Verification of high-level transformations with inductive refinement types

Abstract

High-level transformation languages like Rascal include expressive features for manipulating large abstract syntax trees: first-class traversals, expressive pattern matching, backtracking and generalized iterators. We present the design and implementation of an abstract interpretation tool, Rabit, for verifying inductive type and shape properties for transformations written in such languages. We describe how to perform abstract interpretation based on operational semantics, specifically focusing on the challenges arising when analyzing the expressive traversals and pattern matching. Finally, we evaluate Rabit on a series of transformations (normalization, desugaring, refactoring, code generators, type inference, etc.) showing that we can effectively verify stated properties.

Verification of Program Transformations with Inductive Refinement Types

“…Unlike the conference version of the paper [5], we are able to verify P3 in this version. This is because of two first we run the transformation with a nominalized version of the key abstraction to the class map, and then we have refined the preciseness of the map operations for deletion and updating.…”

“…Derivative. (DER) computes the derivative 5 of an additive-multiplicative expression w.r.t. a particular variable 𝑥. P21 Additive expressions containing variables 𝑦 ≠ 𝑥 and constants should produce a constant 0 when differentiated.…”

“…(4) Schmidt-style abstract operational semantics [47] for a significant subset of Rascal adapting the idea of trace memoization to support arbitrary recursive calls with input from infinite domains. The main changes in our contributions in this journal extension are [5]:…”