# Characterisation of Strongly Normalising lambda-mu-Terms

@inproceedings{Bakel2012CharacterisationOS,
title={Characterisation of Strongly Normalising lambda-mu-Terms},
author={Steffen van Bakel and Franco Barbanera and Ugo de'Liguoro},
booktitle={ITRS},
year={2012}
}
• Published in ITRS 30 July 2013
• Mathematics
We provide a characterisation of strongly normalising terms of the lambda-mu-calculus by means of a type system that uses intersection and product types. The presence of the latter and a restricted use of the type omega enable us to represent the particular notion of continuation used in the literature for the definition of semantics for the lambda-mu-calculus. This makes it possible to lift the well-known characterisation property for strongly-normalising lambda-terms - that uses intersection…
8 Citations

### Characterisation of Approximation and (Head) Normalisation for λμ using Strict Intersection Types

A notion of approximants of lambda-mu-terms is defined, it is shown that it generates a semantics, and that for each typeable term there is an approximant that has the same type.

### A Translation of Intersection and Union Types for the λμ-Calculus

• Mathematics
APLAS
• 2014
An intersection and union type system for the λμ-calculus is introduced, which includes a restricted version of the traditional union-elimination rule and the terms typable in the system coincide with the strongly normalising terms of the $$\overline\lambda\mu\widetilde$$-calculus.

### 32 : 2 Types as Resources for Classical Natural Deduction

• Mathematics
• 2017
We define two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments –based

### Types as Resources for Classical Natural Deduction

• Mathematics
FSCD
• 2017
Two resource aware typing systems for the λμ-calculus based on non-idempotent intersection and union types are defined and typability provides upper bounds for the length of head-reduction sequences and maximal reduction sequences.

### Characterizing of Strong Normalization for Λμ-Calculus

• Mathematics
Journal of Physics: Conference Series
• 2019
λμ-calculus is introduced by Parigot as an extension isomorphic to an alternative presentation of classical natural deduction. Since then, many properties of it have been studied and, in particular,

### Characterizing Strongly Normalizing λGtz-terms via Non-Idempotent Intersection Types

• Mathematics
CSAE
• 2019
This paper introduces a non-idempotent intersection system for λGtz-calculus, which is in sequent calculus style, to show that a λ Gtz-term is typeable if and only if it is strongly normalizing.

### Intersection types and (positive) almost-sure termination

• Computer Science, Mathematics
Proc. ACM Program. Lang.
• 2021
It is shown that intersection types are capable of precisely characterizing both notions of termination inside a single system of types: the probability of convergence of any λ-term can be underapproximated by its type, while the underlying derivation's weight gives a lower bound to the term’s expected number of steps to normal form.

### The approximation theorem for the Λμ-calculus

• Ugo de'Liguoro
• Mathematics
Mathematical Structures in Computer Science
• 2015
An intersection type assignment system for de Groote–Saurin Λμ-calculus is introduced which is invariant under subject conversion and establishes the approximation theorem, stating that a type can be assigned to a term in the system if and only if it can be assign to same of its approximations.

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