

• An open platform for Event-B modelling and proving
• Designed to model reactive discrete systems by

engineers (no PhD required)

• Based on the Eclipse IDE
• Contains an open proving framework for both

automated and interactive proof

• see http://www.event-b.org

The Event-B mathematical language

• Formally defined
• Based on classical first-order predicate calculus with equality, typed set-

theory and integer arithmetic

• Extensible:
• inductive datatypes (e.g., List)
• (recursively) defined operators (e.g., sequence, append)
• axiomatic types (e.g., Real numbers)
• axiomatic operators (e.g., Real addition)
• Proof system defined using sequent calculus

Proving framework

• From the model, the platform generates proof
• bligations (aka VC)
• Each PO must be discharged
• A proof is a tree where each node carries a sequent
• The root carries the sequent corresponding to the

PO

• The platform maintains the proof tree

Reasoners

• Inference rules are produced by reasoners
• Inference rules can be forward or backward
• A terminating rule has no antecedent


(e.g., H, P |- P)

• Some reasoners are integrated into the platform

(e.g., normalizers and specialized reasoners)

• Some reasoners are provided by external provers

A word about safety

• The platform trusts the external reasoners
• It is not skeptical
• Practical trade-off
• There is more chance that the model is wrong
• Rather than the reasoner you use produces an invalid rule
• You can check each rule with another reasoner to

increase confidence

External provers

• Need to translate from Event-B to the language/

logic of the external prover

• Would need to translate back from the external

prover

• This is easy for terminating rules
• Not attempted for other kinds of rules
• Important note: want minimal rules to facilitate reuse

Examples

• Atelier B provers (translates to classical B)
• SMT solvers (translates to SMT-LIB, uses unsat

core)

• TPTP provers (translates to TPTP)
• Isabelle (experimental, translates to a shallow

embedding in HOL).