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authorbarras-local2001-04-09 18:51:41 +0000
committerbarras-local2001-04-09 18:51:41 +0000
commit12d5de083a373aa69eaa9be812c6be25c79eca60 (patch)
tree5bc0c015dc4f06d7810e1c591141208797729c47
parent12e02f19cdf1bd38935025ca120c7d3043916519 (diff)
mise a jour pour la formation
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@8180 85f007b7-540e-0410-9357-904b9bb8a0f7
-rw-r--r--doc/Coercion.tex66
1 files changed, 33 insertions, 33 deletions
diff --git a/doc/Coercion.tex b/doc/Coercion.tex
index 009d524ab5..47aee61cad 100644
--- a/doc/Coercion.tex
+++ b/doc/Coercion.tex
@@ -222,13 +222,13 @@ rules to show the inserted coercions.
%\begin{\small}
\begin{coq_example}
-Variables C:nat->Set; D:nat->bool->Set; E:bool->Set.
-Variable f : (n:nat)(C n) -> (D (S n) true).
+Parameters C:nat->Set; D:nat->bool->Set; E:bool->Set.
+Parameter f : (n:nat)(C n) -> (D (S n) true).
Coercion f : C >-> D.
-Variable g : (n:nat)(b:bool)(D n b) -> (E b).
+Parameter g : (n:nat)(b:bool)(D n b) -> (E b).
Coercion g : D >-> E.
-Variable c : (C O).
-Variable T : (E true) -> nat.
+Parameter c : (C O).
+Parameter T : (E true) -> nat.
Check (T c).
\end{coq_example}
%\end{small}
@@ -240,7 +240,7 @@ We give now an example using identity coercions.
Definition D' := [b:bool](D (S O) b).
Identity Coercion IdD'D : D' >-> D.
Print IdD'D.
-Variable d' : (D' true).
+Parameter d' : (D' true).
Check (T d').
\end{coq_example}
%\end{small}
@@ -253,10 +253,10 @@ is given below:
%\begin{small}
\begin{coq_example}
-Variables A,B:Set; h:A->B.
+Parameters A,B:Set; h:A->B.
Coercion h : A >-> B.
-Variable U : (A -> (E true)) -> nat.
-Variable t : B -> (C O).
+Parameter U : (A -> (E true)) -> nat.
+Parameter t : B -> (C O).
Check (U t).
\end{coq_example}
%\end{small}
@@ -266,8 +266,8 @@ previous example.
%\begin{small}
\begin{coq_example}
-Variable U' : ((C O) -> B) -> nat.
-Variable t' : (E true) -> A.
+Parameter U' : ((C O) -> B) -> nat.
+Parameter t' : (E true) -> A.
Check (U' t').
\end{coq_example}
%\end{small}
@@ -283,13 +283,13 @@ Check (U' t').
%\begin{small}
\begin{coq_example}
-Variable Graph : Type.
-Variable Node : Graph -> Type.
+Parameter Graph : Type.
+Parameter Node : Graph -> Type.
Coercion Node : Graph >-> SORTCLASS.
-Variable G : Graph.
-Variable Arrows : G -> G -> Type.
+Parameter G : Graph.
+Parameter Arrows : G -> G -> Type.
Check Arrows.
-Variable fg : G -> G.
+Parameter fg : G -> G.
Check fg.
\end{coq_example}
%\end{small}
@@ -301,10 +301,10 @@ Check fg.
%\begin{small}
\begin{coq_example}
-Variable bij : Set -> Set -> Set.
-Variable ap : (A,B:Set)(bij A B) -> A -> B.
+Parameter bij : Set -> Set -> Set.
+Parameter ap : (A,B:Set)(bij A B) -> A -> B.
Coercion ap : bij >-> FUNCLASS.
-Variable b : (bij nat nat).
+Parameter b : (bij nat nat).
Check (b O).
\end{coq_example}
%\end{small}
@@ -382,23 +382,23 @@ coercions. To validate \verb|true=O|, the coercion is searched from
Reset Graph.
\end{coq_eval}
\begin{coq_example}
-Variable Graph : Type.
-Variable Node : Graph -> Type.
+Parameter Graph : Type.
+Parameter Node : Graph -> Type.
Coercion Node : Graph >-> SORTCLASS.
-Variable G : Graph.
-Variable Arrows : G -> G -> Type.
+Parameter G : Graph.
+Parameter Arrows : G -> G -> Type.
Check Arrows.
-Variable fg : G -> G.
+Parameter fg : G -> G.
Check fg.
\end{coq_example}
\item Coercion to a function
\begin{coq_example}
-Variable bij : Set -> Set -> Set.
-Variable ap : (A,B:Set)(bij A B) -> A -> B.
+Parameter bij : Set -> Set -> Set.
+Parameter ap : (A,B:Set)(bij A B) -> A -> B.
Coercion ap : bij >-> FUNCLASS.
-Variable b : (bij nat nat).
+Parameter b : (bij nat nat).
Check (b O).
\end{coq_example}
@@ -407,13 +407,13 @@ Check (b O).
Reset C.
\end{coq_eval}
\begin{coq_example}
-Variables C : nat -> Set; D : nat -> bool -> Set; E : bool -> Set.
-Variable f : (n:nat)(C n) -> (D (S n) true).
+Parameters C : nat -> Set; D : nat -> bool -> Set; E : bool -> Set.
+Parameter f : (n:nat)(C n) -> (D (S n) true).
Coercion f : C >-> D.
-Variable g : (n:nat)(b:bool)(D n b) -> (E b).
+Parameter g : (n:nat)(b:bool)(D n b) -> (E b).
Coercion g : D >-> E.
-Variable c : (C O).
-Variable T : (E true) -> nat.
+Parameter c : (C O).
+Parameter T : (E true) -> nat.
Check (T c).
\end{coq_example}
@@ -423,7 +423,7 @@ Check (T c).
Definition D' := [b:bool](D (S O) b).
Identity Coercion IdD'D : D' >-> D.
Print IdD'D.
-Variable d' : (D' true).
+Parameter d' : (D' true).
Check (T d').
\end{coq_example}