aboutsummaryrefslogtreecommitdiff
path: root/doc/RefMan-lib.tex
diff options
context:
space:
mode:
authorbarras2003-12-19 17:48:34 +0000
committerbarras2003-12-19 17:48:34 +0000
commitc1e8b8c5cbc0e19703b9b7326401e242cd751b80 (patch)
tree1d09fa39c291fa810158a5e46d44a000c96f5296 /doc/RefMan-lib.tex
parentbef467cfac0b718bffdbb5444b2a4364b3941b09 (diff)
*** empty log message ***
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@8424 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'doc/RefMan-lib.tex')
-rwxr-xr-xdoc/RefMan-lib.tex18
1 files changed, 10 insertions, 8 deletions
diff --git a/doc/RefMan-lib.tex b/doc/RefMan-lib.tex
index 0d87023155..a8aefe781d 100755
--- a/doc/RefMan-lib.tex
+++ b/doc/RefMan-lib.tex
@@ -141,10 +141,10 @@ First, we find propositional calculus connectives:
\begin{coq_eval}
Set Printing Depth 50.
-\end{coq_eval}
-\begin{coq_example*}
(********** Next parsing errors for /\ and \/ are harmless ***********)
(******************* since output is not displayed *******************)
+\end{coq_eval}
+\begin{coq_example*}
Inductive True : Prop := I.
Inductive False : Prop := .
Definition not (A: Prop) := A -> False.
@@ -161,14 +161,14 @@ Abort All.
\ttindex{or\_introl}
\ttindex{or\_intror}
\ttindex{iff}
-\ttindex{IF}
+\ttindex{IF_then_else}
\begin{coq_example*}
End Projections.
Inductive or (A B:Prop) : Prop :=
| or_introl (_:A)
| or_intror (_:B).
Definition iff (P Q:Prop) := (P -> Q) /\ (Q -> P).
-Definition IF (P Q R:Prop) := P /\ Q \/ ~ P /\ R.
+Definition IF_then_else (P Q R:Prop) := P /\ Q \/ ~ P /\ R.
\end{coq_example*}
\subsubsection{Quantifiers} \label{Quantifiers}
@@ -188,7 +188,7 @@ Definition all (A:Set) (P:A -> Prop) := forall x:A, P x.
Inductive ex (A: Set) (P:A -> Prop) : Prop :=
ex_intro (x:A) (_:P x).
Inductive ex2 (A:Set) (P Q:A -> Prop) : Prop :=
- ex_intro2 : (x:A) (_:P x) (_:Q x).
+ ex_intro2 (x:A) (_:P x) (_:Q x).
\end{coq_example*}
The following abbreviations are allowed:
@@ -389,7 +389,7 @@ provided.
\begin{coq_example*}
Inductive sig (A:Set) (P:A -> Prop) : Set := exist (x:A) (_:P x).
Inductive sig2 (A:Set) (P Q:A -> Prop) : Set :=
- exist2 : (x:A) (_:P x) (_:Q x).
+ exist2 (x:A) (_:P x) (_:Q x).
\end{coq_example*}
A ``strong (dependent) sum'' \verb+{x:A & (P x)}+ may be also defined,
@@ -412,10 +412,12 @@ Variable A : Set.
Variable P : A -> Set.
Definition projS1 (H:sigS A P) := let (x, h) := H in x.
Definition projS2 (H:sigS A P) :=
- let (x, h) return P (projS1 H) := H in h.
+ match H return P (projS1 H) with
+ existS x h => h
+ end.
End sigSprojections.
Inductive sigS2 (A: Set) (P Q:A -> Set) : Set :=
- existS2 : (x:A) (_:P x) (_:Q x).
+ existS2 (x:A) (_:P x) (_:Q x).
\end{coq_example*}
A related non-dependent construct is the constructive sum