Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/association-for-computing-machinery/relations-and-the-actual-meaning-of-renaming-SQegYs1z1n
References (87)
-
H. Madarász (2007)
Algebraic logic -
H. Barendregt (1985)
The Lambda Calculus: Its Syntax and Semantics -
H. Barendregt (1971)
Some extensional term models for combinatory logics and l - calculi -
A. M. Pitts (2003)
Nominal logic, a first order theory of names and bindingInformation and Computation, 186
-
J. Seldin (2009)
The Logic of Church and Curry -
A. Tarski (1964)
A simplified formalization of predicate logic with identityArchiv für mathematische Logik und Grundlagenforschung, 7
-
W. J. Blok, D. Pigozzi (1989)
Algebraizable Logics -
Sören Stenlund (2011)
Combinators, λ-Terms and Proof Theory -
(1972)
Combinatory Logic, Volume II. North–Holland -
(1964)
The Church–Rosser Property and a Result in Combinatory Logic -
Michele Basaldella (2019)
Lambda Congruences and ExtensionalityArXiv, abs/1903.06775
-
J. von Neumann (1967)
An axiomatization of set theoryFrom Frege to Gödel. A Source Book in Mathematical Logic
-
L. Henkin, J. Monk, A. Tarski, L. Henkin, J. Monk, A. Tarski (1988)
Cylindric Algebras. Part IIJournal of Symbolic Logic, 53
-
A. Church (1940)
A formulation of the simple theory of typesJournal of Symbolic Logic, 5
-
P. Andrews (1965)
A transfinite type theory with type variables -
D. Pigozzi, A. Salibra (1998)
Lambda abstraction algebras: Coordinatizing models of lambda calculusFundamenta Informaticae, 33
-
J. Myhill, Bob Flagg (1989)
A Type-Free System Extending (ZFC)Ann. Pure Appl. Log., 43
-
J. Stoy (1981)
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory -
A. Pitts (2001)
Nominal Logic: A First Order Theory of Names and BindingInf. Comput., 186
-
H. B. Curry, J. R. Hindley, J. P. Seldin (1972)
Combinatory Logic, Volume IINorth--Holland. DOI:https://doi.org/10.1016/S0049-237X(09)70633-0
-
S. Lusin, A. Salibra (2004)
The Lattice of Lambda TheoriesJ. Log. Comput., 14
-
T. Coquand (1986)
An Analysis of Girard's Paradox -
N. G. de Bruijn (1972)
Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church--Rosser theoremIndagationes Mathematicae, 75
-
György Révész (1988)
Lambda-calculus, combinators, and functional programming, 4
-
D. Kesner (2007)
The Theory of Calculi with Explicit Substitutions Revisited -
D. Monk (1965)
Substitutionless predicate logic with identityArchiv für mathematische Logik und Grundlagenforschung, 7
-
C. Hankin (1995)
Lambda Calculi: A Guide for Computer Scientists -
H. Curry (1929)
An Analysis of Logical SubstitutionAmerican Journal of Mathematics, 51
-
G. Plotkin (1974)
The λ-calculus is ω-incompleteJournal of Symbolic Logic, 39
-
D. Pigozzi, A. Salibra (1993)
An introduction to lambda abstraction algebras, 38
-
Peter Selinger (2008)
Lecture notes on the lambda calculusArXiv, abs/0804.3434
-
(2006)
Graph models of λ–calculus at work, and variations -
M. Sørensen, P. Urzyczyn (2013)
Lectures on the Curry-Howard Isomorphism -
(1963)
A theory of propositional types -
E. Engeler (1981)
Algebras and combinatorsalgebra universalis, 13
-
Giulio Manzonetto, A. Salibra (2010)
Applying Universal Algebra to Lambda CalculusJ. Log. Comput., 20
-
N. Cocchiarella (1969)
A substitution free axiom set for second order logicNotre Dame J. Formal Log., 10
-
P. B. Andrews (1965)
A Transfinite Type Theory with Type VariablesNorth--Holland. DOI:https://doi.org/10.1016/S0049-237X(08)71167-4
-
G. Plotkin (2007)
Set-theoretical and Other Elementary Models of the -calculus Part 1: a Set-theoretical Deenition of Applica- Tion 1 Introduction -
A. Meyer (1982)
What is a Model of the Lambda Calculus?Inf. Control., 52
-
C. Hankin (1994)
Lambda CalculiA Guide for Computer Scientists. Clarendon Press.
