15,419 research outputs found
On Isomorphism of "Functional" Intersection and Union Types
Type isomorphism is useful for retrieving library components, since a
function in a library can have a type different from, but isomorphic to, the
one expected by the user. Moreover type isomorphism gives for free the coercion
required to include the function in the user program with the right type. The
present paper faces the problem of type isomorphism in a system with
intersection and union types. In the presence of intersection and union,
isomorphism is not a congruence and cannot be characterised in an equational
way. A characterisation can still be given, quite complicated by the
interference between functional and non functional types. This drawback is
faced in the paper by interpreting each atomic type as the set of functions
mapping any argument into the interpretation of the type itself. This choice
has been suggested by the initial projection of Scott's inverse limit
lambda-model. The main result of this paper is a condition assuring type
isomorphism, based on an isomorphism preserving reduction.Comment: In Proceedings ITRS 2014, arXiv:1503.0437
Toward Isomorphism of Intersection and Union types
This paper investigates type isomorphism in a lambda-calculus with
intersection and union types. It is known that in lambda-calculus, the
isomorphism between two types is realised by a pair of terms inverse one each
other. Notably, invertible terms are linear terms of a particular shape, called
finite hereditary permutators. Typing properties of finite hereditary
permutators are then studied in a relevant type inference system with
intersection and union types for linear terms. In particular, an isomorphism
preserving reduction between types is defined. Type reduction is confluent and
terminating, and induces a notion of normal form of types. The properties of
normal types are a crucial step toward the complete characterisation of type
isomorphism. The main results of this paper are, on one hand, the fact that two
types with the same normal form are isomorphic, on the other hand, the
characterisation of the isomorphism between types in normal form, modulo
isomorphism of arrow types.Comment: In Proceedings ITRS 2012, arXiv:1307.784
A monotone isomorphism theorem
In the simple case of a Bernoulli shift on two symbols, zero and one, by
permuting the symbols, it is obvious that any two equal entropy shifts are
isomorphic. We show that the isomorphism can be realized by a factor that maps
a binary sequence to another that is coordinatewise smaller than or equal to
the original sequence.Comment: 22 page
Session Type Isomorphisms
There has been a considerable amount of work on retrieving functions in
function libraries using their type as search key. The availability of rich
component specifications, in the form of behavioral types, enables similar
queries where one can search a component library using the behavioral type of a
component as the search key. Just like for function libraries, however,
component libraries will contain components whose type differs from the
searched one in the order of messages or in the position of the branching
points. Thus, it makes sense to also look for those components whose type is
different from, but isomorphic to, the searched one.
In this article we give semantic and axiomatic characterizations of
isomorphic session types. The theory of session type isomorphisms turns out to
be subtle. In part this is due to the fact that it relies on a non-standard
notion of equivalence between processes. In addition, we do not know whether
the axiomatization is complete. It is known that the isomorphisms for arrow,
product and sum types are not finitely axiomatisable, but it is not clear yet
whether this negative results holds also for the family of types we consider in
this work.Comment: In Proceedings PLACES 2014, arXiv:1406.331
Deligne pairings and families of rank one local systems on algebraic curves
For smooth families of projective algebraic curves, we extend the notion of
intersection pairing of metrized line bundles to a pairing on line bundles with
flat relative connections. In this setting, we prove the existence of a
canonical and functorial "intersection" connection on the Deligne pairing. A
relationship is found with the holomorphic extension of analytic torsion, and
in the case of trivial fibrations we show that the Deligne isomorphism is flat
with respect to the connections we construct. Finally, we give an application
to the construction of a meromorphic connection on the hyperholomorphic line
bundle over the twistor space of rank one flat connections on a Riemann
surface.Comment: 48 pp. 1 figur
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