Lambda: the ultimate syntax-semantics interface ⋆ Oleg Kiselyov 1 and Chung-chieh Shan 2
Abstract. Spreadsheets in accounting and Matlab in engineering are immensely popular because these glorified calculators let domain experts play: write down a problem in familiar terms and quickly try a number of solutions. Natural-language semanticists have a better tool. Not only does it compute grammar yields and truth values, it also infers types, normalizes terms, and displays truth conditions as formulas. Its modularity facilities make it easy to try fragments out, scale them up, and abstract encoding details out of semantic theories. This tool is a combination of techniques created by functional programmers, who are as unaware of its application to semantics as most semanticists. This paper breaks the barrier. We express extensible interpreters of natural- and formal-language fragments as functional programs. Specifically, we work our way from the simply-typed lambda calculus and a context-free grammar to a dynamic treatment of quantification and anaphora. We strive to be comprehensible and informative to both linguists and programmers.