
Summary: We introduce \(\lambda\varepsilon\), a simply typed calculus with environments as first class values. As well as the usual constructs of \(\lambda\) and application, we have \(e[[a]]\), which evaluates term \(a\) in an environment \(e\). Our environments are sets of variable-value pairs, but environments can also be computed by function application and evaluation in some other environment. 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 \(\lambda\beta\)-calculus and strong normalizability.
simply typed lambda calculus, strong normalizability, confluence, Combinatory logic and lambda calculus, explicit environments, subject reduction, Functional programming and lambda calculus, conservativity
simply typed lambda calculus, strong normalizability, confluence, Combinatory logic and lambda calculus, explicit environments, subject reduction, Functional programming and lambda calculus, conservativity
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