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authorGravatar filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7>2003-09-26 09:01:01 +0000
committerGravatar filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7>2003-09-26 09:01:01 +0000
commite35fd10c4ef3c257e91156e07e65234e81672036 (patch)
treeb915c91bd2e2aa972007cfa8cfd33ff60baa480e /doc/Coercion.tex
parent5dc7b25578b16a8508b3317b2c240d7b322629e0 (diff)
passage V8
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@8343 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'doc/Coercion.tex')
-rw-r--r--doc/Coercion.tex42
1 files changed, 21 insertions, 21 deletions
diff --git a/doc/Coercion.tex b/doc/Coercion.tex
index 69e81f6aa..96fb49272 100644
--- a/doc/Coercion.tex
+++ b/doc/Coercion.tex
@@ -337,11 +337,11 @@ We first give an example of coercion between atomic inductive types
%\begin{\small}
\begin{coq_example}
-Definition bool_in_nat := [b:bool]if b then O else (S O).
+Definition bool_in_nat (b:bool) := if b then 0%N else 1%N.
Coercion bool_in_nat : bool >-> nat.
-Check O=true.
+Check (0%N = true).
Set Printing Coercions.
-Check O=true.
+Check (0%N = true).
\end{coq_example}
%\end{small}
@@ -357,13 +357,13 @@ We give an example of coercion between classes with parameters.
%\begin{\small}
\begin{coq_example}
-Parameters C:nat->Set; D:nat->bool->Set; E:bool->Set.
-Parameter f : (n:nat)(C n) -> (D (S n) true).
+Parameters (C : nat -> Set) (D : nat -> bool -> Set) (E : bool -> Set).
+Parameter f : forall n:nat, C n -> D (S n) true.
Coercion f : C >-> D.
-Parameter g : (n:nat)(b:bool)(D n b) -> (E b).
+Parameter g : forall (n:nat) (b:bool), D n b -> E b.
Coercion g : D >-> E.
-Parameter c : (C O).
-Parameter T : (E true) -> nat.
+Parameter c : C 0.
+Parameter T : E true -> nat.
Check (T c).
Set Printing Coercions.
Check (T c).
@@ -378,10 +378,10 @@ We give now an example using identity coercions.
%\begin{small}
\begin{coq_example}
-Definition D' := [b:bool](D (S O) b).
+Definition D' (b:bool) := D 1 b.
Identity Coercion IdD'D : D' >-> D.
Print IdD'D.
-Parameter d' : (D' true).
+Parameter d' : D' true.
Check (T d').
Set Printing Coercions.
Check (T d').
@@ -400,10 +400,10 @@ is given below:
%\begin{small}
\begin{coq_example}
-Parameters A,B:Set; h:A->B.
+Parameters (A B : Set) (h : A -> B).
Coercion h : A >-> B.
-Parameter U : (A -> (E true)) -> nat.
-Parameter t : B -> (C O).
+Parameter U : (A -> E true) -> nat.
+Parameter t : B -> C 0.
Check (U t).
Set Printing Coercions.
Check (U t).
@@ -419,8 +419,8 @@ previous example.
%\begin{small}
\begin{coq_example}
-Parameter U' : ((C O) -> B) -> nat.
-Parameter t' : (E true) -> A.
+Parameter U' : (C 0 -> B) -> nat.
+Parameter t' : E true -> A.
Check (U' t').
Set Printing Coercions.
Check (U' t').
@@ -444,7 +444,7 @@ Unset Printing Coercions.
\begin{coq_example}
Parameter Graph : Type.
Parameter Node : Graph -> Type.
-Coercion Node : Graph >-> SORTCLASS.
+Coercion Node : Graph >-> Sortclass.
Parameter G : Graph.
Parameter Arrows : G -> G -> Type.
Check Arrows.
@@ -466,12 +466,12 @@ Unset Printing Coercions.
%\begin{small}
\begin{coq_example}
Parameter bij : Set -> Set -> Set.
-Parameter ap : (A,B:Set)(bij A B) -> A -> B.
-Coercion ap : bij >-> FUNCLASS.
-Parameter b : (bij nat nat).
-Check (b O).
+Parameter ap : forall A B:Set, bij A B -> A -> B.
+Coercion ap : bij >-> Funclass.
+Parameter b : bij nat nat.
+Check (b 0%N).
Set Printing Coercions.
-Check (b O).
+Check (b 0%N).
\end{coq_example}
%\end{small}