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Sunday, November 22, 2020 | History

2 edition of Constructing recursions operators in intuitionistic type theory. found in the catalog.

Constructing recursions operators in intuitionistic type theory.

Lawrence C. Paulson

Constructing recursions operators in intuitionistic type theory.

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  • 32 Currently reading

Published by University of Cambridge,Computer Laboratory in Cambridge .
Written in English


Edition Notes

SeriesTechnical report -- No.57
ContributionsUniversity of Cambridge. Computer Laboratory.
The Physical Object
Pagination46p.
Number of Pages46
ID Numbers
Open LibraryOL13934354M


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Constructing recursions operators in intuitionistic type theory. by Lawrence C. Paulson Download PDF EPUB FB2

Intuitionistic type theory - Wikipedia. Constructing Recursion Operators in Intuitionistic Type Theory Lawrence C Paulson Computer Laboratory Corn Exchange Street Cambridge CB2 3QG England October Abstract Martin-L˜of’s Intuitionistic Theory.

J. Symbolic Computation () 2, Constructing Recursion Operators in Intuitionistic Type Theory LAWRENCE C. PAULSON Computer Laboratory, Corn Exchange Street, Cambridge CB2 3QG, England (Received 28 March ) Martin-L6f's Intuitionistic Theory Cited by: Constructing Recursion Operators in Intuitionistic Type Theory.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Martin-Löf's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs.

To handle recursion schemes other than primitive recursion, a theory. Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, Brand: Springer Netherlands.

This book describes different type theories (theories of types, polymorphic and monomorphic sets, and subsets) from a computing science perspective. to allow a general recursion operator in. Intuitionistic Type Theory Per Martin-L of Notes by Giovanni Sambin of a series of lectures given in Padua, June operator by means of which the binary application operation can of type theory.

Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of ionistic type theory was created by Per Martin-Löf, a Swedish mathematician and philosopher, who first published it in There are multiple versions of the type theory.

In, authors advanced the theory of operators and relations for intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets. Bustince and Burillo [8] and Deschrijver and Kerre [11] made theoretical development relating to composition of intuitionistic. 16 Empirical Constructing recursions operators in intuitionistic type theory.

book in Fuzzy Set Theory Formal Theories vs. Factual Theories vs. Decision Technologies Models in Operations Research and Management Science Testing Factual Models Empirical Research on Membership Functions Type A-Membership Model Type. A construction of ˚^ consists of a construction of ˚and a construction of.

A construction of ˚ 1 _˚ 2 consists of an index i2f1;2gand a construc-tion of ˚ i. A construction of ˚. consists of a function that transforms con-structions of ˚into constructions of. This also gives a reason to suspect that intuitionistic.

Here we present a methodology, in the framework of a type theory, that supports both these activities. We show how modular specifications may be incrementally constructed by combining individual specification units or modules with the use of appropriately defined specification building operators.

The AF2 type system is a way of interpreting the proof rules for second-order intuitionistic logic plus equational reasoning as construction rules for terms. Krivine (b) has shown that, by using Gödel translation from classical to intuitionistic logic (denoted byg), we can find in system AF2 a very simple type for storage operators.

Our development is based on Paulson’s paper Constructing recursion operators in intuitionistic type theory, but we specifically address two possibilities raised in the conclusion of his paper. While intuitionistic (or constructive) set theory IST has received a certain attention from mathematical logicians, so far as I am aware no book providing a systematic introduction to the subject has yet been published.

This may be the case in part because, as a form of higher-order intuitionistic Author: John L. Bell. L. Paulson, Constructing recursion operators in intuitionistic type theory, technical report no, University of Cambridge Computer Laboratory ().

Google Scholar J. Smith, On the relation between a type theoretic and a logical formulation of the theory. In mathematics, logic, and computer science, a type system is a formal system in which every term has a "type" which defines its meaning and the operations that may be performed on it.

Type theory is the academic study of type systems. Some type theories serve as alternatives to set theory. 1 day ago  This paper aims toward the improvement of the limitations of traditional failure mode and effect analysis (FMEA) and examines the crucial failure modes and components for railway train operation.

