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Algebra of programming in Agda: Dependent types for relational program derivation

Part of: JFP Research Articles

Published online by Cambridge University Press:  23 July 2009

SHIN-CHENG MU ,
HSIANG-SHANG KO  and
PATRIK JANSSON
SHIN-CHENG MU
Affiliation:
Institute of Information Science, Academia Sinica, Taiwan (e-mail: scm@iis.sinica.edu.tw)
HSIANG-SHANG KO
Affiliation:
Department of Computer Science and Information Engineering, National Taiwan University, Taiwan (e-mail: joshs@mail2000.com.tw)
PATRIK JANSSON
Affiliation:
Department of Computer Science and Engineering, Chalmers University of Technology, and University of Gothenburg, Sweden (e-mail: patrikj@chalmers.se)
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Abstract

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Relational program derivation is the technique of stepwise refining a relational specification to a program by algebraic rules. The program thus obtained is correct by construction. Meanwhile, dependent type theory is rich enough to express various correctness properties to be verified by the type checker. We have developed a library, AoPA (Algebra of Programming in Agda), to encode relational derivations in the dependently typed programming language Agda. A program is coupled with an algebraic derivation whose correctness is guaranteed by the type system. Two non-trivial examples are presented: an optimisation problem and a derivation of quicksort in which well-founded recursion is used to model terminating hylomorphisms in a language with inductive types.

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Type
Articles
Information
Journal of Functional Programming , Volume 19 , Issue 5 , September 2009 , pp. 545 - 579
Copyright
Copyright © Cambridge University Press 2009

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