TWAM: A Certifying Abstract Machine for Logic Programs

Abstract

Type-preserving (or typed) compilation uses typing derivations to certify correctness properties of compilation. We have designed and implemented a type-preserving compiler for a simply-typed dialect of Prolog we call T-Prolog. The crux of our approach is a new certifying abstract machine which we call the Typed Warren Abstract Machine (TWAM). The TWAM has a dependent type system strong enough to specify the semantics of a logic program in the logical framework LF. We present a soundness metatheorem which constitutes a partial correctness guarantee: well-typed programs implement the logic program specified by their type. This metatheorem justifies our design and implementation of a certifying compiler from T-Prolog to TWAM. Abstract Machine ACM Reference Format: Brandon Bohrer and Karl Crary. 2017. TWAM: A Certifying Abstract Machine for Logic Programs. ACM Trans. The TWAM borrows heavily from the Warren Abstract Machine, the abstract machine targeted by most Prolog implementations [25]. For a thorough, readable description of the WAM, see Aït-Kaci [1]. Readers familiar with the WAM may wish to skim this section and observe the differences from the standard WAM, while readers unfamiliar with the WAM will wish to use this section as a primer or even consult Aït-Kaci's book. In this section we present our simplified instruction set for the WAM using examples. Notable simplifications include the usage of continuation-passing style and omission of many optimizations (with the exception of tail-call optimization in Section 6.5) in order to simplify the formalism. The description here is informal; the formal semantics are given in Section 4.5.