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Explicit environments

Sato M, Sakurai T., Burstall R.

Fundamenta Informaticae

2001

Vol. 45, nr 1,2

79-115

We introduce le, a simply typed calculus with environments as first class values. As well as the usual constructs of l and application, we have e\lbrack\lbrack a\rbrack\rbrack 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 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 lb-calculus and strong normalizability.