In his PhD dissertation (in Mathematics, at ETH Zurich, 1951; published in 1954) he describes for the first time a full meta-circular compiler, that is a translation mechanism of a programming language, written in that same language. His most influential contribution is the so-called structured program theorem, published in 1966 together with Giuseppe Jacopini. In lambda-calculus, he established an important separation theorem between normal forms. Together with Alessandro Berarducci, he demonstrated an isomorphism between the strictly-positive algebraic data types and the polymorphic lambda-terms, otherwise known as Böhm–Berarducci encoding.
A special issue of Theoretical Computer Science was dedicated to him in 1993, on his 70th birthday. He is the recipient of the 2001 EATCS Award for a distinguished career in theoretical computer science.