Embedding a logical theory of constructions in Agda

We propose a new way to reason about general recursive functional programs in the dependently typed programming language Agda, which is based on Martin-L¨of’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 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. Categories and Subject Descriptors F.3.1 [Logics and meanings of programs]: Specifying and Verifying and Reasoning about Programs–Logics of programs; D.2.4 [Software Engineering]: Software/Program Verification–C...

• Type: Conference
• Year: 2009
• Where: PLPV
• Authors: Ana Bove, Peter Dybjer, Andrés Sicard-Ramírez
• Keywords: Intuitionistic Predicate Logic, Intuitionistic Type Theory, PLPV 2009, Programming Language Agda, Programming Languages