scholarly journals Full abstraction for the quantum lambda-calculus

2020 ◽  
Vol 4 (POPL) ◽  
pp. 1-28
Author(s):  
Pierre Clairambault ◽  
Marc de Visme
Keyword(s):  
Lambda Calculus ◽  
Full Abstraction

Parameterizing higher-order processes on names and processes

2019 ◽  
Vol 53 (3-4) ◽  
pp. 153-206
Author(s):  
Xian Xu
Keyword(s):  
Lambda Calculus ◽  
Higher Order ◽  
The Other ◽  
First Order ◽  
Full Abstraction

Parameterization extends higher-order processes with the capability of abstraction and application (like those in lambda-calculus). As is well-known, this extension is strict, meaning that higher-order processes equipped with parameterization are strictly more expressive than those without parameterization. This paper studies strictly higher-order processes (i.e., no name-passing) with two kinds of parameterization: one on names and the other on processes themselves. We present two main results. One is that in presence of parameterization, higher-order processes can interpret first-order (name-passing) processes in a quite elegant fashion, in contrast to the fact that higher-order processes without parameterization cannot encode first-order processes at all. We present two such encodings and analyze their properties in depth, particularly full abstraction. In the other result, we provide a simpler characterization of the standard context bisimilarity for higher-order processes with parameterization, in terms of the normal bisimilarity that stems from the well-known normal characterization for higher-order calculus. As a spinoff, we show that the bisimulation up-to context technique is sound in the higher-order setting with parameterization.

scholarly journals Full Abstraction for the Resource Lambda Calculus with Tests, through Taylor Expansion

2012 ◽  
Vol 8 (4) ◽  
Author(s):  
Thomas Ehrhard ◽  
Antonio Bucciarelli ◽  
Alberto Carraro ◽  
Giulio Manzonetto
Keyword(s):  
Taylor Expansion ◽  
Lambda Calculus ◽  
Full Abstraction

scholarly journals Full Abstraction in the Lazy Lambda Calculus

1993 ◽  
Vol 105 (2) ◽  
pp. 159-267 ◽  
Author(s):  
S. Abramsky ◽  
C.H.L. Ong
Keyword(s):  
Lambda Calculus ◽  
Full Abstraction

Lambda Calculus with Types

2009 ◽  
Author(s):  
Henk Barendregt ◽  
Wil Dekkers ◽  
Richard Statman
Keyword(s):  
Lambda Calculus

A lambda calculus with naive substitution

1979 ◽  
Vol 28 (3) ◽  
pp. 269-282 ◽  
Author(s):  
John Staples
Keyword(s):  
Lambda Calculus ◽  
Classical Case ◽  
Syntactic Theory ◽  
Alternative Approach ◽  
New Formulation

AbstractAn alternative approach is proposed to the basic definitions of the lassical lambda calculus. A proof is sketched of the equivalence of the approach with the classical case. The new formulation simplifies some aspects of the syntactic theory of the lambda calculus. In particular it provides a justification for omitting in syntactic theory discussion of changes of bound variable.

scholarly journals Backpropagation in the simply typed lambda-calculus with linear negation

2020 ◽  
Vol 4 (POPL) ◽  
pp. 1-27 ◽  
Author(s):  
Aloïs Brunel ◽  
Damiano Mazza ◽  
Michele Pagani
Keyword(s):  
Lambda Calculus ◽  
Typed Lambda Calculus

scholarly journals Algebras and coalgebras in the light affine Lambda calculus

2015 ◽  
Vol 50 (9) ◽  
pp. 114-126 ◽  
Author(s):  
Marco Gaboardi ◽  
Romain Péchoux
Keyword(s):  
Lambda Calculus

scholarly journals The Limits of Computation

Axiomathes ◽  
2021 ◽  
Author(s):  
Andrew Powell
Keyword(s):  
Natural Number ◽  
Set Theory ◽  
Lambda Calculus ◽  
Second Order ◽  
Functional Interpretation ◽  
Arbitrary Type ◽  
Computable Functions

AbstractThis article provides a survey of key papers that characterise computable functions, but also provides some novel insights as follows. It is argued that the power of algorithms is at least as strong as functions that can be proved to be totally computable in type-theoretic translations of subsystems of second-order Zermelo Fraenkel set theory. Moreover, it is claimed that typed systems of the lambda calculus give rise naturally to a functional interpretation of rich systems of types and to a hierarchy of ordinal recursive functionals of arbitrary type that can be reduced by substitution to natural number functions.

scholarly journals Maximal sharing in the Lambda calculus with letrec

2014 ◽  
Vol 49 (9) ◽  
pp. 67-80 ◽  
Author(s):  
Clemens Grabmayer ◽  
Jan Rochel
Keyword(s):  
Lambda Calculus
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