Explicit Substitutions for the Lambda � Mu Calculus �

Strong normalization of lambda-bar-mu-mu-tilde-calculus with explicit substitutions

Strong Normalization of lambda-mu-mu/tilde-Calculus with Explicit Substitutions

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Characterising Explicit Substitutions whichPreserve

Contrary to all expectations, the-calculus, the canonical simply-typed lambda-calculus with explicit substitutions, is not strongly normalising. This result has led to a proliferation of calculi with explicit substitutions. This paper shows that the reducibility method provides a general criterion when a calculus of explicit substitution is strongly normalising for all untyped lambda-terms that...

Explicit Substitutions and Intersection Types

Calculi of explicit substitutions have been introduced to give an account to the substitution process in lambda calculus. The idea is to introduce a notation for substitutions explicitely in the calculus. In other words one makes substitutions first class citizens whereas the classical lambda calculus leaves them in the meta-theory. Originally, the expression “explicit substitution” and the con...

Strong Normalization of λμμ̃-Calculus with Explicit Substitutions

The λμμ̃-calculus, defined by Curien and Herbelin [7], is a variant of the λμ-calculus that exhibits symmetries such as term/context and call-by-name/call-by-value. Since it is a symmetric, and hence a non-deterministic calculus, usual proof techniques of normalization needs some adjustments to be made to work in this setting. Here we prove the strong normalization (SN) of simply typed λμμ̃-calcu...