Improved Graph-Based Lambda Lifting

Lambda lifting is a technique for transforming a program with local function definitions into a program consisting only of global function definitions. The best known lambda lifting algorithm computes the minimal set of extraneous parameters needed by each function in O(n) steps by solving a system of set equations which are recursive if the functions in the program are mutually recursive. Mutually recursive functions give rise to strongly connected components in the call graph of a program. Danvy and Schultz observed that all functions in a strongly connected component can be given the same set of free variables as extraneous parameters. Based on this observation, they developed an O(n) graph-based lambda lifting algorithm. This article illustrates how Danvy’s and Schultz’s algorithm is an approximation of Johnsson’s algorithm for a certain class of programs and describes an O(n) graph-based lambda lifting algorithm that yields the same results as Johnsson’s algorithm.