From OBJ to ML to Coq

Rigorous program development is notoriously difficult because it involves many aspects, among which specification, programming, verification, code reuse, maintenance, and version management. Besides, these various tasks are interdependent, requiring going back and forth between them. In this paper, we are interested in certain language features and in languages which help make the user’s life easier for developing programs satisfying their specifications. Our interest focuses on three implemented specification/programming languages, OBJ [14, 18], ML[27] and Coq [10], which have played an important historical role in the process of coming up with better languages. And indeed, both OBJ and ML had many successors or dialects, among which OBJ3 [20], Cafe-OBJ [28], Maude [9] and ELAN [2] for OBJ, and SML [23], CAML [30] and OCaml [29] among others for ML. Coq has evolved with many different versions keeping the same name, following the evolution of type theory from the calculus of constructions [11] to the extended calculus of constructions [22] and the development of the theory of inductive types from Martin-Löf’s type theory [25, 26] to the calculus of inductive constructions [12, 31]. Other proof assistants based on a similar historical development include Lego [21], Alf [24] and Agda/Alfa [1]. Coq remains the most mature and widely used of them all. We explain briefly in the introduction what important properties are shared by these three languages, and how OBJ has been influential in