Compiling with continuations, correctly

In this paper we present a novel simulation relation for proving correctness of program transformations that combines syntactic simulations and logical relations. In particular, we establish a new kind of simulation diagram that uses a small-step or big-step semantics in the source language and an untyped, step-indexed logical relation in the target language. Our technique provides a practical solution for proving semantics preservation for transformations that do not preserve reductions in the source language. This is common when transformations generate new binder names, and hence α-conversion must be explicitly accounted for, or when transformations introduce administrative redexes. Our technique does not require reductions in the source language to correspond directly to reductions in the target language. Instead, we enforce a weaker notion of semantic preorder, which suffices to show that semantics are preserved for both whole-program and separate compilation. Because our logical relation is transitive, we can transition between intermediate program states in a small-step fashion and hence the shape of the proof resembles that of a simple small-step simulation. We use this technique to revisit the semantic correctness of a continuation-passing style (CPS) transformation and we demonstrate how it allows us to overcome well-known complications of this proof related to α-conversion and administrative reductions. In addition, by using a logical relation that is indexed by invariants that relate the resource consumption of two programs, we are able show that the transformation preserves diverging behaviors and that our CPS transformation asymptotically preserves the running time of the source program. Our results are formalized in the Coq proof assistant. Our continuation-passing style transformation is part of the CertiCoq compiler for Gallina, the specification language of Coq.

Compositional optimizations for CertiCoq

Compositional compiler verification is a difficult problem that focuses on separate compilation of program components with possibly different verified compilers. Logical relations are widely used in proving correctness of program transformations in higher-order languages; however, they do not scale to compositional verification of multi-pass compilers due to their lack of transitivity. The only known technique to apply to compositional verification of multi-pass compilers for higher-order languages is parametric inter-language simulations (PILS), which is however significantly more complicated than traditional proof techniques for compiler correctness. In this paper, we present a novel verification framework for lightweight compositional compiler correctness . We demonstrate that by imposing the additional restriction that program components are compiled by pipelines that go through the same sequence of intermediate representations , logical relation proofs can be transitively composed in order to derive an end-to-end compositional specification for multi-pass compiler pipelines. Unlike traditional logical-relation frameworks, our framework supports divergence preservation—even when transformations reduce the number of program steps. We achieve this by parameterizing our logical relations with a pair of relational invariants . We apply this technique to verify a multi-pass, optimizing middle-end pipeline for CertiCoq, a compiler from Gallina (Coq’s specification language) to C. The pipeline optimizes and closure-converts an untyped functional intermediate language (ANF or CPS) to a subset of that language without nested functions, which can be easily code-generated to low-level languages. Notably, our pipeline performs more complex closure-allocation optimizations than the state of the art in verified compilation. Using our novel verification framework, we prove an end-to-end theorem for our pipeline that covers both termination and divergence and applies to whole-program and separate compilation, even when different modules are compiled with different optimizations. Our results are mechanized in the Coq proof assistant.

Modular Compilation for a Hybrid Non-Causal Modelling Language

Non-causal modelling is a powerful approach to modelling physical systems in a variety of domains from science and engineering. Non-causal modelling languages enable a high-level and modular approach to modelling. However, it is hard to compile non-causal languages modularly (in the sense of separate compilation). This causes difficulties when simulating large models for which code generation takes a long time, or structurally singular models in which parts of the model are allowed to change at runtime. In this work, we introduce a technique we call order-parametric differentiation to allow truly modular compilation. The idea is to generate (machine) code that can compute derivatives of any order of an expression as needed, thus allowing for ahead-of-time modular compilation of a hybrid non-causal language. We also develop a compilation scheme that enables using partial models as first-class objects in a seamless way and simulating them without the need for just-in-time compilation, even in the presence of structural dynamism. We present a performance evaluation of the scheme we used and study its shortcomings and possible improvements, demonstrating that it is a feasible complement to existing implementation techniques for cases where true modular compilation is a primary objective.