Open AccessA Concrete Framework for Environment Machines
Author(s) -
Małgorzata Biernacka,
Olivier Danvy
Publication year - 2006
Publication title -
brics report series
Language(s) - English
Resource type - Journals
eISSN - 1601-5355
pISSN - 0909-0878
DOI - 10.7146/brics.v13i3.21909
Subject(s) - abstract machine , computer science , closure (psychology) , lambda calculus , calculus (dental) , reduction (mathematics) , programming language , implementation , term (time) , algorithm , theoretical computer science , mathematics , geometry , medicine , physics , dentistry , quantum mechanics , economics , market economy
We materialize the common understanding that calculi with explicit substitutions provide an intermediate step between an abstract specification of substitution in the lambda-calculus and its concrete implementations. To this end, we go back to Curien's original calculus of closures (an early calculus with explicit substitutions), we extend it minimally so that it can also express one-step reduction strategies, and we methodically derive a series of environment machines from the specification of two one-step reduction strategies for the lambda-calculus: normal order and applicative order. The derivation extends Danvy and Nielsen's refocusing-based construction of abstract machines with two new steps: one for coalescing two successive transitions into one, and the other for unfolding a closure into a term and an environment in the resulting abstract machine. The resulting environment machines include both the Krivine machine and the original version of Krivine's machine, Felleisen et al.'s CEK machine, and Leroy's Zinc abstract machine.