Exact Real Computer Arithmetic with Continued Fractions
IEEE Transactions on Computers
Infinite objects in type theory
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
Vicious circles: on the mathematics of non-wellfounded phenomena
Vicious circles: on the mathematics of non-wellfounded phenomena
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
A Universal Characterization of the Closed Euclidean Interval
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
A certified, corecursive implementation of exact real numbers
Theoretical Computer Science - Real numbers and computers
Metamorphisms: Streaming representation-changers
Science of Computer Programming
Affine functions and series with co-inductive real numbers
Mathematical Structures in Computer Science
Productivity of Edalat-Potts Exact Arithmetic in Constructive Type Theory
Theory of Computing Systems
Coinductive proofs for basic real computation
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Partial recursive functions in martin-löf type theory
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Filters on coinductive streams, an application to eratosthenes' sieve
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Certified exact real arithmetic using co-induction in arbitrary integer base
FLOPS'08 Proceedings of the 9th international conference on Functional and logic programming
Hi-index | 0.00 |
In this article we present a method for formally proving the correctness of the lazy algorithms for computing homographic and quadratic transformations -- of which field operations are special cases-- on a representation of real numbers by coinductive streams. The algorithms work on coinductive stream of Möbius maps and form the basis of Edalat-Potts exact real arithmetic. We build upon our earlier work of formalising the homographic and quadratic algorithms in constructive type theory via general corecursion. Based on the notion of cofixed point equations for general corecursive definitions we prove by coinduction the correctness of the algorithms. We use the machinery of the Coq proof assistant for coinductive types to present the formalisation. The material in this article is fully formalised in the Coq proof assistant.