Abstract
We introduce λε, a simply typed calculus with environments as first class values. As well as the usual constructs of λ and application, we have e[[a]] which evaluates term a in an environment e. Our environments are a set of variable-value pairs, but environments can also be computed by function application and evaluation in some other environments. The notion of environments here is a generalization of explicit substitutions and records. We show that the calculus has desirable properties such as subject reduction, confluence, conservativity over the simply typed λβ-calculus and strong normalizability.
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© 1999 Springer-Verlag Berlin Heidelberg
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Sato, M., Sakurai, T., Burstall, R. (1999). Explicit Environments. In: Girard, JY. (eds) Typed Lambda Calculi and Applications. TLCA 1999. Lecture Notes in Computer Science, vol 1581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48959-2_24
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DOI: https://doi.org/10.1007/3-540-48959-2_24
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