Embedding a Logical Theory of Constructions in Agda
Paper in proceedings, 2009

We propose a new way to reason about general recursive functional programs in the dependently typed programming language Agda, which is based on Martin-Löf's intuitionistic type theory. We show how to embed an external programming logic, Aczel's Logical Theory of Constructions (LTC) inside Agda. To this end we postulate the existence of a domain of untyped functional programs and the conversion rules for these programs. Furthermore, we represent the inductive notions in LTC (intuitionistic predicate logic with equality, and totality predicates) as inductive notions in Agda. To illustrate our approach we specify an LTC-style logic for PCF, and show how to prove the termination and correctness of a general recursive algorithm for computing the greatest common divisor of two numbers.

Logical theory of constructions

general recursion

type theory

Author

Ana Bove

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Peter Dybjer

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Andres Sicard-Ramirez

Proceedings of the 2009 ACM SIGPLAN Workshop on Programming Languages meets Program Verification (PLPV) 2009

59-66

Subject Categories

Computer Science

ISBN

978-160558330-3

More information

Created

10/7/2017