Lambda-Dropping: Transforming Recursive Equations into Programs with Block Structure

Abstract

Lambda-lifting a block-structured program transforms it into a set of
recursive equations. We present the symmetric transformation: lambda-dropping. Lambda-dropping a set of recursive equations restores block structure and lexical scope.
For lack of block structure and lexical scope, recursive equations must
carry around all the parameters that any of their callees might possibly
need. Both lambda-lifting and lambda-dropping thus require one to compute Def/Use paths:

- for lambda-lifting: each of the functions occurring in the path of a
free variable is passed this variable as a parameter;

- for lambda-dropping: parameters which are used in the same scope
as their definition do not need to be passed along in their path.

A program whose blocks have no free variables is scope-insensitive. Its
blocks are then free to float (for lambda-lifting) or to sink (for lambda-dropping) along the vertices of the scope tree.