103 research outputs found
Bounding normalization time through intersection types
Non-idempotent intersection types are used in order to give a bound of the
length of the normalization beta-reduction sequence of a lambda term: namely,
the bound is expressed as a function of the size of the term.Comment: In Proceedings ITRS 2012, arXiv:1307.784
Inhabitation for Non-idempotent Intersection Types
The inhabitation problem for intersection types in the lambda-calculus is
known to be undecidable. We study the problem in the case of non-idempotent
intersection, considering several type assignment systems, which characterize
the solvable or the strongly normalizing lambda-terms. We prove the
decidability of the inhabitation problem for all the systems considered, by
providing sound and complete inhabitation algorithms for them
A Quantitative Version of Simple Types
This work introduces a quantitative version of the simple type assignment system, starting from a suitable restriction of non-idempotent intersection types. The resulting system is decidable and has the same typability power as the simple type system; thus, assigning types to terms supplies the very same qualitative information given by simple types, but at the same time can provide some interesting quantitative information. It is well known that typability for simple types is equivalent to unification; we prove a similar result for the newly introduced system. More precisely, we show that typability is equivalent to a unification problem which is a non-trivial extension of the classical one: in addition to unification rules, our typing algorithm makes use of an expansion operation that increases the cardinality of multisets whenever needed
Light Logics and the Call-by-Value Lambda Calculus
The so-called light logics have been introduced as logical systems enjoying
quite remarkable normalization properties. Designing a type assignment system
for pure lambda calculus from these logics, however, is problematic. In this
paper we show that shifting from usual call-by-name to call-by-value lambda
calculus allows regaining strong connections with the underlying logic. This
will be done in the context of Elementary Affine Logic (EAL), designing a type
system in natural deduction style assigning EAL formulae to lambda terms.Comment: 28 page
Standardization of a Call-By-Value Lambda-Calculus
We study an extension of Plotkin\u27s call-by-value lambda-calculus by means of two commutation rules (sigma-reductions). Recently, it has been proved that this extended calculus provides elegant characterizations of many semantic properties, as for example solvability. We prove a standardization theorem for this calculus by generalizing Takahashi\u27s approach of parallel reductions. The standardization property allows us to prove that our calculus is conservative with respect to the Plotkin\u27s one. In particular, we show that the notion of solvability for this calculus coincides with that for Plotkin\u27s call-by-value lambda-calculus
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