A Class of Data Compression Where The Codeword Is a Computer Program Generating The Data

The Kolmogorov complexity of a string is defined as the shortest length of the program on a Turing machine used to represent the string. On the other hand, it is proved that lambda calculus has the same computational power as the Turing machine. This paper proposes a data compression method using computer programs as the codeword. We use the Haskell programming language, which is a functional programming language implemented on the basis of the lambda calculus. As a computational model, we use a context-free grammar and its corresponding computer model, push-down automaton. A relationship between this program and these models is described. In addition to showing the universality of this coding for finite-state information sources, we also show that coding and decoding are possible in linear time.