An implementation model of the typed lambda-calculus based on Linear Chemical Abstract Machine

Shinya Sato, Toru Sugimoto and Shinichi Yamada

In Proc. of the International Workshop on Functional and (Constraint) Logic Programming (WFLP 2001) , Report No. 2017, University of Kiel

Abstract

Abramsky's Linear Chemical Abstract Machine is a term calculus which corresponds to Linear Logic, via the Curry-Howard isomorphism. We show that the typed lambda-calculus is embedded into Linear Chemical Abstract Machine by Girard's embedding of Intuitionistic Logic into Linear Logic. Then we extend our result to a simple functional programming language obtained from the typed lambda-calculus by adding constants from PCF. We show that the call-by-value evaluation of terms of ground types (Booleans and Natural numbers) are preserved and reflected by this translation. Finally, we discuss an operational perspective of our result. We give a sequential execution model of Linear CHAM based on Abramsky's idea of a stack of coequations and a name queue, and then we consider a concurrent multi-thread implementation of the model.