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Folding of Finite Program Terms to Recursive Program Schemes (2002)

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@MISC{Kitzelmann02foldingof,
    author = {Emanuel Kitzelmann and Ute Schmid and Martin Mühlpfordt and Fritz Wysotzki},
    title = {Folding of Finite Program Terms to Recursive Program Schemes},
    year = {2002}
}

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Abstract:

We present an approach to inductive synthesis of functional programs based on the detection of recurrence relations. A given term is considered as the kth unfolding of an unknown recursive program. If a recurrence relations can be identified in the term, it can be folded into a recursive program which (a) can reproduce the term and (b) generalizes over it. Our approach goes beyond Summers' classical approach in several aspects: It is language independent and works for terms belonging to an arbitrary term algebra; it allows induction of sets of recursive equations which are in some arbitrary `calls' relation; induced equations can be dependent on more than one input parameters and we can detect interdependencies of variable substitutions in recursive calls; the given input terms can represent incomplete unfoldings of an hypothetical recursive program.

Citations

56	A methodology for LISP program construction from examples – Summers - 1977
13	The synthesis of LISP programs from examples: A survey – Smith - 1984
8	Applying inductive programm synthesis to macro learning – Schmid, Wysotzki - 2000
7	Inductive synthesis of functional programs – Learning domain-specific control rules and abstract schemes. http://www.inf.uos.de/schmid/pub-ps/habil.ps.gz, Mai 2001. unpublished habilitation thesis – Schmid - 2003
2	Inferring flow of control in program synthesis by example – Schrödl, Edelkamp - 1999