An Implementation of the Language Lambda Prolog Organized around Higher-Order Pattern Unification

TL;DR

This paper presents an implementation of Lambda Prolog, a higher-order logic programming language, featuring a virtual machine, compilation strategies, and an emulator, to effectively support higher-order unification and lambda-tree syntax.

Contribution

It introduces a novel implementation framework for Lambda Prolog based on a restricted higher-order unification model, including a virtual machine and a portable emulator.

Findings

Efficient handling of higher-order unification in Lambda Prolog

Successful implementation of Teyjus Version 2 system

Experimental validation of design choices

Abstract

This thesis concerns the implementation of Lambda Prolog, a higher-order logic programming language that supports the lambda-tree syntax approach to representing and manipulating formal syntactic objects. Lambda Prolog achieves its functionality by extending a Prolog-like language by using typed lambda terms as data structures that it then manipulates via higher-order unification and some new program-level abstraction mechanisms. These additional features raise new implementation questions that must be adequately addressed for Lambda Prolog to be an effective programming tool. We consider these questions here, providing eventually a virtual machine and compilation based realization. A key idea is the orientation of the computation model of Lambda Prolog around a restricted version of higher-order unification with nice algorithmic properties and appearing to encompass most interesting applications. Our virtual machine embeds a treatment of this form of unification within the structure of the Warren Abstract Machine that is used in traditional Prolog implementations. Along the way, we treat various auxiliary issues such as the low-level representation of lambda terms, the implementation of reduction on such terms and the optimized processing of types in computation. We also develop an actual implementation of Lambda Prolog called Teyjus Version 2. A characteristic of this system is that it realizes an emulator for the virtual machine in the C language a compiler in the OCaml language. We present a treatment of the software issues that arise from this kind of mixing of languages within one system and we discuss issues relevant to the portability of our virtual machine emulator across arbitrary architectures. Finally, we assess the the efficacy of our various design ideas through experiments carried out using the system.