doc/cross-compilation: cleanup some grammar

These all should be uncontroversial changes. Just some awkward wording and
double words, etc.

1 files changed, 4 insertions, 4 deletions

diff --git a/doc/cross-compilation.xml b/doc/cross-compilation.xml
index 728616a9f263..b66205dda91c 100644
--- a/doc/cross-compilation.xml
+++ b/doc/cross-compilation.xml
@@ -62,8 +62,8 @@
             The "target platform" is black sheep.
             The other two intrinsically apply to all compiled software—or any build process with a notion of "build-time" followed by "run-time".
             The target platform only applies to programming tools, and even then only is a good for for some of them.
-            Briefly, GCC, Binutils, GHC, and certain other tools are written in such a way such that a single build can only compiler code for a single platform.
-            Thus, when building them, one must think ahead about what platforms they wish to use the tool to produce machine code for, and build binaries for each.
+            Briefly, GCC, Binutils, GHC, and certain other tools are written in such a way such that a single build can only compile code for a single platform.
+            Thus, when building them, one must think ahead about which platforms they wish to use the tool to produce machine code for, and build binaries for each.
           </para>
           <para>
             There is no fundamental need to think about the target ahead of time like this.
@@ -158,10 +158,10 @@
       The depending package's target platform is unconstrained by the sliding window principle, which makes sense in that one can in principle build cross compilers targeting arbitrary platforms.
     </para></note>
     <para>
-      How does this work in practice? Nixpkgs is now structured so that build-time dependencies are taken from from <varname>buildPackages</varname>, whereas run-time dependencies are taken from the top level attribute set.
+      How does this work in practice? Nixpkgs is now structured so that build-time dependencies are taken from <varname>buildPackages</varname>, whereas run-time dependencies are taken from the top level attribute set.
       For example, <varname>buildPackages.gcc</varname> should be used at build time, while <varname>gcc</varname> should be used at run time.
       Now, for most of Nixpkgs's history, there was no <varname>buildPackages</varname>, and most packages have not been refactored to use it explicitly.
-      Instead, one can use the four attributes used for specifying dependencies as documented in <link linkend="ssec-stdenv-attributes" />.
+      Instead, one can use the four attributes used for specifying dependencies as documented in <xref linkend="ssec-stdenv-attributes"/>.
       We "splice" together the run-time and build-time package sets with <varname>callPackage</varname>, and then <varname>mkDerivation</varname> for each of four attributes pulls the right derivation out.
       This splicing can be skipped when not cross compiling as the package sets are the same, but is a bit slow for cross compiling.
       Because of this, a best-of-both-worlds solution is in the works with no splicing or explicit access of <varname>buildPackages</varname> needed.