Functors for proofs and programs

In a series of papers we have been using a modification of the ideas of Curry and Howard to obtain reliable programs from formal proofs. In this paper we extend our earlier work by presenting a new approach for constructing correct SML structures and SML functors from CASL structured and parametrized specifications by extracting the SML programs from constructive proofs of the axioms of the specifications.

The process of verification exhibited two small errors in the balancing scheme, which have been fixed and then verified. Beyond these verification results, this article illustrates the use and benefits of modules and functors in a logical framework. Skip to main content Skip to sections.

This service is more advanced with JavaScript available. Advertisement Hide. European Symposium on Programming. Functors for Proofs and Programs. Conference paper. This process is experimental and the keywords may be updated as the learning algorithm improves. File Handling. Table of Contents. Improve Article. Save Article. Like Article. Take a step-up from those "Hello World" programs. Learn to implement data structures like Heap, Stacks, Linked List and many more!

Check out our Data Structures in C course to start learning today. Category theory has many important connections to logic. We shall in particular show how it illuminates the study of formal proofs as mathematical objects in their own right. This will involve looking at the Curry-Howard isomorphism between proofs and programs, and at Linear Logic, a resource-sensitive logic. Both of these topics have many important applications in Computer Science.

Category theory has also deeply influenced the design of modern especially functional programming languages, and the study of program transformations.