--- a/doc-src/AxClass/Group/Semigroups.thy Mon Jun 26 11:21:49 2000 +0200
+++ b/doc-src/AxClass/Group/Semigroups.thy Mon Jun 26 11:43:56 2000 +0200
@@ -1,7 +1,7 @@
-header {* Semigroups *};
+header {* Semigroups *}
-theory Semigroups = Main:;
+theory Semigroups = Main:
text {*
\medskip\noindent An axiomatic type class is simply a class of types
@@ -14,13 +14,13 @@
We illustrate these basic concepts by the following formulation of
semigroups.
-*};
+*}
consts
- times :: "'a \\<Rightarrow> 'a \\<Rightarrow> 'a" (infixl "\<Otimes>" 70);
+ times :: "'a \\<Rightarrow> 'a \\<Rightarrow> 'a" (infixl "\<Otimes>" 70)
axclass
semigroup < "term"
- assoc: "(x \<Otimes> y) \<Otimes> z = x \<Otimes> (y \<Otimes> z)";
+ assoc: "(x \<Otimes> y) \<Otimes> z = x \<Otimes> (y \<Otimes> z)"
text {*
\noindent Above we have first declared a polymorphic constant $\TIMES
@@ -38,18 +38,18 @@
Below, class $plus_semigroup$ represents semigroups of the form
$(\tau, \PLUS^\tau)$, while the original $semigroup$ would correspond
to semigroups $(\tau, \TIMES^\tau)$.
-*};
+*}
consts
- plus :: "'a \\<Rightarrow> 'a \\<Rightarrow> 'a" (infixl "\<Oplus>" 70);
+ plus :: "'a \\<Rightarrow> 'a \\<Rightarrow> 'a" (infixl "\<Oplus>" 70)
axclass
plus_semigroup < "term"
- assoc: "(x \<Oplus> y) \<Oplus> z = x \<Oplus> (y \<Oplus> z)";
+ assoc: "(x \<Oplus> y) \<Oplus> z = x \<Oplus> (y \<Oplus> z)"
text {*
\noindent Even if classes $plus_semigroup$ and $semigroup$ both
represent semigroups in a sense, they are certainly not quite the
same.
-*};
+*}
-end;
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+end
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