A Higher-Order Colon Translation

Olivier Danvy
Lasse R. Nielsen

December 2000


A lambda-encoding such as the CPS transformation gives rise to administrative redexes. In his seminal article ``Call-by-name, call-by-value and the lambda-calculus'', 25 years ago, Plotkin tackled administrative reductions using a so-called ``colon translation.'' 10 years ago, Danvy and Filinski integrated administrative reductions in the CPS transformation, making it operate in one pass. The technique applies to other lambda-encodings (e.g., variants of CPS), but we do not see it used in practice--instead, Plotkin's colon translation appears to be favored. Therefore, in an attempt to link both techniques, we recast Plotkin's proof of Indifference and Simulation to the higher-order specification of the one-pass CPS transformation. To this end, we extend his colon translation from first order to higher order

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