A Brief Overview of PVS - Computer Science Laboratory - SRI ...
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A Brief Overview of PVS - Computer Science Laboratory - SRI ...
Aug 19, 2008 - PVS is a verification system combining language expressiveness with automated tools. It features an interactive ..... Mailing lists. PVS is open ...
A Brief Overview of PVS Sam Owre Computer Science Laboratory SRI International Menlo Park, CA
August 19, 2008
Language & Prover Example - Ordered Binary Trees More Features of PVS Libraries & Applications Conclusion
Introduction
PVS - Prototype Verification System PVS is a verification system combining language expressiveness with automated tools. It features an interactive theorem prover with powerful commands and user-definable strategies PVS has been available since 1993 It has hundreds of users It is open source
Sam Owre
A Brief Overview of PVS
Language & Prover Example - Ordered Binary Trees More Features of PVS Libraries & Applications Conclusion
The PVS language is based on higher-order logic (type theory) Many other systems use higher-order logic including Coq, HOL, Isabelle/HOL, Nuprl PVS uses classical (non-constructive) logic It has a set-theoretic semantics
Sam Owre
A Brief Overview of PVS
Language & Prover Example - Ordered Binary Trees More Features of PVS Libraries & Applications Conclusion
PVS has a rich type system Basic types: number, boolean, etc. New basic types may be introduced Enumeration types: {red, green, blue} Function, record, tuple, and cotuple types: [number -> number] [# flag: boolean, value: [boolean, number] [boolean + number]
Sam Owre
number #]
A Brief Overview of PVS
Language & Prover Example - Ordered Binary Trees More Features of PVS Libraries & Applications Conclusion
Subtypes PVS has two notions of subtype: Predicate subtypes: {x: real | x /= 0} {f: [real -> real] | injective?(f)}
The type {x: T | P(x)} may be abbreviated as (P). Structural subtypes: [# x, y: real, c: color #] {m: nat | m boolean]): (p(leaf) AND (FORALL (node1_var: T, node2_var: binary_tree, node3_var: binary_tree): p(node2_var) AND p(node3_var) IMPLIES p(node(node1_var, node2_var, node3_var)))) IMPLIES (FORALL (binary_tree_var: binary_tree): p(binary_tree_var)); Sam Owre
A Brief Overview of PVS
Language & Prover Example - Ordered Binary Trees More Features of PVS Libraries & Applications Conclusion
Binary Tree Datatype Generated Theories Ordered Binary Trees Theory Demo of main insertion property
Ordered Binary Trees Theory Ordered binary trees can be introduced by a theory that is parametric in the value type as well as the total ordering relation. obt [T: TYPE,
