We discuss here constraint programming (CP) by using a proof-theoretic perspective. To this end we identify three levels of abstraction. Each level sheds light on the essence of CP. In particular, the highest level allows us to bring CP closer to the computation as deduction paradigm. At the middle level we can explain various constraint propagation algorithms. Finally, at the lowest level we can address the issue of automatic generation and optimization of the constraint propagation algorithms.

15 pages, appeared in "Processes, Terms and Cycles: Steps on the Road to Infinity", (A. Middeldorp, V. van Oostrom, F. van Raamsdonk, R. de Vrijer, eds.), LNCS 3838, pp. 55-69. (2005)