--- a/doc-src/Intro/advanced.tex Mon May 05 18:09:31 1997 +0200
+++ b/doc-src/Intro/advanced.tex Mon May 05 18:50:26 1997 +0200
@@ -368,7 +368,7 @@
theories, inheriting their types, constants, syntax, etc. The theory
\thydx{Pure} contains nothing but Isabelle's meta-logic. The variant
\thydx{CPure} offers the more usual higher-order function application
-syntax $t\,u@1\ldots\,u@n$ instead of $t(u@1,\ldots,u@n)$.
+syntax $t\,u@1\ldots\,u@n$ instead of $t(u@1,\ldots,u@n)$ in \Pure.
Each theory definition must reside in a separate file, whose name is
the theory's with {\tt.thy} appended. Calling
@@ -429,9 +429,9 @@
the keyword {\tt defs} instead of {\tt rules}. {\bf Definitions} are
rules of the form $s \equiv t$, and should serve only as
abbreviations. The simplest form of a definition is $f \equiv t$,
-where $f$ is a constant. Also allowed are $\eta$-equivalent forms,
-where the arguments of~$f$ appear applied on the left-hand side of the
-equation instead of abstracted on the right-hand side.
+where $f$ is a constant. Also allowed are $\eta$-equivalent forms of
+this, where the arguments of~$f$ appear applied on the left-hand side
+of the equation instead of abstracted on the right-hand side.
Isabelle checks for common errors in definitions, such as extra
variables on the right-hand side, but currently does not a complete
--- a/doc-src/Intro/foundations.tex Mon May 05 18:09:31 1997 +0200
+++ b/doc-src/Intro/foundations.tex Mon May 05 18:50:26 1997 +0200
@@ -1,4 +1,5 @@
%% $Id$
+
\part{Foundations}
The following sections discuss Isabelle's logical foundations in detail:
representing logical syntax in the typed $\lambda$-calculus; expressing
@@ -642,8 +643,8 @@
Resolution expects the rules to have no outer quantifiers~($\Forall$).
It may rename or instantiate any schematic variables, but leaves free
variables unchanged. When constructing a theory, Isabelle puts the
-rules into a standard form containing only schematic variables;
-for instance, $({\imp}E)$ becomes
+rules into a standard form with all free variables converted into
+schematic ones; for instance, $({\imp}E)$ becomes
\[ \List{\Var{P}\imp \Var{Q}; \Var{P}} \Imp \Var{Q}.
\]
When resolving two rules, the unknowns in the first rule are renamed, by