103 research outputs found
On sets of terms with a given intersection type
We are interested in how much of the structure of a strongly normalizable
lambda term is captured by its intersection types and how much all the terms of
a given type have in common. In this note we consider the theory BCD
(Barendregt, Coppo, and Dezani) of intersection types without the top element.
We show: for each strongly normalizable lambda term M, with beta-eta normal
form N, there exists an intersection type A such that, in BCD, N is the unique
beta-eta normal term of type A. A similar result holds for finite sets of
strongly normalizable terms for each intersection type A if the set of all
closed terms M such that, in BCD, M has type A, is infinite then, when closed
under beta-eta conversion, this set forms an adaquate numeral system for
untyped lambda calculus. A number of related results are also proved
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Genus distributions for two classes of graphs
The set of orientable imbeddings of a graph can be partitioned according to the genus of the imbedding surfaces. A genus-respecting breakdown of the number of orientable imbeddings is obtained for every graph in each of two infinite classes. It is proved that the genus distribution of any member of either class is strongly unimodal. These are the first two infinite classes of graphs for which such calculations have been achieved, except for a few classes, such as trees and cycles, whose members have all their cellular orientable imbeddings in the sphere
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Genus Distributions for Two Classes of Graphs
The set of orientable imbeddings of a graph can be partitioned according to the genus of the imbedding surfaces. A genus-respecting breakdown of the number of orientable imbeddings is obtained for every graph in each of two infinite classes. These are the first two infinite classes of graphs for which such calculations have been achieved, except for a few classes, such as trees and cycles, whose members have all their polygonal orientable imbeddings in the sphere
On sets of terms having a given intersection type
Working in a variant of the intersection type assignment system of Coppo,
Dezani-Ciancaglini and Venneri [1981], we prove several facts about sets of
terms having a given intersection type. Our main result is that every strongly
normalizing term M admits a *uniqueness typing*, which is a pair
such that
1)
2)
We also discuss several presentations of intersection type algebras, and the
corresponding choices of type assignment rules.
Moreover, we show that the set of closed terms with a given type is uniformly
separable, and, if infinite, forms an adequate numeral system. The proof of
this fact uses an internal version of the B\"ohm-out technique, adapted to
terms of a given intersection type
Solution of a Problem of Barendregt on Sensible lambda-Theories
H is the theory extending β-conversion by identifying all closed
unsolvables. Hω is the closure of this theory under the ω-rule
(and β-conversion). A long-standing conjecture of H. Barendregt states
that the provable equations of Hω form
Π11-complete set. Here we prove that conjecture.Comment: 17 page
Soft Session Types
We show how systems of session types can enforce interactions to be bounded
for all typable processes. The type system we propose is based on Lafont's soft
linear logic and is strongly inspired by recent works about session types as
intuitionistic linear logic formulas. Our main result is the existence, for
every typable process, of a polynomial bound on the length of any reduction
sequence starting from it and on the size of any of its reducts.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407
Analytic Tableaux for Simple Type Theory and its First-Order Fragment
We study simple type theory with primitive equality (STT) and its first-order
fragment EFO, which restricts equality and quantification to base types but
retains lambda abstraction and higher-order variables. As deductive system we
employ a cut-free tableau calculus. We consider completeness, compactness, and
existence of countable models. We prove these properties for STT with respect
to Henkin models and for EFO with respect to standard models. We also show that
the tableau system yields a decision procedure for three EFO fragments
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