Completeness of Conversion between Reactive Programs for Ultrametric Models
نویسندگان
چکیده
In 1970 Friedman proved completeness of beta eta conversion in the simply-typed lambda calculus for the set-theoretical model. Recently Krishnaswami and Benton have captured the essence of Hudak’s reactive programs in an extension of simply typed lambda calculus with causal streams and a temporal modality and provided this typed lambda calculus for reactive programs with a sound ultrametric semantics. We show that beta eta conversion in the typed lambda calculus of reactive programs is complete for the ultrametric model.
منابع مشابه
Completeness in Generalized Ultrametric Spaces
Γ-ultrametric spaces are spaces which satisfy all the axioms of an ultrametric space except that the distance function takes values in a complete lattice Γ instead of R≥0. Γ-ultrametric spaces have been extensively studied as a way to weaken the notion of an ultrametric space while still providing enough structure to be useful (see for example [17], [18], [8]). The many uses of Γ-ultrametric sp...
متن کاملAn Ultrametric Model of Reactive Programming
We describe a denotational model of higher-order functional reactive programming using ultrametric spaces, which provide a natural Cartesian closed generalization of causal stream functions. We define a domain-specific language corresponding to the model. We then show how reactive programs written in this language may be implemented efficiently using an imperatively updated dataflow graph and g...
متن کاملUltrametric Dynamics
This paper is concerned with dynamics in general ultrametric spaces. We prove the Fixed Point Theorem, the Stability Theorem, the Common Point Theorem, the Local Fixed Point Theorem, the Attractor Theorem and we derive conditions for a mapping to be surjective. We also discuss tightly continuous mappings and prove a theorem about the transfer of the property of principal completeness by a mappi...
متن کاملA Common Generalization of Metric and Ultrametric Fixed Point Theorems
We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach’s Fixed Point Theorem and ultrametric fixed point theorems. It works in a minimal setting, not involving any metrics, only based on the notion of “ball” and the property of “spherical completeness”. We demonstrate its applications to the metric and the ultrametric cases, and (in ...
متن کاملVector ultrametric spaces and a fixed point theorem for correspondences
In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013