A constructive approach for developing probabilistic programs

Probabilistic techniques in computer programs are becoming more and more widely used. Therefore, there is a big interest in the formal specification, verification, and development of probabilistic programs. On the other hand, Martin-Löf's theory of types is an appropriate notation for formal program development since it allows us to express both specifications and programs within the same formalism. Furthermore, the proof rules of this theory can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. In this paper, we augment Martin-Löf's theory of types with a simple probabilistic construct enabling us to specify probabilistic programs formally. Furthermore, having such a construct, we can derive functional, probabilistic programs from correctness proofs of their formal specifications written in the new type theoretical formalism.