+\subsection{β-reduction}
+β-reduction is a well known transformation from lambda calculus, where it is
+the main reduction step. It reduces applications of labmda abstractions,
+removing both the lambda abstraction and the application.
+
+In our transformation system, this step helps to remove unwanted lambda
+abstractions (basically all but the ones at the top level). Other
+transformations (application propagation, non-representable inlining) make
+sure that most lambda abstractions will eventually be reducable by
+β-reduction.
+
+TODO: Define substitution syntax
+
+\starttrans
+(λx.E) M
+-----------------
+E[M/x]
+\stoptrans
+
+% And an example
+\startbuffer[from]
+(λa. 2 * a) (2 * b)
+\stopbuffer
+
+\startbuffer[to]
+2 * (2 * b)
+\stopbuffer
+
+\transexample{β-reduction}{from}{to}
+
+\subsection{Application propagation}