diff options
| author | barras-local | 2001-04-09 18:51:41 +0000 |
|---|---|---|
| committer | barras-local | 2001-04-09 18:51:41 +0000 |
| commit | 12d5de083a373aa69eaa9be812c6be25c79eca60 (patch) | |
| tree | 5bc0c015dc4f06d7810e1c591141208797729c47 | |
| parent | 12e02f19cdf1bd38935025ca120c7d3043916519 (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.tex | 66 |
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} |
