In this talk I will present a novel pictorial interpretation of relational terms, and a completeness result that allows relational equations to be proved by the appealing process of reasoning using pictures. I will also give a number of practical applications of this result. This talk is based upon joint work with Carolyn Brown. 19th January, Mark P. Jones , University of Nottingham. Using parameterized signatures to express modular structure.
Module systems are a powerful, practical tool for managing the complexity of large software systems.
Previous attempts to formulate a type-theoretic foundation for modular programming have been based on existential, dependent, or manifest types. These approaches can be distinguished by their use of different quantifiers to package the operations that a module exports together with appropriate implementation types. In each case, the underlying type theory is simple and elegant, but significant and sometimes complex extensions are needed to account for features that are important in practical systems, such as separate compilation and propagation of type information between modules. This talk presents a simple type-theoretic framework for modular programming using parameterized signatures. The use of quantifiers is treated as a necessary, but independent concern.