One way to view a programming language is to distinguish its control from its data. Graphically
Programming Language = Control + Data
Lisp and Scheme are characterized roughly as ``untyped'' programming languages whose control mechanism is based on the lambda calculus. This is suggestive, and we explore the idea in more detail. It will turn out that these languages have one data type, Sexpression, and a control mechanism that extends the lambda calculus (unnecessarily).
The control mechanism decomposes into function evaluation, conditionals and recursive function definition. Graphically
The conditional is written but a simple binary case, the if_then_else is
sufficient. It turns out that this can be defined. First we consider
a version that works for lazy evaluation.
Exercise: Define an eager version of a conditional (recall lecture solution).