ar X iv : 0 90 5 . 03 57 v 1 [ m at h . L O ] 4 M ay 2 00 9 A completeness result for the simply typed λ μ - calculus

ar X iv : 0 90 5 . 04 56 v 1 [ m at h . L O ] 4 M ay 2 00 9 Non deterministic classical logic : the λ μ + + - calculus

In this paper, we present an extension of λμ-calculus called λμcalculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on data types. This calculus allows also to program the parallel-or.

ar X iv : 0 90 5 . 03 71 v 1 [ m at h . L O ] 4 M ay 2 00 9 Complete Types in an Extension of the System AF 2

In this paper, we extend the system AF2 in order to have the subject reduction for the βη-reduction. We prove that the types with positive quantifiers are complete for models that are stable by weak-head expansion.

ar X iv : 0 90 5 . 04 58 v 1 [ m at h . L O ] 4 M ay 2 00 9 LES I - TYPES DU SYSTÈME F I - TYPES OF SYSTEM

We prove in this paper that the types of system F inhabited uniquely by λI-terms (the I-types) have a positive quantifier. We give also consequences of this result and some examples. Mathematics Subject Classification : 03B40, 68Q60

ar X iv : 0 90 5 . 27 40 v 1 [ m at h . C O ] 1 7 M ay 2 00 9 Graphs with many ± 1 or ± √ 2 eigenvalues

A pseudo (v, k, λ)-design is a pair (X,B) where X is a v-set and B = {B1, . . . , Bv−1} is a collection of k-subsets (blocks) of X such that each two distinct Bi, Bj intersect in λ elements; and 0 < λ < k < v − 1. We use the notion of pseudo designs to characterize graphs of order n whose spectrum contains either ±1 or ± √ 2 with multiplicity (n − 2)/2 or (n− 3)/2. It turns out that the subdivi...

ar X iv : h ep - p h / 04 05 03 9 v 1 5 M ay 2 00 4 η , η ′ → π + π − γ with coupled channels