PVS Workflow

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PVS Workflow
System
PROOFS
PVS File
Properties
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Conversion of system (Program, circuit,
protocol)and property. Can be automated or
donemanually
Proof construction Interaction with the theorem
prover
A
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The Gentzen Sequent

• COPY duplicates a formulaWhy? When you
  instantiate a quantified formula, the original
  one is lost
• DELETE removes unnecessary formulae keep your
  proof easy to follow

3
Propositional Rules

• BDDSIMP simplify propositional structure using
  BDDs
• CASE case splittingusage (CASE i!15)
• FLATTEN Flattens conjunctions, disjunctions, and
  implications
• IFF Convert ab to altgtb for a, b boolean
• LIFT-IF move up case splits inside a formula

4
Quantifiers

• INST Instantiate Quantifiers
• Do this if you have EXISTS in the consequent, or
  FORALL in the antecedent
• Usage (INST -10 100x)
• SKOLEM! Introduce Skolem Constants
• Do this if you have FORALL in the consequent (and
  do not want induction), or EXISTS in the
  antecedent
• If the type of the variable matters, use
  SKOLEM-TYPEPRED

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Equality

• REPLACE If you have an equality in the
  antecedent, you can use REPLACE
• Example (REPLACE -1)-1 lr replace l by
  r
• Example (REPLACE -1 RL)-1 lr replace r
  by l

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Induction

• INDUCT Performs induction
• Usage (INDUCT i)
• There should be a FORALL i equation in the
  consequent
• You get two subgoals, one for the induction base
  and one for the step
• PVS comes with many induction schemes. Look in
  the prelude for the full list