Forth Semantics for Compiler Verification

Proceedings of the 2003 workshop on Mechanized reasoning about languages with variable binding - MERLIN '03, 2003

The task of designing and implementing a compiler can be a difficult and error-prone process. In this paper, we present a new approach based on the use of higher-order abstract syntax and term rewriting in a logical framework. All program transformations, from parsing to code generation, are cleanly isolated and specified as term rewrites. This has several advantages. The correctness of the compiler depends solely on a small set of rewrite rules that are written in the language of formal mathematics. In addition, the logical framework guarantees the preservation of scoping, and it automates many frequently-occurring tasks including substitution and rewriting strategies. As we show, compiler development in a logical framework can be easier than in a general-purpose language like ML, in part because of automation, and also because the framework provides extensive support for examination, validation, and debugging of the compiler transformations. The paper is organized around a case study, using the MetaPRL logical framework to compile an ML-like language to Intel x86 assembly. We also present a scoped formalization of x86 assembly in which all registers are immutable.

1996

We present a new programming language ProFun which is aimed for the specification and prototype implementation of reactive systems. ProFun combines the paradigms of concurrent and functional programming. A formal operational semantics is developed as a basis for verification techniques. We have implemented a ProFun-compiler which uses C++ as its target language.

Journal of Automated Reasoning, 2009

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its soundness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well.

Higher-Order and Symbolic Computation, 2006

The task of designing and implementing a compiler can be a difficult and error-prone process. In this paper, we present a new approach based on the use of higher-order abstract syntax and term rewriting in a logical framework. All program transformations, from parsing to code generation, are cleanly isolated and specified as term rewrites. This has several advantages. The correctness of the compiler depends solely on a small set of rewrite rules that are written in the language of formal mathematics. In addition, the logical framework guarantees the preservation of scoping, and it automates many frequently-occurring tasks including substitution and rewriting strategies. As we show, compiler development in a logical framework can be easier than in a general-purpose language like ML, in part because of automation, and also because the framework provides extensive support for examination, validation, and debugging of the compiler transformations. The paper is organized around a case study, using the MetaPRL logical framework to compile an ML-like language to Intel x86 assembly. We also present a scoped formalization of x86 assembly in which all registers are immutable.

1993

The paper presents a practical verification tool that helps in the development of provably correct compilers. The tool is based on the approach of proving termination of PROLOG-like programs using term-rewriting techniques and a technique of testing whether a given PROLOG program can be soundly executed on PROLOG interpreters without the Occur-check test. The tool has been built on top of the theorem prover, RRL (Rewrite Rule Laboratory).

We present a view on the problem of formal verification of imperative programs. Formal verification is usually associated to functional programming languages, but a real-world application will probably be written in imperative mainstream languages. To have the power of formal verification in an imperative language, we present, for demonstrative purposes, an instance of a technique to extend a language with support for logical annotations. We present a short description of LISS (the imperative language chosen to be extended) and Why (the verification condition generator), and after a detailed analysis of the mechanisms used to generate proof-obligations, we conclude, analyzing the global quality of the result.

Programming Languages and Systems, 2016

We describe an approach to the verified implementation of transformations on functional programs that exploits the higher-order representation of syntax. In this approach, transformations are specified using the logic of hereditary Harrop formulas. On the one hand, these specifications serve directly as implementations, being programs in the language λProlog. On the other hand, they can be used as input to the Abella system which allows us to prove properties about them and thereby about the implementations. We argue that this approach is especially effective in realizing transformations that analyze binding structure. We do this by describing concise encodings in λProlog for transformations like typed closure conversion and code hoisting that are sensitive to such structure and by showing how to prove their correctness using Abella.

Lecture Notes in Computer Science, 2005

Provably correct compilation is an important aspect in development of high assurance software systems. In this paper we explore approaches to provably correct code generation based on programming language semantics, particularly Horn logical semantics, and partial evaluation. We show that the definite clause grammar (DCG) notation can be used for specifying both the syntax and semantics of imperative languages. We next show that continuation semantics can also be expressed in the Horn logical framework.

Electr. Notes Theor. Comput. Sci., 2015

In this paper we prove the correctness of a compiler for a call-by-name language using step-indexed logical relations and biorthogonality. The source language is an extension of the simply typed lambda-calculus with recursion, and the target language is an extension of the Krivine abstract machine. We formalized the proof in the Coq proof assistant.

Lecture Notes in Computer Science, 2014

Existing verified compilers are proved correct under a closed-world assumption, i.e., that the compiler will only be used to compile whole programs. We present a new methodology for verifying correct compilation of program components, while formally allowing linking with target code of arbitrary provenance. To demonstrate our methodology, we present a two-pass type-preserving open compiler and prove that compilation preserves semantics. The central novelty of our approach is that we define a combined language that embeds the source, intermediate, and target languages and formalizes a semantics of interoperability between them, using boundaries in the style of Matthews and Findler. Compiler correctness is stated as contextual equivalence in the combined language. Note to reader: We use blue, red, and purple to typeset terms in various languages. This paper will be difficult to follow unless read/printed in color.