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Induction of recursive program schemes [chapter]

Ute Schmid, Fritz Wysotzki
1998 Lecture Notes in Computer Science  
In this paper we present an approach to the induction of recursive structures from examples which is based on the notion of recursive program schemes.  ...  By this separation, the induction of recursive program schemes can be reduced to a pattern-matching problem which can be handled by a generic algorithm.  ...  Acknowledgements We thank a number of students participating in our students projects for supporting the implementation of the IPAL system, especially: Mark Miiller and Martin Miihlpfordt.  ... 
doi:10.1007/bfb0026692 fatcat:fvhs7zimt5g3zdnfi6qpkokfxq

Representation and Induction of Infinite Concepts and Recursive Action Sequences

Fritz Wysotzki
1983 International Joint Conference on Artificial Intelligence  
It is based on the so called algebraic semantics of recursive program schemes and in this paper mainly applied to the representation and induction of infinite concepts and recursive action sequences (which  ...  Additionally, the use of recursive program schemes leads to a new principle of generalization in the sense that families of structures or classes of programs could be treated simultaneously and that already  ...  Our method is based on the so called algebraic semantics and recursive program schemes /1/, /2/ and it is intended to provide a general framework for the abovementioned representation and induction problems  ... 
dblp:conf/ijcai/Wysotzki83 fatcat:hkc5jwlp5zdptdjvylglibi76i

Middle-Out Reasoning for Synthesis and Induction [chapter]

Ina Kraan, David Basin, Alan Bundy
1996 Automated Mathematical Induction  
We propose a novel approach to automating the synthesis of logic programs: Logic programs are synthesized as a by-product of the planning of a veri cation proof.  ...  The approach is a two-level one: At the object level, we prove program veri cation conjectures in a sorted, rst-order theory. The conjectures are of the form 8args ????! : prog(args ????!  ...  for synthesis is that the appropriate induction scheme is closely related to the recursion scheme of the program|which is precisely part of what we want to synthesize.  ... 
doi:10.1007/978-94-009-1675-3_4 fatcat:hlrfxol3oreppivyqvd5k7rzyy

Inductive Programming [chapter]

Pierre Flener, Ute Schmid
2017 Encyclopedia of Machine Learning and Data Mining  
We can show that our approach compares very well to other systems of inductive programming and we will discuss applications in the domains of cognitive modelling, end-user programming and automated software  ...  We developed an efficient, analytical approach for learning recursive functional programs from examples. Igor2 is a realization of this approach as constructor term rewriting system.  ...  As a special application of machine learning (Mitchell, 1997) , inductive programming creates program hypotheses, that is, generalised, typically recursive, programs.  ... 
doi:10.1007/978-1-4899-7687-1_137 fatcat:b6fty7wa4nambftmt2twxg4m4y

Syntheses of Knowledges Based on Inductive Generalization [chapter]

Sergey V. Astanin, Tatyana G. Kalashnikova
1999 Lecture Notes in Computer Science  
(cadr(x),nil), cons(cddr(x),nil)))) { of function variables Φ = {G 1 , . . . , G n } with arity α(G i ) > 0 for all i ∈ [1; n], and a set of variables X with Σ ∩ Φ ∩ X = ∅, then a recursive program scheme  ...  (x, f 1 (x)) f k+1 (x) = cons Recursive Program Schemes last(x) = if(empty(tl(x)), x, last(tl(x))) }, m = 1.  ... 
doi:10.1007/3-540-48774-3_74 fatcat:4bjboj2kznewhp4nrksyjlxtju

Fantastic Morphisms and Where to Find Them: A Guide to Recursion Schemes [article]

Zhixuan Yang, Nicolas Wu
2022 arXiv   pre-print
Structured recursion schemes have been widely used in constructing, optimising, and reasoning about programs over inductive and coinductive datatypes.  ...  To fill this gap, this expository paper introduces structured recursion schemes from a practical point of view: a variety of recursion schemes are motivated and explained in contexts of concrete programming  ...  We dedicate this paper to the memory of Richard Bird.  ... 
arXiv:2202.13633v3 fatcat:nt7pccuktrdarpy236nuuiifba

Recursive Programs as Definitions in First-Order Logic

Robert Cartwright
1984 SIAM journal on computing (Print)  
Since the data domain D is a finitely generated set, the first order axiomatization of D includes a structural induction axiom scheme.  ...  This axiom scheme serves as the fundamental "proof rule" of first order programming logic.  ...  The proof proceeds by induction on n. Basis: n O. This case is trivial by simplification: zero (n) =if 0 equal 0 then 0 else zero (n-1) =0. Induction step: n > O.  ... 
doi:10.1137/0213026 fatcat:siw3ngdcwjaqzghovtrolkrgli

A Logic Programming and Verification System for Recursive Quantificational Logic

Frank M. Brown, Peiya Liu
1985 International Joint Conference on Artificial Intelligence  
Finally, it provides a method of mathematical induction applicable to recursive definitions involving quantifiers.  ...  In this paper, we describe a logic programming and program verification system which is based on quantifier elimination techniques and axiomatization rather than on more common method of doing logic programming  ...  Norman Martin and Ruey-Juin Ghang for their helpful comments to earlier drafts of this paper. Our thanks also go to the referees for their use ful suggestions.  ... 
dblp:conf/ijcai/BrownL85 fatcat:joyu42sc75dkvkoyuk3alaziue

