We present a method for approximating the semanti s of probabilisti programs to the purpose of onstru ting semanti s-based analyses of su h programs. The method resembles the one based on Galois onne tion as developed in the Cousot framework for abstra t interpretation. The main di eren e between our approa h and the standard theory of abstra t interpretation is the hoi e of linear spa e stru tures instead of order-theoreti ones as semanti al ( on rete and abstra t) domains. We show that our method generates \best approximations" a ording to an appropriate notion of pre ision de ned in terms of a norm. Moreover, if reasted in a order-theoreti setting these approximations are orre t in the sense of lassi al abstra t interpretation theory. We use Con urrent Constraint Programming as a referen e programming paradigm. The basi on epts and ideas an nevertheless be applied to any other paradigm. The results we present are intended to be the rst step towards a general theory of probabilisti abstra t interpretation, whi h re-formulates the lassi al theory in a setting suitable for a quantitative reasoning about programs.