71,110 research outputs found
Schubert calculus and Gelfand-Zetlin polytopes
We describe a new approach to the Schubert calculus on complete flag
varieties using the volume polynomial associated with Gelfand-Zetlin polytopes.
This approach allows us to compute the intersection products of Schubert cycles
by intersecting faces of a polytope.Comment: 33 pages, 4 figures, introduction rewritten, Section 4 restructured,
typos correcte
Indexed linear logic and higher-order model checking
In recent work, Kobayashi observed that the acceptance by an alternating tree
automaton A of an infinite tree T generated by a higher-order recursion scheme
G may be formulated as the typability of the recursion scheme G in an
appropriate intersection type system associated to the automaton A. The purpose
of this article is to establish a clean connection between this line of work
and Bucciarelli and Ehrhard's indexed linear logic. This is achieved in two
steps. First, we recast Kobayashi's result in an equivalent infinitary
intersection type system where intersection is not idempotent anymore. Then, we
show that the resulting type system is a fragment of an infinitary version of
Bucciarelli and Ehrhard's indexed linear logic. While this work is very
preliminary and does not integrate key ingredients of higher-order
model-checking like priorities, it reveals an interesting and promising
connection between higher-order model-checking and linear logic.Comment: In Proceedings ITRS 2014, arXiv:1503.0437
Retractions in Intersection Types
This paper deals with retraction - intended as isomorphic embedding - in
intersection types building left and right inverses as terms of a lambda
calculus with a bottom constant. The main result is a necessary and sufficient
condition two strict intersection types must satisfy in order to assure the
existence of two terms showing the first type to be a retract of the second
one. Moreover, the characterisation of retraction in the standard intersection
types is discussed.Comment: In Proceedings ITRS 2016, arXiv:1702.0187
Complete Call-by-Value Calculi of Control Operators II: Strong Termination
We provide characterization of the strong termination property of the CCV
(complete call-by-value) lambda-mu calculus introduced in the first part of
this series of the paper. The calculus is complete with respect to the standard
continuation-passing style (CPS) semantics. The union-intersection type systems
for the calculus is developed in the previous paper. We characterize the strong
normalizability of terms of the calculus in terms of the CPS semantics and
typeability
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