scholarly journals A New Proof of P-time Completeness of Linear Lambda Calculus

10.29007/svwc ◽  
2018 ◽  
Author(s):  
Satoshi Matsuoka
Keyword(s):  
Lambda Calculus ◽  
Standard Ml

We give a new proof of P-time completeness ofthe Linear Lambda Calculus, which was originally given by H. Mairson in 2003.Our proof uses an essentially different Boolean type from the type that Mairson used.Moreover the correctness of our proof can be machined-checked using an implementation of Standard ML.

scholarly journals Names, Equations, Relations: Practical Ways to Reason about 'new'

1996 ◽  
Vol 3 (31) ◽  
Author(s):  
Ian Stark
Keyword(s):  
Lambda Calculus ◽  
Simple Representation ◽  
First Order ◽  
Standard Ml ◽  
Typed Lambda Calculus ◽  
Pi Calculus ◽  
Private And Public ◽  
Mobile Processes ◽  
Contextual Equivalence ◽  
Accessible Form

The nu-calculus of Pitts and Stark is a typed lambda-calculus, extended with state in the form of dynamically-generated names. These names can be created locally, passed around, and compared with one another. Through the interaction between names and functions, the language can capture notions of scope, visibility and sharing. Originally motivated by the study of references in Standard ML, the nu-calculus has connections to other kinds of local declaration, and to the mobile processes of the pi-calculus.<br /> <br />This paper introduces a logic of equations and relations which allows one to reason about expressions of the nu-calculus: this uses a simple representation of the private and public scope of names, and allows straightforward proofs of contextual equivalence (also known as observational, or observable, equivalence). The logic is based on earlier operational techniques, providing the same power but in a much more accessible form. In particular it allows intuitive and direct proofs of all contextual equivalences between first-order functions with local names.<br /><br />See the revised version BRICS-RS-97-39.

scholarly journals Names, Equations, Relations: Practical Ways to Reason about new

1997 ◽  
Vol 4 (39) ◽  
Author(s):  
Ian Stark
Keyword(s):  
Lambda Calculus ◽  
Security Protocols ◽  
First Order ◽  
Standard Ml ◽  
The Third ◽  
Pi Calculus ◽  
Private And Public ◽  
Mobile Processes ◽  
Contextual Equivalence ◽  
Accessible Form

<p>The nu-calculus of Pitts and Stark is a typed lambda-calculus, extended with state<br />in the form of dynamically-generated names. These names can be created locally, passed around, and compared with one another. Through the interaction between<br />names and functions, the language can capture notions of scope, visibility and sharing. Originally motivated by the study of references in Standard ML, the nu-calculus<br />has connections to local declarations in general; to the mobile processes of the pi-calculus; and to security protocols in the spi-calculus. <br /> This paper introduces a logic of equations and relations which allows one to<br />reason about expressions of the nu-calculus: this uses a simple representation of the private and public scope of names, and allows straightforward proofs of<br />contextual equivalence (also known as observational, or observable, equivalence). The logic is based on earlier operational techniques, providing the same power but<br />in a much more accessible form. In particular it allows intuitive and direct proofs of all contextual equivalences between first-order functions with local names.</p><p>This supersedes the earlier BRICS Report RS-96-31. It also expands on the paper presented in Typed Lambda Calculi and Applications: Proceedings of the Third<br />International Conference TLCA '97, Lecture Notes in Computer Science 1210, Springer-Verlag 1997.</p>

Lambda Calculus with Types

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

Standard ML Signatures for a Protocol Stack

1993 ◽  
Author(s):  
Edoardo Biagioni ◽  
Robert Harper ◽  
Peter Lee
Keyword(s):  
Protocol Stack ◽  
Standard Ml

Incremental Recompilation for Standard ML of New Jersey

1994 ◽  
Author(s):  
Robert Harper ◽  
Frank Pfenning ◽  
Peter Lee ◽  
Eugene Rollins
Keyword(s):  
New Jersey ◽  
Standard Ml

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
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