Flow Analysis of Lambda Expressions

We describe a method to analyze the data and control flow during mechanical evaluation of lambda expressions. The method produces a finite approximate description of the set of all states entered by a call-by-value lambda-calculus interpreter; a similar approach can easily be seen to work for call-by-name. A proof is given that the approximation is ''safe'' i.e. that it includes descriptions of every intermediate lambda-expression which occurs in the evaluation. From a programming languages point of view the method extends previously developed interprocedural analysis methods to include both local and global variables, call-by-name or call-by-value parameter transmission and the use of procedures both as arguments to other procedures and as the results returned by them.