We a give an intrinsic characterization of the class of functions which are computable in
that is by a uniform, logarithmic depth and polynomial size family circuit. Recall that the class of functions in
, that is in logarithmic time on an Alternating Turing Machine, is
. Our characterization is in terms of first order functional programming languages. We define measure-tools called Sup-interpretations, which allow to give space and time bounds and allow also to capture a lot of program schemas. This study is part of a research on static analysis in order to predict program resources. It is related to the notion of Quasi-interpretations and belongs to the implicit computational complexity line of research.