Theorem Proving and Model Checking in PVS Workflow

Theorem Proving and Model Checking in PVS Workflow System PVS File PROOFS Properties of system Proof construction Conversion (Program, circuit, protocol…) Interaction with theorem prover and property. Can be automated or done manually 1 A

Theorem Proving and Model Checking in PVS The Gentzen Sequent • COPY duplicates a formula Why? When you instantiate a quantified formula, the original one is lost • DELETE removes unnecessary formulae – keep your proof easy to follow 2

Theorem Proving and Model Checking in PVS Propositional Rules • BDDSIMP simplify propositional structure using BDDs • CASE: case splitting usage: (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 3

Theorem Proving and Model Checking in PVS 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 4

Theorem Proving and Model Checking in PVS 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 5

Theorem Proving and Model Checking in PVS 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 6