doc: polish the docs of checkpointBuildTools

... following suggestions from @phip1611 and @infinisil.

doc/build-helpers/special/checkpoint-build.section.md

@@ -2,35 +2,38 @@
 
 `pkgs.checkpointBuildTools` provides a way to build derivations incrementally. It consists of two functions to make checkpoint builds using Nix possible.
 
-For hermeticity, Nix derivations do not allow any state to carry over between builds, making a transparent incremental build within a derivation impossible.
+For hermeticity, Nix derivations do not allow any state to be carried over between builds, making a transparent incremental build within a derivation impossible.
 
 However, we can tell Nix explicitly what the previous build state was, by representing that previous state as a derivation output. This allows the passed build state to be used for an incremental build.
 
 To change a normal derivation to a checkpoint based build, these steps must be taken:
-  - apply `prepareCheckpointBuild` on the desired derivation
-    e.g.:
+  - apply `prepareCheckpointBuild` on the desired derivation, e.g.
 ```nix
 checkpointArtifacts = (pkgs.checkpointBuildTools.prepareCheckpointBuild pkgs.virtualbox);
 ```
-  - change something you want in the sources of the package. (e.g. using a source override)
+  - change something you want in the sources of the package, e.g. use a source override:
 ```nix
 changedVBox = pkgs.virtualbox.overrideAttrs (old: {
   src = path/to/vbox/sources;
-}
+});
 ```
-  - use `mkCheckpointBuild changedVBox incrementalBuildArtifacts`
+  - use `mkCheckpointBuild changedVBox checkpointArtifacts`
   - enjoy shorter build times
 
 ## Example {#sec-checkpoint-build-example}
 ```nix
-{ pkgs ? import <nixpkgs> {} }: with (pkgs) checkpointBuildTools;
+{ pkgs ? import <nixpkgs> {} }:
 let
-  helloCheckpoint = checkpointBuildTools.prepareCheckpointBuild pkgs.hello;
+  inherit (pkgs.checkpointBuildTools)
+    prepareCheckpointBuild
+    mkCheckpointBuild
+    ;
+  helloCheckpoint = prepareCheckpointBuild pkgs.hello;
   changedHello = pkgs.hello.overrideAttrs (_: {
     doCheck = false;
     patchPhase = ''
       sed -i 's/Hello, world!/Hello, Nix!/g' src/hello.c
     '';
   });
-in checkpointBuildTools.mkCheckpointBuild changedHello helloCheckpoint
+in mkCheckpointBuild changedHello helloCheckpoint
 ```

pkgs/build-support/checkpoint-build.nix

@@ -14,39 +14,40 @@ in
 rec {
   /* Prepare a derivation for local builds.
     *
-    * This function prepares checkpoint builds by provinding,
-    * containing the build output and the sources for cross checking.
+    * This function prepares checkpoint builds by storing
+    * the build output and the sources for cross checking.
     * The build output can be used later to allow checkpoint builds
     * by passing the derivation output to the `mkCheckpointBuild` function.
     *
-    * To build a project with checkpoints follow these steps:
-    * - run prepareIncrementalBuild on the desired derivation
-    *   e.G `incrementalBuildArtifacts = (pkgs.checkpointBuildTools.prepareCheckpointBuild pkgs.virtualbox);`
-    * - change something you want in the sources of the package( e.G using source override)
-    *   changedVBox = pkgs.virtuabox.overrideAttrs (old: {
-    *      src = path/to/vbox/sources;
-    *   }
-    * - use `mkCheckpointBuild changedVBox incrementalBuildArtifacts`
+    * To build a project with checkpoints, follow these steps:
+    * - run `prepareCheckpointBuild` on the desired derivation, e.g.
+    *     checkpointArtifacts = prepareCheckpointBuild virtualbox;
+    * - change something you want in the sources of the package,
+    *   e.g. using source override:
+    *     changedVBox = pkgs.virtuabox.overrideAttrs (old: {
+    *       src = path/to/vbox/sources;
+    *     };
+    * - use `mkCheckpointBuild changedVBox checkpointArtifacts`
     * - enjoy shorter build times
   */
   prepareCheckpointBuild = drv: drv.overrideAttrs (old: {
     outputs = [ "out" ];
     name = drv.name + "-checkpointArtifacts";
     # To determine differences between the state of the build directory
-    # from an earlier build and  a later one we store the state of the build
+    # from an earlier build and a later one we store the state of the build
     # directory before build, but after patch phases.
     # This way, the same derivation can be used multiple times and only changes are detected.
-    # Additionally Removed files are handled correctly in later builds.
+    # Additionally, removed files are handled correctly in later builds.
     preBuild = (old.preBuild or "") + ''
       mkdir -p $out/sources
       cp -r ./* $out/sources/
     '';
 
-    # After the build the build directory is copied again
+    # After the build, the build directory is copied again
     # to get the output files.
-    # We copy the complete build folder, to take care for
-    # Build tools, building in the source directory, instead of
-    # having a build root directory, e.G the Linux kernel.
+    # We copy the complete build folder, to take care of
+    # build tools that build in the source directory, instead of
+    # having a separate build directory such as the Linux kernel.
     installPhase = ''
       runHook preCheckpointInstall
       mkdir -p $out/outputs
@@ -56,18 +57,18 @@ rec {
   });
 
   /* Build a derivation based on the checkpoint output generated by
-    * the `prepareCheckpointBuild function.
+    * the `prepareCheckpointBuild` function.
     *
     * Usage:
     * let
-    *   checkpointArtifacts = prepareCheckpointBuild drv
+    *   checkpointArtifacts = prepareCheckpointBuild drv;
     * in mkCheckpointBuild drv checkpointArtifacts
   */
   mkCheckpointBuild = drv: checkpointArtifacts: drv.overrideAttrs (old: {
     # The actual checkpoint build phase.
-    # We compare the changed sources from a previous build with the current and create a patch
-    # Afterwards we clean the build directory to copy the previous output files (Including the sources)
-    # The source difference patch is applied to get the latest changes again to allow short build times.
+    # We compare the changed sources from a previous build with the current and create a patch.
+    # Afterwards we clean the build directory and copy the previous output files (including the sources).
+    # The source difference patch is then applied to get the latest changes again to allow short build times.
     preBuild = (old.preBuild or "") + ''
       set +e
       sourceDifferencePatchFile=$(${mktemp}/bin/mktemp)