We introduce Refinement Reflection, a new framework for building SMT-based deductive verifiers. The key idea is to reflect the code implementing a user-defined function into the function’s (output) refinement type. As a consequence, at uses of the function, the function definition is instantiated in a precise fashion that permits decidable verification. We show how reflection allows the user to write equational proofs of programs just by writing other programs e.g., using pattern-matching and recursion to perform case-splitting and induction. Thus, via, the propositions-as-types principle we show that reflection permits the specification of arbitrary functional correctness properties. While equational proofs are easy, writing them out can be exhausting. We introduce a proof-search algorithm called Proof by Logical Evaluation that uses techniques from model checking and abstract interpretation, to completely automate equational reasoning. We have implemented reflection in Liquid Haskell and used it to verify that the widely used instances of the Monoid, Applicative, Functor, and Monad typeclasses actually satisfy key algebraic laws required to make the clients safe, and to build the first library that actually verifies assumptions about associativity and ordering that are crucial for safe deterministic parallelism.
Fri 12 JanDisplayed time zone: Tijuana, Baja California change
13:30 - 15:20
Benjamin Delaware Purdue University
|Refinement Reflection: Complete Verification with SMT|
|Non-Linear Reasoning For Invariant Synthesis|
|A Practical Construction for Decomposing Numerical Abstract Domains|
|Verifying Equivalence of Database-Driven Applications|