Algebra of Programming Using Dependent Types

Authors:
Shin-Cheng Mu;Hsiang-Shang Ko;Patrik Jansson
Affiliations:
Institute of Information Science, Academia Sinica, Taiwan;Department of Computer Science and Information Engineering, National Taiwan University, Taiwan;Department of Computer Science and Engineering, Chalmers University of Technology & University of Gothenburg, Sweden
Venue:
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
Year:
2008

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Abstract

Dependent type theory is rich enough to express that a program satisfies an input/output relational specification, but it could be hard to construct the proof term. On the other hand, squiggolists know very well how to show that one relation is included in another by algebraic reasoning. We demonstrate how to encode functional and relational derivations in a dependently typed programming language. A program is coupled with an algebraic derivation from a specification, whose correctness is guaranteed by the type system.