Open AccessOn the Equivalence between Small-Step and Big-Step Abstract Machines: A Simple Application of Lightweight Fusion
Author(s) -
Olivier Danvy,
Kevin Millikin
Publication year - 2007
Publication title -
brics report series
Language(s) - English
Resource type - Journals
eISSN - 1601-5355
pISSN - 0909-0878
DOI - 10.7146/brics.v14i16.21935
Subject(s) - equivalence (formal languages) , computer science , simple (philosophy) , function (biology) , abstract machine , algorithm , theoretical computer science , programming language , mathematics , discrete mathematics , philosophy , epistemology , evolutionary biology , biology
We show how Ohori and Sasano's recent lightweight fusion by fixed-point promotion provides a simple way to prove the equivalence of the two standard styles of specification of abstract machines: (1) in small-step form, as a state-transition function together with a `driver loop,' i.e., a function implementing the iteration of this transition function; and (2) in big-step form, as a tail-recursive function that directly maps a given configuration to a final state, if any. The equivalence hinges on our observation that for abstract machines, fusing a small-step specification yields a big-step specification. We illustrate this observation here with a recognizer for Dyck words, the CEK machine, and Krivine's machine with call/cc. The need for such a simple proof is motivated by our current work on small-step abstract machines as obtained by refocusing a function implementing a reduction semantics (a syntactic correspondence), and big-step abstract machines as obtained by CPS-transforming and then defunctionalizing a function implementing a big-step semantics (a functional correspondence).