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Ulrich Berger, Monika Seisenberger
2005 From Sets and Types to Topology and Analysis  
The first method removes any reference to infinite sequences and transforms the theorem into a system of inductive definitions, the other applies a combination of Gödel's negativeand Friedman's A-translation  ...  We describe two methods of extracting constructive content from classical proofs, focusing on theorems involving infinite sequences and nonconstructive choice principles.  ...  For example, ∀-introduction and -elimination translate into λ-abstraction and application, and introduction and elimination rules for an inductive definition become constructors and recursion operators  ... 
doi:10.1093/acprof:oso/9780198566519.003.0008 fatcat:n4z453pujrenfgte7abt4tkjhi

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  ...  Synthesis with Would-be Appeal to Predicate Invention Conclusions We have outlined principles for inductive synthesis of logic programs based on composition of building blocks in the form of logical  ... 
doi:10.1007/3-540-48958-4_8 fatcat:ndvfpzjkb5gkxgzeujadumtr34

Formal methods for automated program improvement [chapter]

Peter Madden
1994 Lecture Notes in Computer Science  
synthesis of efficient programs from standard equational definitions.  ...  However, formal methods, and in partieular theorem proving, are providing a growing foundation of techniques for automatie program development (synthesis, improvement, transformation and verification).  ...  The synthesis of efficient programs from standard equational definitions is achieved through the use of (meta-level) proof-planning techniques.  ... 
doi:10.1007/3-540-58467-6_32 fatcat:jckmgdfumngshiffwn7ibcsc5q

A general technique for automatically optimizing programs through the use of proof plans [chapter]

Peter Madden, Ian Green
1995 Lecture Notes in Computer Science  
The proof planning approach to controlling the synthesis of efficient programs was originally investigated within the context of synthesizing tail-recursive pro grams from naive definitions by using a  ...  to synthesizing efficient programs with existing optimization strategies and discuss its advantages.  ...  In general terms, MOR allows us to delay choice commitments by introducing (higher-order) meta-variables at the meta-level application of rules of inference.  ... 
doi:10.1007/3-540-60156-2_6 fatcat:2qc6rwkbknbzjfbidypieybqpm

Book announcements

1996 Discrete Applied Mathematics  
Chapter 12: Induction over the natural numbers. Inductive definitions. Peano arithmettc. Induction and well-founded sets. Induction for inducttve definitions, The correctness of loops.  ...  English to predicate logic. Chapter IO: Predicutes and Programminy. Specification of programs. Reasoning about the assignment statement. Mathematical Induction.  ... 
doi:10.1016/0166-218x(96)90069-4 fatcat:eswucpcizbfdxbpbqejedzpsyu

Combinatorial Techniques for Proof-Based Synthesis of Sorting Algorithms

Isabela Dramnesc, Tudor Jebelean, Sorin Stratulat
2015 2015 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)  
We present the main principles and the application of this technique to merging of sorted binary trees into a sorted one.  ...  Remarkably, merging requires a nested recursion, for which an appropriate induction principle is difficult to guess.  ...  Induction Principles and Algorithm Extraction The illustration of the induction principles and algorithm extraction in this subsection is similar to the one from [5] , but the induction principles are  ... 
doi:10.1109/synasc.2015.30 dblp:conf/synasc/DramnescJS15 fatcat:zfymky4kifgbtpb5oboskj35je

Ideas for connecting inductive program synthesis and bidirectionalization

Janis Voigtländer
2012 Proceedings of the ACM SIGPLAN 2012 workshop on Partial evaluation and program manipulation - PEPM '12  
We share a vision of connecting the topics of bidirectional transformation and inductive program synthesis, by proposing to use the latter in approaching problematic aspects of the former.  ...  This research perspective does not present accomplished results, rather opening discussion and describing experiments designed to explore the potential of inductive program synthesis for bidirectionalization  ...  Acknowledgments I would like to thank Ute Schmid for hospitality and encouraging discussions on inductive program synthesis in general and Igor-II specifically, as well as perspectives for future work.  ... 
doi:10.1145/2103746.2103757 dblp:conf/pepm/Voigtlander12 fatcat:qsckgnqzmvdffgbgx324ezeia4

CM-Strategy: A Methodology for Inductive Theorem Proving or Constructive Well-Generalized Proofs

Marta Franová
1985 International Joint Conference on Artificial Intelligence  
The main problem, when automatically proving theorems by Induction is the problem of strategy, or, how to automati cally direct deductions.  ...  programming [f04].  ...  ACKNOWLEDGEMENTS I would like to express my warmest thanks to Yves Kodratoff. I also thank Professor Georg Kreiscl for his encouragement. Professor Jean-Luc Remy provided many helpful remarks.  ... 
dblp:conf/ijcai/Franova85 fatcat:mxszzafrajhefjmt22cnwpxxb4


