Reversible, irreversible and optimal λ-machines

• Published in: Theoretical computer science Vol. 227; no. 1; pp. 79 - 97
• Main Authors: Danos, Vincent, Regnier, Laurent
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 28-09-1999; Elsevier
• Subjects: Abstract machines; Applied sciences; Automata. Abstract machines. Turing machines; Computer science; control theory; systems; Exact sciences and technology; General logic; Geometry of interaction; Linear head reduction; Linear logic; Logic and foundations; Mathematical logic, foundations, set theory; Mathematics; Reversible computations; Sciences and techniques of general use; Theoretical computing; λ-calculus; Linear logic; Reversible computations; Linear head reduction; λ-calculus; Geometry of interaction; Abstract machines; Abstract machine; Krivine abstract machine; Interaction; Lambda calculus; Reversible machine; Reversible computation; Logic; Functional programming; Logical reduction
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/S0304-3975(99)00049-3

Lambda-calculus is the core of functional programming, and many different ways to evaluate lambda-terms have been considered. One of the nicest, from the theoretical point of view, is
head linear reduction.
We compare two ways of implementing that specific evaluation strategy: “Krivine's abstract machine” and the “interaction abstract machine”. Runs on those machines stand in a relation which can be accurately described using the call/return symmetry discovered by Asperti and Laneve.