Summary: The essence of compiling with continuations is that conversion to continuation-passing style (CPS) is equivalent to a source language transformation converting to administrative normal form (ANF). Taking as source language E. Moggi’s [Logic in computer science, Proc. 4th Annual Symp., Pacific Grove/CA (USA) 1989, 14–23 (1989; Zbl 0716.03007)] computational lambda-calculus \((\lambda\text{C})\), we define an alternative to the CPS-translation with target in the sequent calculus LJQ, named value-filling style (VFS) translation, and making use of the ability of the sequent calculus to represent contexts formally. The VFS-translation requires no type translation: indeed, double negations are introduced only when encoding the VFS target language in the CPS target language. This optional encoding, when composed with the VFS-translation reconstructs the original CPS-translation. Going back to direct style, the ëssenceöf the VFS-translation is that it reveals a new sublanguage of ANF, the value-enclosed style (VES), next to another one, the continuation-enclosing style (CES): such an alternative is due to a dilemma in the syntax of \(\lambda\text{C}\), concerning how to expand the application constructor. In the typed scenario, VES and CES correspond to an alternative between two proof systems for call-by-value, LJQ and natural deduction with generalized applications, confirming proof theory as a foundation for intermediate representations.
For the entire collection see [Zbl 1518.68012].