Simply Typed Lambda Calculus with First-Class Environments

We propose a lambda calculus X^nv where it is possible to handle first-class environments. This calculus is based on the idea of explicit substitution, that is; /la-calculus. Syntax of /i^t, is obtained by merging the class of terms and the one of substitutions. Reduction is made from the weak reduction of Acr-calculus. Its type system also originates in the one of Aer-calculus. Confluence of /L^r is proved by Hardin's interpretation method which is originally used for proving confluence of Acr-calculus. We proved strong normalizability of A^t, by reducing it to strong normalizability of a simply typed record calculus. Finally, we propose a type inference algorithm which produced a principal typing for each typable term. §