Automated Termination Analysis for Incompletely Defined Programs

Walther, Christoph; Schweitzer, Stephan

doi:10.1007/978-3-540-32275-7_22

Cited by 5 publications

(13 citation statements)

References 21 publications

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“…Equality is based on conversion, rather than reduction, and hence no reduction strategy is privileged in the axiomatization of the theory. VeriFun supports reasoning about generalrecursive, possibly underdefined functions [19]. The language of VeriFun does have call-by-value semantics and polymorphic types, but only first-order functions.…”

Section: Related Workmentioning

confidence: 99%

Equational reasoning about programs with general recursion and call-by-value semantics

Kimmell¹,

Stump²,

Eades³

et al. 2013

Prog. Inform.

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Dependently typed programming languages provide a mechanism for integrating verification and programming by encoding invariants as types. Traditionally, dependently typed languages have been based on constructive type theories, where the connection between proofs and programs is based on the Curry-Howard correspondence. This connection comes at a price, however, as it is necessary for the languages to be normalizing to preserve logical soundness. Trellys is a call-by-value dependently typed programming language currently in development that is designed to integrate a type theory with unsound programming features, such as general recursion, Type:Type, and others. In this paper we outline one core language design for Trellys, and demonstrate the use of the key language constructs to facilitate sound reasoning about potentially unsound programs.

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Section: Related Workmentioning

confidence: 99%

Equational reasoning about programs with general recursion and call-by-value semantics

Kimmell¹,

Stump²,

Eades³

et al. 2013

Prog. Inform.

View full text Add to dashboard Cite

show abstract

“…Definition 4 extends the calculus from [15,18] by type positions π and rule (7) for data constructors such as mkpair (Fig. 2) that just wrap the item of interest; e. g., to show #(t, ) ≥ #(mkpair (t 1 , t 2 ), 1) it suffices to show #(t, ) ≥ #(t 1 , ).…”

Section: Rcons(t1) and C ?Ircons(t2)mentioning

confidence: 99%

“…Our approach extends the method of argument-bounded functions [15,18] that is used, for instance, in the semi-automated verifier eriFun [17] for termination analysis and the synthesis of suitable induction axioms. Using this approach, termination of every can be easily proved: Selector tl is argument-bounded, which intuitively means #(k) ≥ #(tl (k)) for all lists k = / ø, where #(k) counts the occurrences of list-constructors ø and :: in k (and thus corresponds to the length of list k plus 1).…”

Section: Introductionmentioning

confidence: 99%

“…3). These extensions allow our approach to prove termination of several purely first-order procedures that cannot be handled by the original approach in [15,18]. (2) The novel notion of call-boundedness to automatically prove termination of procedures with second-order recursion (Sect.…”

Section: Introductionmentioning

confidence: 99%

“…Using this approach, termination of every can be easily proved: Selector tl is argument-bounded, which intuitively means #(k) ≥ #(tl (k)) for all lists k = / ø, where #(k) counts the occurrences of list-constructors ø and :: in k (and thus corresponds to the length of list k plus 1). A system-generated difference procedure [15,18] ∆ tl : list[@A] → bool decides if this inequality is strict for a given list k, which is the case if k = / ø. To prove that the second argument of procedure every gets strictly smaller in the recursive call every(p, tl (k)), it suffices to show the trivial termination hypothesis…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Automated Termination Analysis for Programs with Second-Order Recursion

Aderhold

2010

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Many algorithms on data structures such as terms (finitely branching trees) are naturally implemented by second-order recursion: A first-order procedure f passes itself as an argument to a second-order procedure like map, every, foldl , foldr , etc. to recursively apply f to the direct subterms of a term. We present a method for automated termination analysis of such procedures. It extends the approach of argumentbounded functions (i) by inspecting type components and (ii) by adding a facility to take care of second-order recursion. Our method has been implemented and automatically solves the examples considered in the literature. This improves the state of the art of inductive theorem provers, which (without our approach) require user interaction even for termination proofs of simple second-order recursive procedures.

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Reasoning About Incompletely Defined Programs

Walther

Schweitzer

2005

Logic for Programming, Artificial Intelligence, and Reasoning

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Automated Termination Analysis for Incompletely Defined Programs

Cited by 5 publications

References 21 publications

Equational reasoning about programs with general recursion and call-by-value semantics

Equational reasoning about programs with general recursion and call-by-value semantics

Automated Termination Analysis for Programs with Second-Order Recursion

Reasoning About Incompletely Defined Programs

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