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PVS Workflow

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

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PVS Workflow

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

  2. 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!1=5”) • FLATTEN: Flattens conjunctions, disjunctions, and implications • IFF: Convert a=b to a<=>b 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 “100+x”) • 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

  5. Equality • REPLACE: If you have an equality in the antecedent, you can use REPLACE • Example: (REPLACE -1){-1} l=r replace l by r • Example: (REPLACE -1 RL){-1} l=r replace r by l

  6. 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

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