Program Verification with Dafny: Ensuring Functional Correctness
"Learn about Dafny, an automatic program verifier for functional correctness, enabling program verification through innovative features like invariants, assertions, theorem-prover commands, and more."
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Presentation Transcript
Dafny An automatic program verifier for functional correctness K. Rustan M. Leino Research in Software Engineering (RiSE) Microsoft Research, Redmond LPAR-16 Dakar, Senegal 27 April 2010
Program verification traditional mechanical program verification functional correctness Dafny and others extended static checking limited checking automatic decision procedures (SMT solvers) interactive proof assistants K. Rustan M. Leino
User interaction Program oriented: invariants, assertions, Formula oriented: theorem-prover commands, tactics Formula K. Rustan M. Leino
Dafny Binary search
Dafny Object-based language generic classes, no subclassing object references, dynamic allocation sequential control Built-in specifications pre- and postconditions framing loop invariants, inline assertions termination Specification support Sets, sequences, algebraic datatypes User-defined functions Ghost variables K. Rustan M. Leino
Top-level grammar Program ::= Type* Type ::= Class | Datatype Class ::= class Name { Member* } Member ::= Field | Method | Function Datatype ::= datatype Name { Constructor* } Generic (that is, accepts type parameters) K. Rustan M. Leino
Types Booleans Mathematical integers Finite sets Sequences Class types Algebraic datatypes K. Rustan M. Leino
Dafny Calculator
Verification architecture Boogie K. Rustan M. Leino
Dafny, Boogie, VC From Dafny to verification-condition formulas
Axiomatizing functions function F(x: T): U { Body } ( x F(x) = Body) datatype Tree { Leaf(int); Split(Tree,Tree); } function G(x: Tree): U { match x case Leaf(n) n case Split(a,b) G(a) + G(b) } ( t G(t) = if else G(left(t)) + G(right(t))) ( n G(Leaf(n)) = n) ( a,b G(Split(a,b)) = G(a) + G(b)) K. Rustan M. Leino
root Dafny prev Schorr-Waite algorithm current
Verifying termination Functions Loops Methods decreases clause lexicographic tuple components of tuple can be of any types to compare, consider longest commonly typed prefix of the lexicographic tuple K. Rustan M. Leino
Dafny Using a program to prover a theorem
Conclusions Full functional-correctness verification is becoming more automatic Interaction is moving closer to the problem domain A well-designed language and verifier, plus a great SMT solver, go a long way Dafny (and Boogie) open source: boogie.codeplex.com K. Rustan M. Leino
