抄録
We propose a lambda calculus λenv→ where it is possible to handle first-class environments. This calculus is based on the idea of explicit substitution, that is; λσ-calculus. Syntax of λenv→ is obtained by merging the class of terms and the one of substitutions. Reduction is made from the weak reduction of λσ-calculus. Its type system also originates in the one of λσ-calculus. Confluence of λenv→ is proved by Hardin's interpretation method which is originally used for proving confluence of λσ-calculus. We proved strong normalizability of λenv→ 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.
