Alberto Ciaffaglione

Certified reasoning on Real Numbers and Objects in Co-inductive Type Theory

PhD thesis, Dipartimento di Matematica e Informatica Università di Udine, Italy, 2003 available as outline


In the thesis we adopt Type Theory-based Formal Methods, namely the proof assistant Coq, for reasoning on two distinct topics. In the first part we encode the Constructive Real Numbers in Coq using infinite sequences of digits. Then we work on such a representation with co-inductive types and co-recursive proofs. The final aim is to prove in Coq that the representation satisfies a set of axioms, proposed for characterizing the constructive reals. In the second part we encode the Abadi-Cardelli's imp-varsigma calculus in Coq using an higher-order approach. We formalize the syntax, the first-order static semantics and the big-step dynamic semantics. Then we prove a Subject Reduction theorem relating the two semantics. The ultimate goal is to obtain a Type Soundness result in Coq.


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