This paper describes a novel general method for automatic programming which can be seen as a generalization of techniques such as genetic programming and ADATE. The approach builds on the assumption that data compression can be used as a metaphor for cognition and intelligence. The proof-of-concept system is evaluated on sequence prediction problems. As a starting point, the process of inferring a general law from a data set is viewed as an attempt to compress the observed data. From an artificial intelligence point of view, compression is a useful way of measuring how deeply the observed data is understood. If the sequence contains redundancy it exists a shorter description i.e. the sequence can be compressed.