Une réponse négative à la conjecture de E. Tronci pour les systèmes numériques typés

Details Une réponse négative à la conjecture de E. Tronci pour les systèmes numériques typés Une réponse négative à la conjecture de E. Tronci pour les systèmes numériques typés

2009-05-05

arxiv.org/abs/0905.0574v1

Informatique Th\'eorique et Applications 31, 6 (1998) 539-558

Mathematics

Logic

Scientific paper

A numeral system is a sequence of an infinite different closed normal $\lambda$-terms which has closed $\lambda$-terms for successor and zero test. A numeral system is said adequate iff it has a closed $\lambda$-term for predecessor. A storage operator for a numeral system is a closed $\lambda$-term which simulate "call-by-value" in the context of a "call-by-name" strategy. E. Tronci conjectured the following result : a numeral system is adequate if it has a storage operator. This paper gives a negative answer to this conjecture for the numeral systems typable in the J.-Y. Girard type system F. The E. Tronci's conjecture remains open in pure $\lambda$-calculus.

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