A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Spector bar recursion over finite partial functions
[article]

2015
*
arXiv
*
pre-print

The

arXiv:1410.6361v3
fatcat:t7l3pg6vg5hstksp6iv6y2rnzi
*recursion*takes place*over**finite**partial**functions*u, where the control parameter φ, used in Spector's*bar**recursion*to terminate the computation at sequences s satisfying φ(ŝ)<|s|, now acts as a ... We introduce a new, demand-driven variant of Spector's*bar**recursion*in the spirit of the Berardi-Bezem-Coquand*functional*. ... Discrete choice Up until now, we have considered*bar**recursion**over*either*finite*sequences or*finite**partial**functions*: in other words*over*objects of type N → X + 1 with*finite*support. ...##
###
Understanding and Using Spector's Bar Recursive Interpretation of Classical Analysis
[chapter]

2006
*
Lecture Notes in Computer Science
*

In this note

doi:10.1007/11780342_44
fatcat:fmwlswznjvg3hdxvgsu2sehuwq
*bar**recursion*is presented as a generalisation of a simpler primitive*recursive**functional*needed for the interpretation of a*finite*(intuitionistic) version of DNS. ... Spector's interpretation makes use of a rather abstruse*recursion*schema, so-called*bar**recursion*, used to interpret the double negation shift DNS. ... In the following σ and τ will denote*finite**partial**functions*from N to N, i.e.*partial**functions*which are defined on a*finite*domain. ...##
###
Parametrised bar recursion: A unifying framework for realizability interpretations of classical dependent choice
[article]

2015
*
arXiv
*
pre-print

In many cases, these are achieved by extending the base interpreting system of primitive

arXiv:1411.0457v2
fatcat:qheau2jvtjebpofgrk4lojwiom
*recursive**functionals*with some form of*bar**recursion*, which realizes the negative translation of either countable ... From this proof, the soundness of most of the existing*bar**recursive*realizability interpretations of choice, including those based on the Berardi-Bezem-Coquand*functional*, modified realizability and the ... Modified*bar**recursion*(≺ u = ∅) Suppose that we retain the simplification ≺ u = ∅, but now allow ⊳ to range*over*arbitrary decidable*partial*orders. ...##
###
Page 139 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 63, Issue 2
[page]

1957
*
American Mathematical Society. Bulletin of the American Mathematical Society
*

Davis: An intrinsic definition of

*recursive**functional*. A definition of*recursive**functional*of arbitrary type is given, in terms of*partial**recursiveness*. ... As w takes on integral values, w* ranges*over*all*functionals*of*finite*domain which are of type a. ...##
###
Page 760 of Mathematical Reviews Vol. 58, Issue 2
[page]

1979
*
Mathematical Reviews
*

Let x, y, z denote elements of A; f, g,h

*partial**functions*A”—»A; and ®, ¥, ©*partial**functionals*with arguments of type (x, /), where*bars*signify*finite*sequences, and values in A. @ is said to be*functional*... In the first is developed a general notion of*recursion**over*any set A. The second part applies and expands this theory for the case where A is the*finite*-type structure*over*the natural numbers. ...##
###
Page 11 of Mathematical Reviews Vol. 41, Issue 1
[page]

1971
*
Mathematical Reviews
*

Let A,™ be the set of n-ary

*recursive**functions*, A,,™ that of n-ary*partial**recursive**functions*. f * g denotes the result of substituting g in every argument in place of f. ... H. 56 Bases in algebras of*partial**recursive**functions*. (Rus- sian) Algebra i Logika 7 (1968), no. 4, 87-105. ...##
###
Primitive Recursion and the Chain Antichain Principle

2012
*
Notre Dame Journal of Formal Logic
*

In the course of the proof we refine Howard's ordinal analysis of

doi:10.1215/00294527-1715716
fatcat:zvw37nq6trbjzcalczwkqpoege
*bar**recursion*. We also discuss the Erdős-Moser principle, which -taken together with CAC-is equivalent to RT 2 2 . ... In detail we show that WKL ω 0 + CAC is Π 0 2 -conservative*over*PRA and that one can extract primitive*recursive*realizers for such statements. ... In Section 1 we refine Howard's ordinal analysis of*bar**recursion*. ...##
###
Solovay's Relative Consistency Proof for FIM and BI
[article]

