@@ -39,7 +39,7 @@ In order to solve the recursive domain equation in \Sref{sec:model} it is also e

\end{defn}

Intuitively, applying a non-expansive function to some data will not suddenly introduce differences between seemingly equal data.

Elements that cannot be distinguished by programs within $n$ steps remain indistinguishable after applying $f$.

The reason that contractive functions are interesting is that for every contractive $f : \cofe\to\cofe$ with $\cofe$ inhabited, there exists a \emph{unique}\footnote{Uniqueness is not proven in Coq.} fixed-point $\fix(f)$ such that $\fix(f)= f(\fix(f))$.

The reason that contractive functions are interesting is that for every contractive $f : \cofe\to\cofe$ with $\cofe$ inhabited, there exists a \emph{unique} fixed-point $\fix(f)$ such that $\fix(f)= f(\fix(f))$.

\begin{defn}

The category $\COFEs$ consists of COFEs as objects, and non-expansive functions as arrows.