The lambda calculus we'll be focusing on for the first part of the course has no types. (Some prefer to say it instead has a single type---but if you say that, you have to say that functions from this type to this type also belong to this type. Which is weird.)
+Here is its syntax:
+
+<blockquote>
+<strong>Variables</strong>: <code>x</code>, <code>y</code>, <code>z</code>...
+</blockquote>
+
+Each variable is an expression. For any expressions M and N and variable a, the following are also expressions:
+
+<blockquote>
+<strong>Abstract</strong>: <code>(λa M)</code>
+</blockquote>
+
+We'll tend to write <code>(λa M)</code> as just `(\a M)`, so we don't have to write out the markup code for the <code>λ</code>. You can yourself write <code>(λa M)</code> or `(\a M)` or `(lambda a M)`.
+
+<blockquote>
+<strong>Application</strong>: <code>(M N)</code>
+</blockquote>
+
Some authors reserve the term "term" for just variables and abstracts. We'll probably just say "term" and "expression" indiscriminately for expressions of any of these three forms.
Examples of expressions:
It's easy to be lulled into thinking this is a kind of imperative construction. *But it's not!* It's really just a shorthand for the compound "let"-expressions we've already been looking at, taking the maximum syntactically permissible scope. (Compare the "dot" convention in the lambda calculus, discussed above.)
+<!--
9. Some shorthand
When a previously-bound variable is rebound in the way we see here, that's called **shadowing**: the outer binding is shadowed during the scope of the inner binding.
+-->
Some more comparisons between Scheme and OCaml
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