A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Induction of recursive program schemes
[chapter]

1998
*
Lecture Notes in Computer Science
*

In this paper we present an approach to the

doi:10.1007/bfb0026692
fatcat:fvhs7zimt5g3zdnfi6qpkokfxq
*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. ...##
###
Representation and Induction of Infinite Concepts and Recursive Action Sequences

1983
*
International Joint Conference on Artificial Intelligence
*

It is based on the so called algebraic semantics

dblp:conf/ijcai/Wysotzki83
fatcat:hkc5jwlp5zdptdjvylglibi76i
*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 ...##
###
Middle-Out Reasoning for Synthesis and Induction
[chapter]

1996
*
Automated Mathematical Induction
*

We propose a novel approach to automating the synthesis

doi:10.1007/978-94-009-1675-3_4
fatcat:hlrfxol3oreppivyqvd5k7rzyy
*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. ...##
###
Inductive Programming
[chapter]

2017
*
Encyclopedia of Machine Learning and Data Mining
*

We can show that our approach compares very well to other systems

doi:10.1007/978-1-4899-7687-1_137
fatcat:b6fty7wa4nambftmt2twxg4m4y
*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*. ...##
###
Syntheses of Knowledges Based on Inductive Generalization
[chapter]

1999
*
Lecture Notes in Computer Science
*

(cadr(x),nil), cons(cddr(x),nil))))
{

doi:10.1007/3-540-48774-3_74
fatcat:4bjboj2kznewhp4nrksyjlxtju
*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. ...##
###
Fantastic Morphisms and Where to Find Them: A Guide to Recursion Schemes
[article]

2022
*
arXiv
*
pre-print

Structured

arXiv:2202.13633v3
fatcat:nt7pccuktrdarpy236nuuiifba
*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. ...##
###
Recursive Programs as Definitions in First-Order Logic

1984
*
SIAM journal on computing (Print)
*

Since the data domain D is a finitely generated set, the first order axiomatization

doi:10.1137/0213026
fatcat:siw3ngdcwjaqzghovtrolkrgli
*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. ...##
###
A Logic Programming and Verification System for Recursive Quantificational Logic

1985
*
International Joint Conference on Artificial Intelligence
*

Finally, it provides a method

dblp:conf/ijcai/BrownL85
fatcat:joyu42sc75dkvkoyuk3alaziue
*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. ...##
###
Middle-out reasoning for synthesis and induction

1996
*
Journal of automated reasoning
*

Finding an appropriate

doi:10.1007/bf00244461
fatcat:ecba53gmabh7zplgxteiy5yu5e
*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 ...##
###
Model Checking Higher-Order Programs

2013
*
Journal of the ACM
*

We first show that a variety

doi:10.1145/2487241.2487246
fatcat:inc4j2zip5dudapfgge4cyesha
*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. ...##
###
Primitive recursive program transformation

1976
*
Proceedings of the 3rd ACM SIGACT-SIGPLAN symposium on Principles on programming languages - POPL '76
*

We describe how to transform certain flowchart

doi:10.1145/800168.811550
dblp:conf/popl/BoyerMS76
fatcat:27cgkyc73vfptdwp5hqkthhxyu
*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 ...##
###
Inductive Synthesis of Functional Programs
[chapter]

2002
*
Lecture Notes in Computer Science
*

We present an approach to folding

doi:10.1007/3-540-45470-5_6
fatcat:4z5b27t7lvhv5j2q2ykz2lb5mi
*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 ¬ . ...##
###
Inductive Synthesis of Logic Programs by Composition of Combinatory Program Schemes
[chapter]

1999
*
Lecture Notes in Computer Science
*

The principle

doi:10.1007/3-540-48958-4_8
fatcat:ndvfpzjkb5gkxgzeujadumtr34
*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*. ...##
###
How complicated is the set of stable models of a recursive logic program?

1992
*
Annals of Pure and Applied Logic
*

We establish that the set

doi:10.1016/0168-0072(92)90069-c
fatcat:zdrru2yornb67es4lxrlz4bioy
*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. ...##
###
Model-checking higher-order functions

2009
*
Proceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming - PPDP '09
*

As shown by Kobayashi, verification problems

doi:10.1145/1599410.1599415
dblp:conf/ppdp/Kobayashi09
fatcat:5lvamxc2pjhyfelzwr6e4hzvoq
*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 ...
« Previous

*Showing results 1 — 15 out of 33,328 results*