منابع مشابه
General Recursion and Formal Topology
It is well known that general recursion cannot be expressed within Martin-Löf’s type theory and various approaches have been proposed to overcome this problem still maintaining the termination of the computation of the typable terms. In this work we propose a new approach to this problem based on the use of inductively generated formal topologies.
متن کاملProgram Schemes, Recursion Schemes, and Formal Languages
This paper presents general methods for studying the problems of translatability between classes of schemes and equivalence of schemes in a given class. There are four methods: applying the theory of formal languages, programming, measuring the complexity of a computation, and "cutting and pasting." These methods are used to answer several questions of translatability and equivalence for classe...
متن کاملVernacular Programming: General Recursion
This paper provides a mathematical analysis of the relationship between vernacular and for-malised derivations of programs; in particular, when the vernacular derivations deploy general recursion. We introduce a calculus VPD to represent vernacular derivations and a constructive theory of operations and types, EOT , to represent formal derivations. We provide an intensional semantics for VPD wi...
متن کاملFormal topology and domains
The theme of this paper is the relation between formal topology and the theory of domains. On one hand, domain theory can be seen as a branch of formal topology. On the other hand, the influence of domain theory on formal topology is twofold. Historically, the presence of the subset Con in Scott’s information systems has been the starting point for the introduction of the positivity predicate P...
متن کاملApartness and formal topology
The theory of formal spaces and the more recent theory of apartness spaces have a priori not much more in common than that each of them was initiated as a constructive approach to general topology. We nonetheless try to do the first steps in relating these competing theories to each other. Formal topology was put forward in the mid 1980s by Sambin [8] in order to make available to Martin–Löf’s ...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2010
ISSN: 2075-2180
DOI: 10.4204/eptcs.43.5