E. Skakalina
2021 Системи управління навігації та зв'язку Збірник наукових праць  
The development of multiprocessor computing and parallel computing makes it important to solve problems of optimization analysis.  ...  Modern development of computer technology and the possibility of implementing calculations in parallel allow to solve increasingly large-scale problems of numerical modeling.  ...  In our case, where the source of multiparametric data functions are solutions to optimization problems and visualization of results, the following definition is used: This definition allows you to formulate  ... 
doi:10.26906/sunz.2021.3.108 fatcat:rqj4zqiepjdyhjp2eh2wrpppkm

FlashMeta: a framework for inductive program synthesis

Oleksandr Polozov, Sumit Gulwani
2015 Proceedings of the 2015 ACM SIGPLAN International Conference on Object-Oriented Programming, Systems, Languages, and Applications - OOPSLA 2015  
Inductive synthesis, or programming-by-examples (PBE) is gaining prominence with disruptive applications for automating repetitive tasks in end-user programming.  ...  However, designing, developing, and maintaining an effective industrialquality inductive synthesizer is an intellectual and engineering challenge, requiring 1-2 man-years of effort.  ...  initiative and for (re)implementation of multiple PBE-based applications on top of FlashMeta.  ... 
doi:10.1145/2814270.2814310 dblp:conf/oopsla/PolozovG15 fatcat:uy7oen2t6fc7hn35m2zdeefxbq

Elaborating Inductive Definitions [article]

Pierre-Evariste Dagand, Conor McBride
2012 arXiv   pre-print
We prove the soundness of our translation and hint at its correctness with respect to Coq's Inductive definitions. The practical benefits of this approach are numerous.  ...  We present an elaboration of inductive definitions down to a universe of datatypes. The universe of datatypes is an internal presentation of strictly positive families within type theory.  ...  Acknowledgements We would like to thank Pierre Boutillier for pointing us to the relevant literature on Coq's treatment of inductives.  ... 
arXiv:1210.6390v2 fatcat:oe7zdyq4zffunbyqtvrpkwvgmu

FlashMeta: a framework for inductive program synthesis

Oleksandr Polozov, Sumit Gulwani
2015 SIGPLAN notices  
Inductive synthesis, or programming-by-examples (PBE) is gaining prominence with disruptive applications for automating repetitive tasks in end-user programming.  ...  However, designing, developing, and maintaining an effective industrialquality inductive synthesizer is an intellectual and engineering challenge, requiring 1-2 man-years of effort.  ...  initiative and for (re)implementation of multiple PBE-based applications on top of FlashMeta.  ... 
doi:10.1145/2858965.2814310 fatcat:dvvw76jbwjgxnm2vfw6b2c5eme

Recursive Program Optimization Through Inductive Synthesis Proof Transformation

Peter Madden, Alan Bundy, Alan Smaill
1999 Journal of automated reasoning  
We compare and contrast this approach with the more traditional approaches to program transformation, and highlight the benefits of proof transformation with regards to search, correctness, automatability  ...  We describe a working proof transformation system which, by exploiting the duality between mathematical induction and recursion, employs the novel strategy of optimizing recursive programs by transforming  ...  ; the control problems associated with when to apply the re-writing step(s) which eliminate any reference to the source definition from the target recursive step, and; the principled application of lemmas  ... 
doi:10.1023/a:1005969312327 dblp:journals/jar/MaddenBS99 fatcat:bfa4t4khaje2donwrokh4u7yc4

Logic Program Synthesis in a Higher-Order Setting [chapter]

David Lacey, Julian Richardson, Alan Smail
2000 Lecture Notes in Computer Science  
The approach is extensible to further classes of synthesis.  ...  The generality of the approach is such that its extension to allow synthesis of higher-order logic programs was straightforward. Some illustrative examples are given.  ...  The research was supported by EPSRC grant GR/M45030, and EPSRC funding for David Lacey's MSc in Artificial Intelligence.  ... 
doi:10.1007/3-540-44957-4_6 fatcat:24o64zh5abdero5uagownflvka

Structuring the synthesis of heap-manipulating programs

Nadia Polikarpova, Ilya Sergey
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
For efficiency, the engine exploits properties of SSL rules, such as invertibility and commutativity of rule applications on separate heaps, to prune the space of derivations it has to consider.  ...  A synthesized program represents a proof term for a transforming entailment statement PQ, and the synthesis procedure corresponds to a proof search.  ...  Their technical feedback has helped immensely to bring out the best of this paper. We also wish to thank Shachar Itzhaky and Ranjit Jhala for their comments on the draft.  ... 
doi:10.1145/3290385 fatcat:ixjdyxkr4fewvgbdottph6nvje
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