Middle-out reasoning for synthesis and induction

Ina Kraan, David Basin, Alan Bundy
1996 Journal of automated reasoning  
Finding an appropriate induction scheme during synthesis is di cult, because the recursion of the program, which is unknown at the outset, determines the induction in the proof.  ...  We develop two applications of middle-out reasoning in inductive proofs: Logic program synthesis and the selection of induction schemes.  ...  Acknowledgements We would like to thank Sophie Renault for her careful reading of this paper. 25  ... 
doi:10.1007/bf00244461 fatcat:ecba53gmabh7zplgxteiy5yu5e

Model Checking Higher-Order Programs

Naoki Kobayashi
2013 Journal of the ACM  
We first show that a variety of program verification problems can be reduced to model checking problems for recursion schemes, by transforming a program into a recursion scheme that generates a tree representing  ...  We propose a novel verification method for higher-order functional programs based on higherorder model checking, or more precisely, model checking of higher-order recursion schemes (recursion schemes,  ...  We would also like to thank Luke Ong, who introduced higher-order recursion schemes to me and gave a number of insightful comments. We have also benefited from working with him on related topics.  ... 
doi:10.1145/2487241.2487246 fatcat:inc4j2zip5dudapfgge4cyesha

Primitive recursive program transformation

R. S. Boyer, J. S. Moore, R. E. Shostak
1976 Proceedings of the 3rd ACM SIGACT-SIGPLAN symposium on Principles on programming languages - POPL '76  
We describe how to transform certain flowchart programs into equivalent explicit primitive recursive proerams.  ...  The input/outl~Ut correctness conditions for the trar~sformed proerams are more amenable to proof thai the verification cow~ditions for the corresponding flowchart programs.  ...  Of course, not all programs compute primitive recursive functions (for example, programs that compute Ackermann's function or that interpret FORTRAN programs compute partial recursive, but not primitive  ... 
doi:10.1145/800168.811550 dblp:conf/popl/BoyerMS76 fatcat:27cgkyc73vfptdwp5hqkthhxyu

Inductive Synthesis of Functional Programs [chapter]

Emanuel Kitzelmann, Ute Schmid, Martin Mühlpfordt, Fritz Wysotzki
2002 Lecture Notes in Computer Science  
We present an approach to folding of finite program terms based on the detection of recurrence relations in a single given term which is considered as the ¦ th unfolding of an unknown recursive program  ...  ; the given input terms can represent incomplete unfoldings of an hypothetical recursive program.  ...  Induction of Recursive Program Schemes Initial Programs An initial program is a ground term 5 ¶ $% ¢ & ¼¯ ½ which contains at least one ¬ .  ... 
doi:10.1007/3-540-45470-5_6 fatcat:4z5b27t7lvhv5j2q2ykz2lb5mi

Inductive Synthesis of Logic Programs by Composition of Combinatory Program Schemes [chapter]

Andreas Hamfelt, Jørgen Fischer Nilsson
1999 Lecture Notes in Computer Science  
The principle of combining programs from combinators admits induction of programs without appealing to most-specific-generalization and predicate invention in contrast to prevailing ILP approaches.  ...  Keywords: logic program schemata, logical combinators, synthesis by composition and specialization of schemas, inductive synthesis, metalogic program environment. P. Flener (Ed.): LOPSTR'98  ...  The induction process then essentially reduces to synthesizing of auxiliary predicates applied as parameters or arguments to the recursion schemes.  ... 
doi:10.1007/3-540-48958-4_8 fatcat:ndvfpzjkb5gkxgzeujadumtr34

How complicated is the set of stable models of a recursive logic program?

W. Marek, A. Nerode, J. Remmel
1992 Annals of Pure and Applied Logic  
We establish that the set of all stable models in a Herbrand universe of a recursive logic program is, up to recursive renaming, the set of all infinite paths of a recursive, countably branching tree,  ...  Remmel, How complicated is the set of stable models of a recursive logic program?, Annals of Pure and Applied Logic 56 (1992) 119-135.  ...  This can easily be proved by induction on the lengths of proof schemes. Thus Tr,+, # B, and so B is not a stable model of P. Suppose A4 were a stable model of P.  ... 
doi:10.1016/0168-0072(92)90069-c fatcat:zdrru2yornb67es4lxrlz4bioy

Model-checking higher-order functions

Naoki Kobayashi
2009 Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming - PPDP '09  
As shown by Kobayashi, verification problems of higher-order functional programs can easily be translated into model checking problems of recursion schemes.  ...  We have implemented a model checker for recursion schemes based on the proposed algorithm, and applied it to verification of functional programs, including reachability, flow analysis and resource usage  ...  The idea was to transform a functional program into a recursion scheme that generates all the possible event sequences of the program, so that the temporal properties of the program can be verified by  ... 
doi:10.1145/1599410.1599415 dblp:conf/ppdp/Kobayashi09 fatcat:5lvamxc2pjhyfelzwr6e4hzvoq
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