Abstract

This paper gives a formal basis for the closure conversion phase of functional programming languages with imperative features, using a graphical semantics for the language. We present normal forms of graphs, one corresponding to procedural languages, and one corresponding to object-oriented languages. Using closure conversion, we can prove normalization results for both normal forms. Thus, we obtain sound algorithms for compiling the language into either procedural or object-oriented code. We discuss efficiency issues of the translation and suggest some improvements on the algorithm. 1 Introduction This paper describes a categorical formalization of an important step in compiling higher-order languages: closure conversion. Closure conversion is a compilation step which takes nested procedures such as: proc f (x : X1) : X2 { rec g; proc g (y : Y1) : Y2 { return G (g, x, y); } return F (g, x); } and lifts the nested procedures up to top level: rec g_lift; proc g_lift (x : X1, y : Y1...

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