Eliminating Redundancy in Higher-Order Unification: A Lightweight Approach

Abstract

Abstract. In this paper, we discuss a lightweight approach to eliminate the overhead due to implicit type arguments during higher-order unification of dependently-typed terms. First, we show that some implicit type information is uniquely determined, and can therefore be safely skipped during higher-order unification. Second, we discuss its impact in practice during type reconstruction and during proof search within the logical framework Twelf. Our experimental results show that implicit type arguments are numerous and large in size, but their impact on run-time is between 10% and 20%. On the other hand optimizations such as eliminating the occurs check are shown to be crucial to achieve significant performance improvements.

A meta-programming approach to realizing dependently typed logic programming

“…A different approach, worthy of investigation, is that of compiling Twelf specifications directly to bytecode for the virtual machine underlying the Teyjus system. Such an approach would make it possible to realize optimizations that have been developed for the direct implementation of Twelf [20,21]. Of special note here are optimizations like the linear heads treatment of unification described by Pientka and Pfenning [21] for minimizing occurs checking, that could make a difference in examples such as the perm program considered in the previous section: direct compilation would allow us to regain opportunities for such improvements that might be lost by translating first to λProlog and then relying on its implementation that is not specially optimized to treat Twelf-specific programs.…”