-
R. Crole (2012)
Alpha equivalence equalitiesTheor. Comput. Sci., 433
-
C. Berline (2006)
Graph models of &lambda--calculus at work, and variationsMathematical Structures in Computer Science, 16
-
Ernesto Copello, Nora Szasz, Álvaro Tasistro (2017)
Formal metatheory of the Lambda calculus using Stoughton's substitutionTheor. Comput. Sci., 685
-
G. E. Révész (1980)
Lambda--calculus without substitutionBulletin of the European Association for Theoretical Computer Science 11 (1980), 11
-
F. Cardone, J. Hindley (2009)
Lambda-Calculus and Combinators in the 20th Century -
P. Welch (1974)
The minimal continuous semantics of the lambda-calculus -
Chantal Berline, K. Grue (2016)
A synthetic axiomatization of Map TheoryTheor. Comput. Sci., 614
-
F. Raamsdonk (2009)
Lambda-Calculus and Combinators, An Introduction, 2nd Edition, J. Roger Hindley and Jonathan P. Seldin, Cambridge University Press, 2008. Hardback, ISBN 9780521898850Theory and Practice of Logic Programming, 9
-
T. Ahmed (2005)
Algebraic Logic, Where Does it Stand Today?Bulletin of Symbolic Logic, 11
-
Christian Urban, Stefan Berghofer, Michael Norrish (2007)
Barendregt's Variable Convention in Rule Inductions -
(1973)
Intermediate propositional logics (a survey) -
M. Sato, R. Pollack (2010)
External an internal syntax of the ?-calculusJournal of Symbolic Computation, 45
-
R. Vestergaard (2003)
The Primitive Proof Theory of the &lambda--CalculusPh.D. Dissertation. Heriot--Watt University. http://hdl.handle.net/10399/415
-
Alley Stoughton (1988)
Substitution RevisitedTheor. Comput. Sci., 59
-
D. Pigozzi, A. Salibra (1995)
Lambda Abstraction Algebras: Representation TheoremsTheor. Comput. Sci., 140
-
René Vestergaard (2003)
The primitive proof theory of the λ-calculus -
A. Salibra (2000)
On the algebraic models of lambda calculusTheor. Comput. Sci., 249
-
A. Salibra, R. Goldblatt (1999)
A Finite Equational Axiomatization of the Functional Algebras for the Lambda CalculusInf. Comput., 148
-
D. Pigozzi, A. Salibra (1998)
Lambda Abstraction Algebras: Coordinatizing Models of Lambda CalculusFundam. Informaticae, 32
-
I. Németi (1991)
Algebraization of quantifier logics, an introductory overviewStudia Logica, 50
-
György Révész (1992)
A List-Oriented Extension of the lambda-Calculus Satisfying the Church-Rosser TheoremTheor. Comput. Sci., 93
-
Peter Andrews (1986)
An introduction to mathematical logic and type theory - to truth through proof -
A. Church (1932)
A Set of Postulates for the Foundation of LogicAnnals of Mathematics, 33
-
(1967)
An axiomatization of set theory. In From Frege to Gödel -
G. Longo (1983)
Set-theoretical models of λ-calculus: theories, expansions, isomorphismsAnn. Pure Appl. Log., 24
-
M. Gabbay, A. Pitts (2002)
A New Approach to Abstract Syntax with Variable BindingFormal Aspects of Computing, 13
-
C. Wadsworth (1976)
The Relation Between Computational and Denotational Properties for Scott's Dinfty-Models of the Lambda-CalculusSIAM J. Comput., 5
-
Z. Diskin, I. Beylin (1993)
Lambda Substitution Algebras -
J. Krivine (1993)
Lambda-calculus, types and models -
A. Salibra (1991)
A general theory of algebras with quantifiers -
D. Bruijn (1972)
Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theoremStudies in logic and the foundations of mathematics, 133
-
D. Pigozzi, A. Salibra (1995)
The abstract variable-binding calculusStudia Logica, 55
-
B. Intrigila, R. Statman (2005)
Some results on extensionality in lambda calculusAnn. Pure Appl. Log., 132
-
A. Church (1941)
The calculi of lambda-conversion -
M. Sato, R. Pollack (2010)
External and internal syntax of the &lambda--calculusJournal of Symbolic Computation, 45
-
György Révész (1985)
Axioms for the Theory of Lambda-ConversionSIAM J. Comput., 14
-
J. R. Hindley, J. P. Seldin (2008)
Lambda--Calculus and Combinators, an Introduction (2nd edCambridge University Press. DOI:https://doi.org/10.1017/CBO9780511809835
-
M. Shönfinkel (1967)
On the building blocks of mathematical logicFrom Frege to Gödel. A Source Book in Mathematical Logic
-
Chantal Berline (2000)
From computation to foundations via functions and application: The -calculus and its webbed modelsTheor. Comput. Sci., 249
-
M. Abadi, L. Cardelli, P. Curien, J. Lévy (1989)
Explicit substitutionsJournal of Functional Programming, 1
-
M. H. Sørensen, P. Urzyczyn (2006)
Lectures on the Curry--Howard IsomorphismElsevier. DOI:https://doi.org/10.1016/S0049-237X(06)80001-7
-
P. Selinger (2003)
Order-incompleteness and finite lambda reduction modelsTheor. Comput. Sci., 309
-
H. P. Barendregt (1984)
The Lambda CalculusIts Syntax and Semantics. Revised edition. North--Holland. DOI:https://doi.org/10.1016/B978-0-444-87508-2.50006-X
-
H. B. Curry, R. Feys (1958)
Combinatory Logic, Volume INorth--Holland. DOI:https://doi.org/10.1016/S0049-237X(08)72029-9
-
I. Gradshteĭn (1963)
THE ELEMENTS OF MATHEMATICAL LOGIC -
Donald Kalish, R. Montague (1965)
On Tarski's formalization of predicate logic with identityArchiv für mathematische Logik und Grundlagenforschung, 7
- Publisher
- Association for Computing Machinery
- Copyright
- Copyright © 2021 ACM
- ISSN
- 1529-3785
- eISSN
- 1557-945X
- DOI
- 10.1145/3426471
- Publisher site
- See Article on Publisher Site
Abstract
In this work we provide an alternative, and equivalent, formulation of the concept of -theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We call -relations our alternative versions of -theories. We also clarify the actual role of -renaming in the lambda calculus: it expresses a property of extensionality for a certain class of terms. To motivate the necessity of -renaming, we construct an unusual denotational model of the lambda calculus that validates all structural and beta conditions but not -renaming. The article also has a survey character.
Journal
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Jan 15, 2021
Keywords: -renaming