2021
*
arXiv
*
pre-print

Combining this result with Kleene's formalized

arXiv:2101.05878v1
fatcat:tbn3xgu6rnemhbsxivxtr74jcu
*recursive*realizability, he established (in primitive*recursive*arithmetic PRA) that FIM + MP and BI have the same consistency strength. ... In 2002 Robert Solovay proved that a subsystem BI of classical second order arithmetic, with*bar*induction and arithmetical countable choice, can be negatively interpreted in the neutral subsystem BSK ... There are the usual*function*symbols 0, S, +, ·, plus a*finite*number of symbols for additional primitive*recursive**functions*and*functionals*sufficient to formalize the theory of*recursive**partial**functionals*...##
###
APPLICATIONS OF INDUCTIVE DEFINITIONS AND CHOICE PRINCIPLES TO PROGRAM SYNTHESIS
[chapter]

2005
*
From Sets and Types to Topology and Analysis
*

Such a model can, for example, be constructed from the total elements of the Scott/Ershov hierarchy of

doi:10.1093/acprof:oso/9780198566519.003.0008
fatcat:n4z453pujrenfgte7abt4tkjhi
*partial*continuous*functionals**over*the flat domains of*partial*booleans and*partial*natural numbers ... by the Scott/Ershov model of*partial*continuous*functionals*). ...##
###
A remark on discovery algorithms for grammars

1962
*
Information and Control
*

If we introduce GSdel numbering, we may alternatively define a discovery algorithm as a

doi:10.1016/s0019-9958(62)90577-6
fatcat:sdin7b3givb3dhqmq57gwkguia
*partial**recursive**function*f which is defined for all numbers m which are GSdel numbers of a G~ E Ct so that, for ... A grammar G is a*finite*device which classifies every string*over*a*finite*set of symbols Z (the alphabet) as accepted or rejected. ...##
###
Logical Approaches to Computational Barriers: CiE 2006

2007
*
Journal of Logic and Computation
*

575
A Computability Theory of Real Numbers
Xizhong Zheng
584
Primitive

doi:10.1093/logcom/exm031
fatcat:lv36duerfvd25inr2f2be56qvq
*Recursive*Selection*Functions**over*Abstract Algebras Jeffery I. ... Peter Schuster, Julia Zappe 481 Inverting Monotone Continuous*Functions*in Constructive Analysis Helmut Schwichtenberg 490*Partial**Recursive**Functions*in Martin-Löf Type Theory Anton Setzer 505 ...##
###
Computational foundations of basic recursive function theory

1993
*
Theoretical Computer Science
*

When reducing to a class

doi:10.1016/0304-3975(93)90085-8
fatcat:rpt27ublabah5pzlfzuz4eabl4
*over*a*bar*type, say CT, the reduction*function*~ES+T might yield a nonterminating computation, so it is a*partial**function*. ... A wide collection of*partial**functions*may be typed with this rule, including all*partial**recursive**functions*. ...##
###
A computational interpretation of open induction

2004
*
Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
*

intuitionistically, open induction and dependent choice are quite different: Unlike dependent choice, open induction is closed under negative-and -translation, and therefore proves the same ¡ £ ¢ ¤ -formulas (

doi:10.1109/lics.2004.1319627
dblp:conf/lics/Berger04
fatcat:aihxty33a5evzetc57jlzwbiz4
*over*...*recursion*in*finite*types. ... Note that being not a*partial*choice*function*is an open property of*partial*sequences. ...##
###
Continuous Functions on Final Coalgebras

2009
*
Electronical Notes in Theoretical Computer Science
*

Among the functors we can deal with are those that arise from countable signatures of

doi:10.1016/j.entcs.2009.07.081
fatcat:rj33jvuzknaszcqwb3a3iyjczy
*finite*-place untyped operators. These have many applications. ... In a previous paper we gave a representation of, and simultaneously a way of programming with, continuous*functions*on streams, whether discrete-valued*functions*, or*functions*between streams. ... Yet the principle of*Bar*induction can clearly be used to model continuous*functions*on streams, and universal quantification*over*streams. ...##
###
A computational interpretation of Zorn's lemma
[article]

2020
*
arXiv
*
pre-print

This is achieved through G\"odel's

arXiv:2001.03540v1
fatcat:bq3i543pdfcp3mirjtgm3eq6vu
*functional*interpretation, and requires the introduction of a novel form of*recursion**over*chain complete*partial*orders whose existence in the model of total continuous ... We show that a realizer for the*functional*interpretation of open induction*over*the lexicographic ordering on sequences follows as a simple application of our main results. ...*Over*the years, they have turned out to form an elegant and robust class of*functionals*, and in particular are the standard model for*bar**recursive*extensions of the primitive*recursive**functionals*. ...
« Previous

*Showing results 1 — 15 out of 21,077 results*