%0 Conference Paper %1 KiScMuWy02a %A Kitzelmann, Emanuel %A Schmid, Ute %A Mühlpfordt, Martin %A Wysotzki, Fritz %B First International IEEE Symposium on Intelligent Systems (IS 2002) %D 2002 %I IEEE %K analytical_ip ifp igor1 induction inductive_programming inproceedings program_synthesis recursive_program_schemes %P 144--149 %T Folding of Finite Program Terms to Recursive Program Schemes %U http://dx.doi.org/10.1109/IS.2002.1044245 %V 1 %X We present an approach to inductive synthesis of functional programs based on the detection of recurrence relations. A given term is considered as the k-th 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 (1977) 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.

@inproceedings{KiScMuWy02a, 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 k-th 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 (1977) 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.}, added-at = {2009-06-21T15:26:38.000+0200}, author = {Kitzelmann, Emanuel and Schmid, Ute and M{\"u}hlpfordt, Martin and Wysotzki, Fritz}, biburl = {https://www.bibsonomy.org/bibtex/22a17973c9201d387584351f85c0fe55a/emanuel}, booktitle = {First International {IEEE} Symposium on Intelligent Systems {(IS 2002)}}, interhash = {051ec0a100e59f9527e9585ab55a7319}, intrahash = {2a17973c9201d387584351f85c0fe55a}, keywords = {analytical_ip ifp igor1 induction inductive_programming inproceedings program_synthesis recursive_program_schemes}, pages = {144--149}, pdf = {http://www.cogsys.wiai.uni-bamberg.de/publications/ieeeis02.pdf}, publisher = {IEEE}, timestamp = {2009-06-21T15:26:38.000+0200}, title = {Folding of Finite Program Terms to Recursive Program Schemes}, url = {http://dx.doi.org/10.1109/IS.2002.1044245}, volume = 1, year = 2002 }