A Rewriting Logic Approach to Type Inference

Abstract

Abstract. Meseguer and Ros , u proposed rewriting logic semantics (RLS) as a programing language definitional framework that unifies operational and algebraic denotational semantics. RLS has already been used to define a series of didactic and real languages, but its benefits in connection with defining and reasoning about type systems have not been fully investigated. This paper shows how the same RLS style employed for giving formal definitions of languages can be used to define type systems. The same termrewriting mechanism used to execute RLS language definitions can now be used to execute type systems, giving type checkers or type inferencers. The proposed approach is exemplified by defining the Hindley-Milner polymorphic type inferencer W as a rewrite logic theory and using this definition to obtain a type inferencer by executing it in a rewriting logic engine. The inferencer obtained this way compares favorably with other definitions or implementations of W . The performance of the executable definition is within an order of magnitude of that of highly optimized implementations of type inferencers, such as that of OCaml.

An executable formal semantics of C with applications

“…In that respect, our definitions conceptually complement each other-his is better for formal proofs about C, while ours is better for searching for behaviors in programs (see Section 6.3.1). Proofs of program correctness [31] as well as semantics-level proofs [8] have already been demonstrated in the framework used by our semantics, but we have not yet applied these techniques to C.…”

Twenty years of rewriting logic

“…As mentioned in Section 4.3, the rewriting semantics of a language can be extended and/or abstracted to provide other kinds of static and dynamic analysis, for example, for units of measurement [91,240], type checking [177], and runtime verification [407,421]. Two extensions of a programming language's rewriting logic semantics to model fault detection (resp.…”

Specifying Languages and Verifying Programs with K

“…K has been used for designing type checkers/inferencers [25], for model checking executions with predicate abstraction [26], [27] and heap awareness [28], for symbolic execution [29]- [31], computing worst case execution times [32], [33], studying program equivalence [34], and runtime verification [24], [35]. Additionally, the C definition mentioned above has been used as a program undefinedness checker to analyze C programs [36].…”