CPS Transformation of Beta-Redexes

The extra compaction of the most compacting CPS transformation in existence, which is due to Sabry and Felleisen, is generally attributed to (1) making continuations occur first in CPS terms and (2) classifying more redexes as administrative. We show that this extra compaction is actually independent of the relative positions of values and continuations and furthermore that it is solely due to a context-sensitive transformation of beta-redexes. We stage the more compact CPS transformation into a first-order uncurrying phase and a context-insensitive CPS transformation. We also define a context-insensitive CPS transformation that provides the extra compaction. This CPS transformation operates in one pass and is dependently typed.