A Rational Deconstruction of Landin’s J Operator

Abstract

Landin's J operator was the first control operator for functional languages, and was specified with an extension of the SECD machine. Through a series of meaning-preserving transformations (transformation into continuation-passing style (CPS) and defunctionalization) and their left inverses (transformation into direct style and refunctionalization), we present a compositional evaluation function corresponding to this extension of the SECD machine. We then characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. Finally, we present a motivated wish to see Landin's name added to the list of co-discoverers of continuations. * Extended version of an article

Refunctionalization at Work

“…Dijkstra's shunting-yard algorithm and Landin's SECD machine were directly written for programming languages of 'old provenience.' In Section 5 and in our earlier work [18,24], we have shown how each is the defunctionalized and CPS-transformed counterpart of a recursive program in direct style. Incidentally, the same can be said of the quicksort algorithm in Wirth's book: CPS-transforming and defunctionalizing the recursive definition that precedes the paragraph above in the book yields the iterative definition that immediately follows in the book.…”

“…Yet his SECD machine is in defunctionalized form and the defunctionalized counterpart of a compositional continuationpassing evaluation function [18]. Furthermore, the J operator captures the current dump, i.e., in refunctionalized form, the continuation of the caller [24]. This observation has led us to suggest that Landin's name be added to the list of co-discoverers of continuations [24].…”

“…Furthermore, the J operator captures the current dump, i.e., in refunctionalized form, the continuation of the caller [24]. This observation has led us to suggest that Landin's name be added to the list of co-discoverers of continuations [24].…”

“…Disentangling Felleisen's version yields a machine that is in defunctionalized form, but this is not so for Landin and Burge's version. We have put it in defunctionalized form by merging its apply functions [24].…”

A Simple Application of Lightweight Fusion to Proving the Equivalence of Abstract Machines

“…Lightweight fusion of iterate o refocus yields a tail-recursive evaluation function in the form of Implementation #2, i.e., an abstract machine such as the CEK machine or the Krivine machine [2][3][4].…”