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Formalizing non-termination of recursive programs

Reinhard Kahle, Thomas Studer
2001 The Journal of Logic and Algebraic Programming  
In applicative theories the recursion theorem provides a term rec which solves recursive equations. However, it is not provable that a solution obtained by rec is minimal.  ...  Still, our theory has a standard recursion theoretic interpretation.  ...  The idea of the given treatment of a least fixed point operator in applicative theories was suggested by Peter Päppinghaus when he supervised the diplom thesis of the first author [17] .  ... 
doi:10.1016/s1567-8326(01)00006-6 fatcat:3hzhugi4zjeohp6vmby5jgfdnq

Formalization of the Undecidability of the Halting Problem for a Functional Language [chapter]

Thiago Mendonça Ferreira Ramos, César Muñoz, Mauricio Ayala-Rincón, Mariano Moscato, Aaron Dutle, Anthony Narkawicz
2018 Lecture Notes in Computer Science  
The formalization is part of a termination analysis library in PVS that includes the specification and equivalence proofs of several notions of termination.  ...  This paper presents a formalization of the proof of the undecidability of the halting problem for a functional programming language.  ...  Let pvso be a, possibly non-terminating, program of type PVS0 and pvso e the PVS0 expression of pvso.  ... 
doi:10.1007/978-3-662-57669-4_11 fatcat:lj2acounojd5fabkdwera4vlpa

Extending the Calculus of Constructions with Tarski's fix-point theorem [article]

Yves Bertot
2006 arXiv   pre-print
We claim that the extended framework makes it possible to reason about terminating and non-terminating computations and we show that common facilities of the calculus of inductive construction, like program  ...  This widens the class of functions that can be modeled in type-theory based theorem proving tool to potentially non-terminating functions.  ...  The author also wishes to remember the late Gilles Kahn, who started work on formalizing domain theory in the context of the calculus of inductive constructions in 1996 [11] .  ... 
arXiv:cs/0610055v1 fatcat:bvuamb63wvhknndm4zgvuxk6au

General Recursion and Formal Topology

Claudio Sacerdoti Coen, Silvio Valentini
2010 Electronic Proceedings in Theoretical Computer Science  
It is well known that general recursion cannot be expressed within Martin-Loef's type theory and various approaches have been proposed to overcome this problem still maintaining the termination of the  ...  In this work we propose a new approach to this problem based on the use of inductively generated formal topologies.  ...  However, in order to ensure the termination of the computation of every well typed program, it does not allow general recursion and hence it does not permit to program in a natural functional style (see  ... 
doi:10.4204/eptcs.43.5 fatcat:vjrvnxqycbet5pp4oregqfrhb4

Guarded attribute grammars

R. A. Frost
1993 Software, Practice & Experience  
A novel technique has been discovered by which the non-termination that would otherwise occur is avoided by 'guarding' top-down left-recursive language processors by non-left-recursive recognizers.  ...  of grammars containing left-recursive productions.  ...  In the next section, we formalize the notion of left-recursion and describe how non-termination that results from it can be avoided.  ... 
doi:10.1002/spe.4380231006 fatcat:wvekcvwh7fcgllyjbnp6mq776a

Guarded attribute grammars

Richard A. Frost
1992 SIGPLAN notices  
A novel technique has been discovered by which the non-termination that would otherwise occur is avoided by 'guarding' top-down left-recursive language processors by non-left-recursive recognizers.  ...  of grammars containing left-recursive productions.  ...  In the next section, we formalize the notion of left-recursion and describe how non-termination that results from it can be avoided.  ... 
doi:10.1145/130981.130990 fatcat:vmnqcjrr2jdidcdj3le4iuur2m

Adapting functional programs to higher order logic

Scott Owens, Konrad Slind
2008 Higher-Order and Symbolic Computation  
However, a possibly unfamiliar aspect of working in such an environment is that formally establishing program termination is necessary.  ...  Higher-order logic proof systems combine functional programming with logic, providing functional programmers with a comfortable setting for the formalization of programs, specifications, and proofs.  ...  Acknowledgments Matthew Flatt and Michael Norrish scrutinized drafts of the paper and made useful comments. Mike Gordon pointed us to Harper's algorithm.  ... 
doi:10.1007/s10990-008-9038-0 fatcat:5dk4ydvakze7je3swx4eoi7yci

Negation and aggregates in recursive rules: the LDL++ approach [chapter]

