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author | Geoffrey Washburn <geoffrey.washburn@epfl.ch> | 2008-04-03 14:35:49 +0000 |
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committer | Geoffrey Washburn <geoffrey.washburn@epfl.ch> | 2008-04-03 14:35:49 +0000 |
commit | 279da87f484b6ac77d87b3efe2d69d3a09492a43 (patch) | |
tree | 169563a6fca8f0911b78ee568d5e9f6a95517607 | |
parent | 4ec9c8abe1b2bb8aff74edaf954453070bef89fd (diff) | |
download | scala-279da87f484b6ac77d87b3efe2d69d3a09492a43.tar.gz scala-279da87f484b6ac77d87b3efe2d69d3a09492a43.tar.bz2 scala-279da87f484b6ac77d87b3efe2d69d3a09492a43.zip |
Decided that it did not make sense to express p...
Decided that it did not make sense to express part of the properties of
a PartialOrdering in terms of an equaivalence relation.
Concluded that downward transitivity for Orderings followed from upward
transitivity and the property on Orderings that does not yet have a
name.
-rw-r--r-- | src/library/scala/Ordering.scala | 14 | ||||
-rw-r--r-- | src/library/scala/PartialOrdering.scala | 4 |
2 files changed, 6 insertions, 12 deletions
diff --git a/src/library/scala/Ordering.scala b/src/library/scala/Ordering.scala index 358cfb5bdf..ef4bbfecd6 100644 --- a/src/library/scala/Ordering.scala +++ b/src/library/scala/Ordering.scala @@ -16,8 +16,8 @@ package scala * latter. * * A <a href="http://en.wikipedia.org/wiki/Total_order">total ordering</a> - * is a binary relation on a type <code>T</code> that is also a partial - * ordering on values of type <code>T</code>. This relation is exposed as + * is a binary relation on a type <code>T</code> that is also an equivalence relation + * and partial ordering on values of type <code>T</code>. This relation is exposed as * the <code>compare</code> method of the <code>Ordering</code> trait. * This relation must be: * <ul> @@ -26,14 +26,8 @@ package scala * <li>(need a name): <code>compare(x, y) == z</code> and <code>compare(y, x) == w</code> * then <code>Math.signum(z) == -Math.signum(w)</code>, for any <code>x</code> and <code>y</code> of * type <code>T</code> and <code>z</code> and <code>w</code> of type <code>Int</code>.</li> - * <li>upward transitive: if <code>compare(x, y) == z</code> and <code>lteq(y, w) == v</code> - * and <code>Math.signum(z) >= 0</code> and <code>Math.signum(v) >= 0</code> then - * <code>compare(x, w) == u</code> and <code>Math.signum(z + v) == Math.signum(u)</code>, - * for any <code>x</code>, <code>y</code>, - * and <code>w</code> of type <code>T</code> and <code>z</code>, <code>v</code>, and <code>u</code> - * of type <code>Int</code>.</li> - * <li>downward transitive: if <code>compare(x, y) == z</code> and <code>lteq(y, w) == v</code> - * and <code>Math.signum(z) <= 0</code> and <code>Math.signum(v) <= 0</code> then + * <li>transitive: if <code>compare(x, y) == z</code> and <code>lteq(y, w) == v</code> + * and <code>Math.signum(z) >= 0</code> and <code>Math.signum(v) >= 0</code> then * <code>compare(x, w) == u</code> and <code>Math.signum(z + v) == Math.signum(u)</code>, * for any <code>x</code>, <code>y</code>, * and <code>w</code> of type <code>T</code> and <code>z</code>, <code>v</code>, and <code>u</code> diff --git a/src/library/scala/PartialOrdering.scala b/src/library/scala/PartialOrdering.scala index 0945121724..2bc755b772 100644 --- a/src/library/scala/PartialOrdering.scala +++ b/src/library/scala/PartialOrdering.scala @@ -20,8 +20,8 @@ package scala * the <code>lteq</code> method of the <code>PartialOrdering</code> trait. * This relation must be: * <ul> - * <li>an equivalence relation: if <code>equiv(x, y)</code> then <code>lteq(x, y)</code>, - * for any <code>x</code> and <code>y</code> of type <code>T</code>.</li> + * <li>reflexive: <code>lteq(x, x) == true</code>, for any <code>x</code> of + * type <code>T</code>.</li> * <li>anti-symmetric: <code>lteq(x, y) == true</code> and <code>lteq(y, x) == true</code> * then <code>equiv(x, y)</code>, for any <code>x</code> and <code>y</code> of * type <code>T</code>.</li> |