Extracting Lisp programs from constructive proofs: a formal theory of constructive mathematics based on Lisp

Inferring LISP Programs From Examples

W i l l i a m R. Swartout

A Formal Pattern Language for Refactoring of Lisp Programs

Refactoring tools are extremely important to prevent errors in legacy systems restructuring. Unfortunately, to be effective, these tools require huge computer resources that cause unacceptable inefficiencies or limit the size of the restructured programs or even the programming language expressiveness. Previous approaches also made it difficult for the programmer to extend the tool with new ref...

Proof Theory and Constructive Mathematics

Constructive Proofs or Constructive Statements?

In this work the following question is considered: is Sergeraert’s “Constructive Algebraic Topology” (CAT, in short) really constructive (in the strict logical sense of the word “constructive”)? We have not an answer to that question, but we are interested in the following: could have a positive (or negative) answer to the previous question an influence in the problem of proving the correctness...

Writing Constructive Proofs Yielding Efficient Extracted Programs

The NuPRL system [3] was designed for interactive writing of machine–checked constructive proofs and for extracting algorithms from the proofs. The extracted algorithms are guaranteed to be correct 1 which makes it possible to use NuPRL as a programming language with built-in verification[1,5,7,8,9,10]. However it turned out that proofs written without algorithmic efficiency in mind often produ...