Dependently-Typed Montague Semantics in the Proof Assistant Agda-flat

Abstract

We apply the Agda-flat proof assistant (Vezzosi, 2019) to computational semantics. Computational semantics in Agda-flat is distinguished from the approach based on Coq (Chatzikyriakidis and Luo, 2014) in that it allows an implementation of the classical, intensional semantic analyses of Montague (1973). That is, it synthesizes the modern dependent type theory and Montague intensional logic traditions in the computational semantics setting. To demonstrate this, we show how to replicate Montague’s analyses in the type theory of Zwanziger (2018), which closely corresponds to the Agda-flat system. Accompanying code type-checks these analyses in Agdaflat.