SMLtoCoq: Automated Generation of Coq Specifications and Proof Obligations from SML Programs with Contracts

TL;DR

SMLtoCoq automates the translation of SML programs and contracts into Coq, enabling formal verification without manual reimplementation, covering complex language features and library calls.

Contribution

It introduces an automatic translation tool from SML to Coq that handles advanced language features and library calls, facilitating formal reasoning.

Findings

Successfully translates SML programs with complex features into Coq

Enables formal proofs of function contracts automatically

Maintains compatibility with SML's basis library in Coq

Abstract

Formally reasoning about functional programs is supposed to be straightforward and elegant, however, it is not typically done as a matter of course. Reasoning in a proof assistant requires "reimplementing" the code in those tools, which is far from trivial. SMLtoCoq provides an automatic translation of SML programs and function contracts into Coq. Programs are translated into Coq specifications, and function contracts into theorems, which can then be formally proved. Using the Equations plugin and other well established Coq libraries, SMLtoCoq is able to translate SML programs without side-effects containing partial functions, structures, functors, records, among others. Additionally, we provide a Coq version of many parts of SML's basis library, so that calls to these libraries are kept almost as is.