Data Conversion Method between a Natural Number and a Binary Tree for an Inductive Proof and Its Application

Kazuko Takahashi, Shizuo Yoshimaru, Mizuki Goto
unpublished
This paper presents modeling ofa binary tree that represents a natural numberand gives an inductive proof for its propertiesusing theorem provers.We define a function for converting data from a natural numberinto a binary treeand give an inductive proof for its well-definedness.We formalize this method, develop a computational model based on it,and apply it to an electronic cash protocol.We also define the payment function on the binary treeand go on to prove the divisibility of electronic
more » ... sing the theorem provers Isabelle/HOL and Coq, respectively.Furthermore, we discuss the effectiveness of this method.
doi:10.29007/w5xk fatcat:uqdd2oj2uzdt3mic6xctxc76ou