From 8a9dede5b78ba7a34e478d19e62e2648f207c3a8 Mon Sep 17 00:00:00 2001
From: Guillaume Melquiond
Date: Tue, 22 Aug 2017 08:07:21 +0200
Subject: Fix obsolete description of real numerals.

---
 doc/refman/RefMan-syn.tex | 14 +++-----------
 1 file changed, 3 insertions(+), 11 deletions(-)

(limited to 'doc/refman/RefMan-syn.tex')

diff --git a/doc/refman/RefMan-syn.tex b/doc/refman/RefMan-syn.tex
index 084317776b..d8a353300f 100644
--- a/doc/refman/RefMan-syn.tex
+++ b/doc/refman/RefMan-syn.tex
@@ -980,7 +980,7 @@ delimited by key {\tt nat}, and bound to the type {\tt nat} (see \ref{bindscope}
 
 This scope includes the standard arithmetical operators and relations on
 type {\tt N} (binary natural numbers). It is delimited by key {\tt N}
-and comes with an interpretation for numerals as closed term of type {\tt Z}.
+and comes with an interpretation for numerals as closed term of type {\tt N}.
 
 \subsubsection{\tt Z\_scope}
 
@@ -1014,16 +1014,8 @@ fractions of an integer and a strictly positive integer.
 
 This scope includes the standard arithmetical operators and relations on
 type {\tt R} (axiomatic real numbers). It is delimited by key {\tt R}
-and comes with an interpretation for numerals as term of type {\tt
-R}. The interpretation is based on the binary decomposition.  The
-numeral 2 is represented by $1+1$.  The interpretation $\phi(n)$ of an
-odd positive numerals greater $n$ than 3 is {\tt 1+(1+1)*$\phi((n-1)/2)$}.
-The interpretation $\phi(n)$ of an even positive numerals greater $n$
-than 4 is {\tt (1+1)*$\phi(n/2)$}.  Negative numerals are represented as the
-opposite of the interpretation of their absolute value. E.g. the
-syntactic object {\tt -11} is interpreted as {\tt
--(1+(1+1)*((1+1)*(1+(1+1))))} where the unit $1$ and all the operations are
-those of {\tt R}.
+and comes with an interpretation for numerals using the {\tt IZR}
+morphism from binary integer numbers to {\tt R}.
 
 \subsubsection{\tt bool\_scope}
 
-- 
cgit v1.2.3