In order to overcome the drawbacks of current FMEA, this paper proposes a novel risk prioritization method based on cumulative prospect theory and type-2 intuitionistic.

This book offers a systematic introduction to the clustering algorithms for intuitionistic fuzzy values, the latest research results in intuitionistic fuzzy aggregation techniques, the extended results in interval-valued intuitionistic. We introduce the concept of a self-interpreted mathematical theory, construing Brouwer’s intuitionistic analysis as an important example of such a theory.

Brouwer’s aim was to show evidence of all the mathematical properties of the continuum by unfolding its intuitionistic. The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory.

For instance,minimal. Foundations of mathematics - Foundations of mathematics - Intuitionistic type theories: Topoi are closely related to intuitionistic type theories.

Such a theory is equipped with certain types, terms, and theorems. Among the types there should be a type Ω for truth-values, a type N for natural numbers, and, for each type A, a type ℘(A) for all sets of entities of type A.

Constructive and intuitionistic Zermelo-Fraenkel set theories are axiomatic theories of sets in the style of Zermelo-Fraenkel set theory (ZF) which are based on intuitionistic were introduced in the ’s and they represent a formal context within which to codify mathematics based on intuitionistic.

As it can be noted in this definition, the intuitionistic fuzzy set theory offers more tools than the traditional fuzzy set theory to model the system to be studied. Definition 2. [ 22, 23 ] Let a and b be. Intuitionistic type theory is generally proffered as a foundation of mathematics that is (in most of its forms) both constructive and predicative.

For purposes of comparing type theory to set theory, it might be nice if ‘intuitionistic’ and ‘constructive’ were distinguished for type. Gilmore addresses the need for languages which can be understood by both humans and computers and, using Intensional Type Theory (ITT), provides a unified basis for mathematics and computer science.

This yields much simpler foundations for recursion theory and the semantics of computer programs than those currently provided by category theory.

In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions-or. Fuzzy sets theory which has become classic since its appearance in the works of L.A.

Zadeh is generally acknowledged as an effective tool for decision-making models [3]. Intuitionistic. MDPI Books Encyclopedia JAMS Proceedings About; Sign In / Sign Up Submit. Search for Articles: Title / Keyword.

Author / Affiliation. Journal. Dependently typed functional language based on intuitionistic Type Theory: Icon: Wide variety of features for processing and presenting symbolic data: XML: Rules for defining semantic tags. Syntax; Advanced Search; New.

All new items; Books; Journal articles; Manuscripts; Topics. All Categories; Metaphysics and Epistemology. In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity.

Additional Physical Format: Online version: Martin-Löf, Per, Intuitionistic type theory. Napoli: Bibliopolis, (OCoLC) Document Type. –––,Intuitionistic type theory: Notes by Giovanni Sambin of a series of lectures given in Padua, JuneNapoli: Bibliopolis.

(Scholar) –––,“Unifying Scott’s theory of domains for denotational semantics and intuitionistic type theory. Directed type theory is an analogue of homotopy type theory where types represent infinity-categories, generalizing groupoids.

A bisimplicial approach to directed type theory, developed by Riehl and Shulman, is based on equipping each type. As a generic theorem prover, Isabelle supports a variety of logics. Distinctive features include Isabelle's representation of logics within a meta-logic and the use of higher-order unification to combine.

Get this from a library. Mathematics of Program Construction: Third International Conference, MPC '95, Kloster Irsee, Germany, JulyProceedings. [Bernhard Möller] -- This volume constitutes the proceedings of the Third International Conference on the Mathematics of Program Construction.

Description; Chapters; Supplementary; This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory.

The subject goes back to Gödel's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type. intuitionist logic (spelling) Incorrect term for "intuitionistic logic". This article is provided by FOLDOC - Free Online Dictionary of Computing () The following article is from The Great Soviet.

on intuitive grounds, or else we can demonstrate its consistency by constructing a standard model in set theory. Every type denotes a non-empty set. Given sets for each basic type, the interpre-tation of ˙! ˝is the set of functions from ˙to ˝.

A closed term of type .