message: Describe changes required to add dependent types to base language.
diff: @@ -41,8 +41,8 @@ h2 {
  This language, our starting point, has the basic features of the later
  languages, but does not use dependent types.
  The purpose of presenting this is to illustrate the
  -basic mechanisms we will be using,
  -and to show by comparison what additional mechanisms are required
  +mechanisms we will be using,
  +and to show by comparison what changes are required
  to implement dependent types.
  <p>
  @@ -96,7 +96,7 @@ $$
  \Sigma x : \text{int}_8(-128, 127) .
  \Sigma y : \text{int}_8(-128, 127) . \text{unit}
  $$
  -by a early phase of compilation.
  +by an early phase of compilation.
  <div class="subsection">
  <h3>Grammar</h3>
  @@ -268,6 +268,34 @@ thus making it dependently-typed.
  We will use this as the basis for several later languages,
  each adding one or more features.
  +<p>
  +We've changed the format slightly from the previous section:
  +we write the kind rules in combined form,
  +and we only give type rules for the host types
  +since the "type" rules for descriptions
  +are entirely contained within the parsing rules.
  +We'll follow this new format in later sections, too.
  +
  +<p>
  +Aside from the format change, there are two important changes to the rules.
  +First, an environment $\Gamma$ is required in the Kind and Type rules,
  +which maps $\Sigma$-quantified variables to their host types.
  +This is needed in the type rules
  +so we can give a type to expressions involving variables,
  +and it is needed in the kind rules because
  +the descriptions can now contain expressions,
  +hence the kind rules for descriptions must invoke the type rules
  +for the expressions they contain.
  +This environment is constructed in the kind rule for $\Sigma$-types,
  +and is used in the type rule for variables.
  +
  +<p>
  +Second, an environment $\theta$ is required in the parsing and
  +evaluation rules,
  +which stores the host values for $\Sigma$-quantified variables in scope.
  +This environment is constructed in the parsing rule for $\Sigma$-types,
  +and is used in the evaluation rule for variables.
  +
  <div class="subsection">
  <h3>Grammar</h3>
  <div class="math">
  @@ -316,7 +344,7 @@ $$
  </div>
  </div>
  -<div class=:subsection">
  +<div class="subsection">
  <h3>Types</h3>
  <div class="math">
  $$
  