Theorems about Composition

Compositional designs require component specifications that can be composed: Designers have to be able to deduce system properties from components specifications. On the other hand, components specifications should be abstract enough to allow component reuse and to hide substantial parts of correctness proofs in components verifications. Part of the problem is that too abstract specifications do not contain enough information to be composed. Therefore, the right balance between abstraction and composability must be found. This paper explores the systematic construction of abstract specifications that can be composed through specific forms of composition called existential and universal.