scholarly journals Light logics and higher-order processes

2014 ◽  
Vol 26 (6) ◽  
pp. 969-992 ◽  
Author(s):  
UGO DAL LAGO ◽  
SIMONE MARTINI ◽  
DAVIDE SANGIORGI
Keyword(s):  
Polynomial Time ◽  
Linear Logic ◽  
Higher Order ◽  
Resource Control ◽  
Process Algebras ◽  
Π Calculus ◽  
Soft Processes

We show that the techniques for resource control that have been developed by the so-calledlight logicscan be fruitfully applied also to process algebras. In particular, we present a restriction of higher-order π-calculus inspired by soft linear logic. We prove that any soft process terminates in polynomial time. We argue that the class of soft processes may be naturally enlarged so that interesting processes are expressible, still maintaining the polynomial bound on executions.

scholarly journals On Polymorphic Sessions and Functions

2021 ◽  
Vol 43 (2) ◽  
pp. 1-55
Author(s):  
Bernardo Toninho ◽  
Nobuko Yoshida
Keyword(s):  
Natural Deduction ◽  
Sequent Calculus ◽  
Linear Logic ◽  
Linear Formulation ◽  
Session Types ◽  
Logical Foundation ◽  
Π Calculus ◽  
Soundness And Completeness ◽  
System F ◽  
Algebraic Representations

This work exploits the logical foundation of session types to determine what kind of type discipline for the Λ-calculus can exactly capture, and is captured by, Λ-calculus behaviours. Leveraging the proof theoretic content of the soundness and completeness of sequent calculus and natural deduction presentations of linear logic, we develop the first mutually inverse and fully abstract processes-as-functions and functions-as-processes encodings between a polymorphic session π-calculus and a linear formulation of System F. We are then able to derive results of the session calculus from the theory of the Λ-calculus: (1) we obtain a characterisation of inductive and coinductive session types via their algebraic representations in System F; and (2) we extend our results to account for value and process passing, entailing strong normalisation.

Bounded Linear Logic: A Modular Approach to Polynomial Time Computability

1990 ◽  
pp. 195-209 ◽  
Author(s):  
Jean-Yves Girard ◽  
Andre Scedrov ◽  
Philip J. Scott
Keyword(s):  
Polynomial Time ◽  
Linear Logic ◽  
Modular Approach ◽  
Bounded Linear

FUNCTIONAL PEARL Linear lambda calculus and PTIME-completeness

2004 ◽  
Vol 14 (6) ◽  
pp. 623-633 ◽  
Author(s):  
HARRY G. MAIRSON
Keyword(s):  
Polynomial Time ◽  
Linear Logic ◽  
Lambda Calculus ◽  
Type Inference ◽  
Decision Problems ◽  
Logical Interpretation

We give transparent proofs of the PTIME-completeness of two decision problems for terms in the λ-calculus. The first is a reproof of the theorem that type inference for the simply-typed λ-calculus is PTIME-complete. Our proof is interesting because it uses no more than the standard combinators Church knew of some 70 years ago, in which the terms are linear affine – each bound variable occurs at most once. We then derive a modification of Church's coding of Booleans that is linear, where each bound variable occurs exactly once. A consequence of this construction is that any interpreter for linear λ-calculus requires polynomial time. The logical interpretation of this consequence is that the problem of normalizing proofnets for multiplicative linear logic (MLL) is also PTIME-complete.

scholarly journals Reversibility in the higher-order π-calculus

2016 ◽  
Vol 625 ◽  
pp. 25-84 ◽  
Author(s):  
Ivan Lanese ◽  
Claudio Antares Mezzina ◽  
Jean-Bernard Stefani
Keyword(s):  
Higher Order ◽  
Π Calculus
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