diff options
author | barras <barras@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2006-09-28 17:51:39 +0000 |
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committer | barras <barras@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2006-09-28 17:51:39 +0000 |
commit | 1040f4258593fa6de309acb2c93b76c41e914188 (patch) | |
tree | aad91dcfecb0b764769de360ee1cb466d201196f /doc/refman | |
parent | 5865dad7bae73b13096a62e3657b02e13771524a (diff) |
separation de RealField
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@9187 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'doc/refman')
-rw-r--r-- | doc/refman/Polynom.tex | 28 | ||||
-rw-r--r-- | doc/refman/RefMan-tac.tex | 2 |
2 files changed, 15 insertions, 15 deletions
diff --git a/doc/refman/Polynom.tex b/doc/refman/Polynom.tex index 49616ff69..0b8e09452 100644 --- a/doc/refman/Polynom.tex +++ b/doc/refman/Polynom.tex @@ -110,9 +110,9 @@ The tactic must be loaded by \texttt{Require Import Ring}. The ring structures must be declared with the \texttt{Add Ring} command (see below). The ring of booleans is predefined; if one wants to use the tactic on \texttt{nat} one must first require the module -\texttt{NewArithRing}; for \texttt{Z}, do \texttt{Require Import -NewZArithRing}; for \texttt{N}, do \texttt{Require Import -NewNArithRing}. +\texttt{ArithRing}; for \texttt{Z}, do \texttt{Require Import +ZArithRing}; for \texttt{N}, do \texttt{Require Import +NArithRing}. \Example \begin{coq_eval} @@ -121,7 +121,7 @@ Require Import ZArith. Open Scope Z_scope. \end{coq_eval} \begin{coq_example} -Require Import NewZArithRing. +Require Import ZArithRing. Goal forall a b c:Z, (a + b + c) * (a + b + c) = a * a + b * b + c * c + 2 * a * b + 2 * a * c + 2 * b * c. @@ -159,11 +159,11 @@ avoided for terms belonging to the same ring theory. Declaring a new ring consists in proving that a ring signature (a carrier set, an equality, and ring operations: {\tt -Ring\_th.ring\_theory} and {\tt Ring\_th.semi\_ring\_theory}) +Ring\_theory.ring\_theory} and {\tt Ring\_theory.semi\_ring\_theory}) satisfies the ring axioms. Semi-rings (rings without $+$ inverse) are also supported. The equality can be either Leibniz equality, or any relation declared as a setoid (see~\ref{setoidtactics}). The definition -of ring and semi-rings (see module {\tt Ring\_th}) is: +of ring and semi-rings (see module {\tt Ring\_theory}) is: \begin{verbatim} Record ring_theory : Prop := mk_rt { Radd_0_l : forall x, 0 + x == x; @@ -251,13 +251,13 @@ describes their syntax and effects: the form {\tt forall x y, x?=!y = true $\rightarrow$ x == y}. \item[morphism \term] declares the ring as a customized one. \term{} is a proof that there exists a morphism between a set of coefficient - and the ring carrier (see {\tt Ring\_th.ring\_morph} and {\tt - Ring\_th.semi\_morph}). + and the ring carrier (see {\tt Ring\_theory.ring\_morph} and {\tt + Ring\_theory.semi\_morph}). \item[setoid \term$_1$ \term$_2$] forces the use of given setoid. \term$_1$ is a proof that the equality is indeed a setoid (see {\tt Setoid.Setoid\_Theory}), and \term$_2$ a proof that the - ring operations are morphisms (see {\tt Ring\_th.ring\_eq\_ext} and - {\tt Ring\_th.sring\_eq\_ext}). This modifier need not be used if the + ring operations are morphisms (see {\tt Ring\_theory.ring\_eq\_ext} and + {\tt Ring\_theory.sring\_eq\_ext}). This modifier need not be used if the setoid and morphisms have been declared. \item[constants [\ltac]] specifies a tactic expression that, given a term, returns either an object of the coefficient set that is mapped to @@ -297,7 +297,7 @@ tactic we used \Coq\ as a programming language and also as a proof environment to build a tactic and to prove it correctness. The interested reader is strongly advised to have a look at the file -\texttt{Pol.v}. Here a type for polynomials is defined: +\texttt{Ring_polynom.v}. Here a type for polynomials is defined: \begin{small} \begin{flushleft} @@ -402,9 +402,9 @@ associative commutative rewriting on every ring. The tactic must be loaded by \texttt{Require Import LegacyRing}. The ring must be declared in the \texttt{Add Ring} command. The ring of booleans is predefined; if one wants to use the tactic on \texttt{nat} one must -first require the module \texttt{ArithRing}; for \texttt{Z}, do -\texttt{Require Import ZArithRing}; for \texttt{N}, do \texttt{Require -Import NArithRing}. +first require the module \texttt{LegacyArithRing}; for \texttt{Z}, do +\texttt{Require Import LegacyZArithRing}; for \texttt{N}, do \texttt{Require +Import LegacyNArithRing}. The terms \term$_1$, \dots, \term$_n$ must be subterms of the goal conclusion. The tactic \texttt{ring} normalizes these terms diff --git a/doc/refman/RefMan-tac.tex b/doc/refman/RefMan-tac.tex index 85499fe10..5f38017b7 100644 --- a/doc/refman/RefMan-tac.tex +++ b/doc/refman/RefMan-tac.tex @@ -2710,7 +2710,7 @@ Goal forall x y:R, \end{coq_example*} \begin{coq_example} -intros; legacy field. +intros; field. \end{coq_example} \begin{coq_eval} |