A Higher-Order Logic for Concurrent Termination-Preserving Refinement

Compiler correctness proofs for higher-order concurrent languages are difficult: they involve establishing a termination-preserving refinement between a concurrent high-level source language and an implementation that uses low-level shared memory primitives. However, existing logics for proving concurrent refinement either neglect properties such as termination, or only handle first-order state. In this paper, we address these limitations by extending Iris, a recent higher-order concurrent separation logic, with support for reasoning about termination-preserving refinements. To demonstrate the power of these extensions, we prove the correctness of an efficient implementation of a higher-order, session-typed language. To our knowledge, this is the first program logic capable of giving a compiler correctness proof for such a language. The soundness of our extensions and our compiler correctness proof have been mechanized in Coq

A Formal Proof of PAC Learnability for Decision Stumps

We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of classifier. Though such a proof appears simple on paper, analytic and measure-theoretic subtleties arise when carrying it out fully formally. Our proof is structured so as to separate reasoning about deterministic properties of a learning function from proofs of measurability and analysis of probabilities.Comment: 13 pages, appeared in Certified Programs and Proofs (CPP) 202

Transfinite Iris: Resolving an Existential Dilemma of Step-Indexed Separation Logic

Contains fulltext : 236635.pdf (Publisher’s version ) (Open Access) Contains fulltext : 236635.pdf (Author’s version preprint ) (Open Access)PLDI 202