Abstract
We study perpetuality in calculi with explicit substitutions having full composition. A simple perpetual strategy is used to define strongly normalising terms inductively. This gives a simple argument to show preservation of β-strong normalisation as well as strong normalisation for typed terms. Particularly, the strong normalisation proof is based on implicit substitution rather than explicit substitution, so that it turns out to be modular w.r.t. the well-known proofs for typed lambda-calculus. All the proofs we develop are constructive.
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