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The approximation theorem for the Λμ-calculus

Published online by Cambridge University Press:  28 July 2015

UGO DE'LIGUORO
UGO DE'LIGUORO*
Affiliation:
Dipartimento di Informatica, Università di Torino, c.so Svizzera 185, 10149 Torino, Italy Email: ugo.deliguoro@unito.it
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Abstract

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We consider a notion of approximation for terms of de Groote–Saurin Λμ-calculus. Then, we introduce an intersection type assignment system for that calculus which is invariant under subject conversion. The type assignment system also induces a filter model, which is an extensional Λμ-model in the sense of Nakazawa and Katsumata. We then establish the approximation theorem, stating that a type can be assigned to a term in the system if and only if it can be assigned to same of its approximations.

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