From Call-by-Value to Interaction by Typed Closure Conversion

The (In)Efficiency of interaction

“…The IAM relies on a different mechanism, thatÐsimilarly to offline Turing machines [Dal Lago and Schöpp 2010]Ðsacrifices time in order to be space-efficient. This phenomenon was first pointed out by Mackie [1995], but it is the extensive work by Schöpp and coauthors [Dal Lago and Schöpp 2010;Schopp 2007;Schöpp 2014Schöpp , 2015 that showed that the IAM allows for capturing sub-linear space computations 1 , something impossible in environment machines. Along the same lines, one can mention the Geometry of Synthesis [Ghica 2007;Ghica and Smith 2010], in which the geometry of interaction is seen as a compilation scheme towards circuits, and computation space is finite, and of paramount importance.…”

The Machinery of Interaction

“…In all these cases, the GoI interpretation, even when given on λ-terms, goes through linear logic (or symmetric monoidal categories) in an essential way. The only notable exceptions are perhaps the recent contributions by Schöpp on the relations between GoI, CPS, and defunctionalization [52,53] in which, indeed, some deep relations are shown to exist between GoI and classic tools in the theory of λ-calculus. Even there, however, GoI is seen as obtained through the INT-construction [1,36], although applied to a syntactic category of terms.…”

“…Muroya and Ghica have recently studied the GoI in combination with rewriting and abstract machines in [47]. The already cited works by Schöpp [52,53] highlight how GoI can be seen as an optimized form of CPS transformation, followed by defunctionalization.…”