Closing the Gap -- Formally Verifying Dynamically Typed Programs like Statically Typed Ones Using Hoare Logic -- Extended Version --

TL;DR

This paper introduces a formal verification approach for dynamically typed programs using Hoare logic, creating an abstraction layer that simulates static typing and integrating type inference for semi-automatic proof development.

Contribution

It presents a novel method combining Hoare logic with type inference to verify dynamically typed programs as if they were statically typed, reducing verification overhead.

Findings

Type inference can be integrated into Hoare logic for dynamic languages.

The approach simplifies verification by hiding dynamic typing complexity.

It provides a formal proof method as an alternative to static typing or runtime checks.

Abstract

Dynamically typed object-oriented languages enable programmers to write elegant, reusable and extensible programs. However, with the current methodology for program verification, the absence of static type information creates significant overhead. Our proposal is two-fold: First, we propose a layer of abstraction hiding the complexity of dynamic typing when provided with sufficient type information. Since this essentially creates the illusion of verifying a statically-typed program, the effort required is equivalent to the statically-typed case. Second, we show how the required type information can be efficiently derived for all type-safe programs by integrating a type inference algorithm into Hoare logic, yielding a semi-automatic procedure allowing the user to focus on those typing problems really requiring his attention. While applying type inference to dynamically typed programs is a well-established method by now, our approach complements conventional soft typing systems by offering formal proof as a third option besides modifying the program (static typing) and accepting the presence of runtime type errors (dynamic typing).