A study in the foundations of programming methodology: Specifications, institutions, charters and parchments

Abstract

The theory of institutions formalizes the intuitive notion of a "logical system." Institutions were introduced (1) to support as much computer science as possible independently of the underlying logical system, (2) to facilitate the transfer of results (and artifacts such as theorem provers) from one logical system to another, and (3) to permit combining a number of different logical systems. In particular, programming-in-the-large (in the style of the Clear specification language) is available for any specification or "logical" programming language based upon a suitable institution. Available features include generic modules, module hierarchies, "data constraints" (for data abstraction), and "multiplex" institutions (for combining multiple logical systems). The basic components of an institution are: a category of signatures (which generally provide symbols for constructing sentences); a set (or category) of Σ-sentences for each signature Σ; a category (or set) of Σ-models for each Σ; and a Σ-satisfaction relation, between Σ-sentences and Σ-models, for each Σ. The intuition of the basic axiom for institutions is that truth (i.e., satisfaction) is invariant under change of notation. This paper enriches institutions with sentence morphisms to model proofs, and uses this to explicate the notion of a logical programming language.To ease constructing institutions, and to clarify various notions, this paper introduces two further concepts. A charter consists of an adjunction, a "base" functor, and a "ground" object; we show that "chartering" is a convenient way to "found" institutions. Parchments provide a notion of sentential syntax, and a simple way to "write" charters and thus get institutions. Parchments capture the insight that the syntax of logic is an initial algebra. Everything is illustrated with the many-sorted equational institution. Parchments also explicate the sense of finitude that is appropriate for specifications. Finally, we introduce generalized institutions, which generalize both institutions and Mayoh's "galleries", and we introduce corresponding generalized charters and parchments.KeywordsLogical SystemEquational LogicSignature MorphismModel MorphismInitial AlgebraThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.