Hindman’s theorem and idempotent types
نویسندگان
چکیده
منابع مشابه
Hindman’s Theorem and Idempotent Types
Motivated by a question of Di Nasso, we show that Hindman’s Theorem is equivalent to the existence of idempotent types in countable complete extensions of Peano Arithmetic.
متن کاملCollapsing non-idempotent intersection types
We proved recently that the extensional collapse of the relational model of linear logic coincides with its Scott model, whose objects are preorders and morphisms are downwards closed relations. This result is obtained by the construction of a new model whose objects can be understood as preorders equipped with a realizability predicate. We present this model, which features a new duality, and ...
متن کاملNon-idempotent intersection types and strong normalisation
We present a typing system with non-idempotent intersection types, typing a term syntax covering three different calculi: the pure λ-calculus, the calculus with explicit substitutions λS, and the calculus with explicit substitutions, contractions and weakenings λlxr. In each of the three calculi, a term is typable if and only if it is strongly normalising, as it is the case in (many) systems wi...
متن کاملInhabitation for Non-idempotent Intersection Types
The inhabitation problem for intersection types in λ-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 λ-terms. We prove the decidability of the inhabitation problem for all the systems considered, by providing sound and complete inhabitati...
متن کاملFilter Models: Non-idempotent Intersection Types, Orthogonality and Polymorphism
This paper revisits models of typed λ-calculus based on filters of intersection types: By using non-idempotent intersections, we simplify a methodology that produces modular proofs of strong normalisation based on filter models. Non-idempotent intersections provide a decreasing measure proving a key termination property, simpler than the reducibility techniques used with idempotent intersection...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Semigroup Forum
سال: 2018
ISSN: 0037-1912,1432-2137
DOI: 10.1007/s00233-018-9943-4