Carlo Zaniolo, Natraj Arni, Kayliang Ong
1993 Lecture Notes in Computer Science  
The problem of allowing non-monotonic constructs, such as negation and aggregates, in recursive programs represents a di cult challenge faced by current research in deductive databases.  ...  A novel and general treatment of set aggregates, allowing for user-de ned aggregates, is also presented.  ...  The primed version Q 0 of an XY-strati ed clique de nes a non-recursive program: thus, the dependency graph of Q 0 contains no cycle.  ... 
doi:10.1007/3-540-57530-8_13 fatcat:rbjr2ebflnfdfbdcjpeklyxbma

A Purely Logical Approach to the Termination of Imperative Loops

Ma Eras, Tudor Jebelean
2010 2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing  
The conditions are (first-order) formulae obtained by certain transformations of the program text. The loops are treated similarly to calls of recursively defined functions.  ...  We present and illustrate a method for the generation of the termination conditions for nested loops with abrupt termination statements.  ...  TERMINATION Non-recursive programs containing nested abrupt terminating while loops terminate if each loop terminates.  ... 
doi:10.1109/synasc.2010.64 dblp:conf/synasc/ErascuJ10 fatcat:3m4hh6ejrzgybiez6nwp2ecbre

On embedding a hardware description language in Isabelle/HOL

Wilayat Khan, David Sanan, Zhe Hou, Liu Yang
2019 Design automation for embedded systems  
In particular, the structure and execution of programs in the context of theorem provers and their impact on the overall language design are discussed.  ...  It requires selection of a language design criteria, host language, grammar, embedding approach and techniques and mechanisms to address determinism and termination issues.  ...  -The peculiarities of formal description of (non)-deterministic behaviour, non-terminating and non-trivially terminating processes are presented with examples (Section 6).  ... 
doi:10.1007/s10617-019-09226-1 fatcat:gyvbq6ijczf4voaqvvqlqylpae

Automatic Termination Analysis of Programs Containing Arithmetic Predicates

Nachum Dershowitz, Naomi Lindenstrauss, Yehoshua Sagiv, Alexander Serebrenik
1999 Electronical Notes in Theoretical Computer Science  
For each query-mapping pair that is potentially non-terminating, a bounded integer-valued termination function is guessed.  ...  For logic programs with arithmetic predicates, showing termination is not easy, since the usual order for the integers is not well-founded.  ...  These are situations in which recursion is not covered by general linear norms, as de ned in 21 . Termination of logic programs in the general case is undecidable see 2 for the formal proof.  ... 
doi:10.1016/s1571-0661(04)00113-6 fatcat:tgpwr355svaehpr3f5z2jjffpy

Memoization of Top Down Parsing [article]

Mark Johnson
1995 arXiv   pre-print
It presents a version of memoization suitable for continuation-passing style programs. When applied to a simple formalization of a top-down recognizer it yields a terminating parser.  ...  Thus in cases of left recursion, memoization does nothing to prevent the illfounded recursion that leads to non-termination.  ...  In a logic programming setting, memoization (specifically, the use of Earley deduction) avoids the non-termination problems associated with left-recursion, even when used with the DCG axiomatization of  ... 
arXiv:cmp-lg/9504016v1 fatcat:l7fztf5fkjeihfkipetqdyxjk4

Page 766 of Mathematical Reviews Vol. 52, Issue 3 [page]

1976 Mathematical Reviews  
R. 5396 On the termination of program schemas. Information and Control 29 (1975), no. 3, 243-251.  ...  that all partial recursive functions can be represented within that formalism.  ... 

Monotonic Properties of Completed Aggregates in Recursive Queries [article]

Carlo Zaniolo, Ariyam Das, Jiaqi Gu, Youfu Li, Mingda li, Jin Wang
2019 arXiv   pre-print
The problem with these languages and systems is that, to avoid the semantic and computational issues created by non-monotonic constructs in recursion, they only allow programs that are stratified with  ...  on sets of facts of predictable cardinality tantamounts to stratified programs where the precomputation of the cardinality of the set is followed by a stratum where recursive rules only use monotonic  ...  issues besetting the use of non-monotonic constructs in recursive programs.  ... 
arXiv:1910.08888v1 fatcat:x3ad3uppdjbeddjjjpjla3vtoe

A Calculus for Imperative Programs: Formalization and Implementation

Madalina Erascu, Tudor Jebelean
2009 2009 11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing  
As an extension of our previous work on imperative program verification, we present a formalism for handling the total correctness of While loops in imperative programs, consisting in functional based  ...  definitions of the verification conditions for both partial correctness and for termination.  ...  The calculus dealing with these situations is under development. 2) Termination of Non-Recursive Programs containing Normal Terminating Non-Nested While Loops: The general idea behind termination of mentioned  ... 
doi:10.1109/synasc.2009.42 dblp:conf/synasc/ErascuJ09 fatcat:7xxlmo46hzgzpm6k6p6bojmkeq
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