François Pottier
Nadji Gauthier
ABSTRACT
Defunctionalization is a program transformation that aims to turn a higher-order functional program into a first-order one, that is, to eliminate the use of functions as first-class values. Its purpose is thus identical to that of closure conversion. It differs from closure conversion, however, by storing a tag, instead of a code pointer, within every closure. Defunctionalization has been used both as a reasoning tool and as a compilation technique.Defunctionalization is commonly defined and studied in the setting of a simply-typed λ-calculus, where it is shown that semantics and well-typedness are preserved. It has been observed that, in the setting of a polymorphic type system, such as ML or System F, defunctionalization is not type-preserving. In this paper, we show that extending System F with guarded algebraic data types allows recovering type preservation. This result allows adding defunctionalization to the toolbox of type-preserving compiler writers.
- Anindya Banerjee, Nevin Heintze, and Jon G. Riecke. Design and correctness of program transformations based on control-flow analysis. In International Symposium on Theoretical Aspects of Computer Software (TACS), volume 2215 of Lecture Notes in Computer Science, pages 420--447. Springer Verlag, October 2001. http://www.cis.ksu.edu/~ab/Publications/pcfa.ps.gz.]] Google Scholar
Digital Library
- Jeffrey M. Bell, Françoise Bellegarde, and James Hook. Type-driven defunctionalization. In ACM International Conference on Functional Programming (ICFP), August 1997. http://doi.acm.org/10.1145/258949.258953.]] Google ScholarDigital Library
- Henry Cejtin, Suresh Jagannathan, and Stephen Weeks. Flow-directed closure conversion for typed languages. In European Symposium on Programming (ESOP), volume 1782 of Lecture Notes in Computer Science, pages 56--71. Springer Verlag, March 2000. http://www.mlton.org/papers/00-esop.ps.gz.]] Google ScholarDigital Library
- James Cheney and Ralf Hinze. First-class phantom types. Technical Report 1901, Cornell University, 2003. http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cis/TR2003-1901.]]Google Scholar
- Olivier Danvy. Functional unparsing. Journal of Functional Programming, 8(6):621--625, November 1998.]] Google ScholarDigital Library
- Olivier Danvy and Lasse R. Nielsen. Defunctionalization at work. In ACM International Conference on Principles and Practice of Declarative Programming (PPDP), pages 162--174, September 2001.]] Google ScholarDigital Library
- Cormac Flanagan, Amr Sabry, Bruce F. Duba, and Matthias Felleisen. The essence of compiling with continuations. In ACM Conference on Programming Language Design and Implementation (PLDI), pages 237--247, 1993. http://www.cs.rice.edu/CS/PLT/Publications/Scheme/pldi93-fsdf.ps.gz.]] Google ScholarDigital Library
- Yasuhiko Minamide, Greg Morrisett, and Robert Harper. Typed closure conversion. In ACM Symposium on Principles of Programming Languages (POPL), pages 271--283, January 1996. http://www.cs.cornell.edu/Info/People/jgm/papers/closure-summary.ps.]] Google ScholarDigital Library
- Greg Morrisett and Robert Harper. Typed closure conversion for recursively-defined functions (extended abstract). In International Workshop on Higher Order Operational Techniques in Semantics (HOOTS), volume 10 of Electronic Notes in Theoretical Computer Science. Elsevier Science, 1998. http://www.cs.cornell.edu/home/jgm/papers/hootsclosure.ps.]]Google Scholar
- Greg Morrisett, David Walker, Karl Crary, and Neal Glew. From system F to typed assembly language. ACM Transactions on Programming Languages and Systems, 21(3):528--569, May 1999. http://www.cs.cornell.edu/talc/papers/tal-toplas.pdf.]] Google ScholarDigital Library
- Lasse R. Nielsen. A denotational investigation of defunctionalization. Technical Report RS-00-47, BRICS, December 2000. http://www.brics.dk/RS/00/47/.]]Google Scholar
- Christine Paulin-Mohring. Inductive definitions in the system coq: Rules and properties. Research Report RR1992-49, ENS Lyon, 1992. ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR1992/RR1992-49.ps.Z.]]Google Scholar
- John C. Reynolds. Definitional interpreters for higher-order programming languages. Higher-Order and Symbolic Computation, 11(4):363--397, December 1998. ftp://ftp.cs.cmu.edu/user/jcr/defint.dvi.gz.]] Google ScholarDigital Library
- John C. Reynolds. Definitional interpreters revisited. Higher-Order and Symbolic Computation, 11(4):355--361, December 1998. ftp://ftp.cs.cmu.edu/user/jcr/defintintro.dvi.gz.]] Google ScholarDigital Library
- Andrew Tolmach. Combining closure conversion with closure analysis using algebraic types. In Workshop on Types in Compilation (TIC), June 1997. http://www.cs.pdx.edu/~apt/tic97.ps.]]Google Scholar
- Andrew Tolmach and Dino P. Oliva. From ML to Ada: Strongly-typed language interoperability via source translation. Journal of Functional Programming, 8(4):367--412, July 1998. http://www.cs.pdx.edu/~apt/jfp98.ps.]] Google ScholarDigital Library
- Hongwei Xi. Dead code elimination through dependent types. In International Workshop on Practical Aspects of Declarative Languages (PADL), volume 1551 of Lecture Notes in Computer Science, pages 228--242. Springer Verlag, January 1999. http://www.cs.bu.edu/~hwxi/academic/papers/padl99.ps.]] Google ScholarDigital Library
- Hongwei Xi, Chiyan Chen, and Gang Chen. Guarded recursive datatype constructors. In ACM Symposium on Principles of Programming Languages (POPL), January 2003. http://www.cs.bu.edu/fac/hwxi/academic/papers/popl03.ps.]] Google ScholarDigital Library
Index Terms
- Polymorphic typed defunctionalization
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Reviews
Michael G. Murphy
The issue of defunctionalization with type preservation is addressed in this paper. Defunctionalization is a program transformation that turns a higher-order functional program into a first-order functional program (with no functions as first-order values). The purpose of this transformation is similar to that of closure conversion, but it differs by storing a tag instead of a code pointer within every closure. Defunctionalization serves both as a reasoning tool and as a compilation technique. Defunctionalization is defined and studied most commonly in the setting of a simply typed lambda-calculus, where semantics and well typedness are preserved. With polymorphic type systems, as in ML or System F, defunctionalization is not type-preserving. The authors extend System F with guarded algebraic data types to preserve types. The problem with defining defunctionalization for a typed-polymorphic lambda-calculus lies in the definition of "apply" that simulates the application of a source function to a source value, then returning its result. The main contribution of this paper is its proof that defunctionalization may be viewed as a type-preserving transformation from System F, as extended with guarded algebraic data types, into itself. Also noted is a similar process that can be applied to ML. Another contribution of this paper is its proof that the transformation is meaning-preserving in an untyped setting; this result can then be lifted to the typed setting. After a carefully prepared introduction, the second section defines the extension of System F with guarded algebraic data types. The third section defines the defunctionalization of well-typed programs, and the fourth section includes a proof that defunctionalization of untyped programs preserves well typedness. The fifth section defines the defunctionalization of untyped programs, and includes a proof of meaning preservation, which also carries over to typed programs. The last section contains closing remarks. The authors' version of defunctionalization does not address optimization or a sophisticated treatment of multiple-argument functions, but it does broaden the case for defunctionalization as a compilation technique, and as a tool to help programmers transform programs and reason about them. The paper is rigorous, well written, and includes sufficient detail to satisfy functional language theorists. Online Computing Reviews Service
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