Coinductive Proofs for Basic Real Computation

We describe two representations for real numbers, signed digit streams and Cauchy sequences. We give coinductive proofs for the correctness of functions converting between these two representations to show the adequacy of signed digit stream representation. We also show a coinductive proof for the correctness of a corecursive program for the average function with regard to the signed digit stream representation. We implemented this proof in the interactive proof system Minlog. Thus, reliable, corecursive functions for real computation can be guaranteed, which is very helpful in formal software development for real numbers.

• Type: Conference
• Year: 2006
• Where: CIE
• Authors: Tie Hou
• Keywords: Applied Computing, CIE 2006, Coinductive Proof, Digit Stream, Digit Stream Representation