Termination Analysis of Higher-Order Functional Programs

Sereni, Damien; Jones, Neil D.

doi:10.1007/11575467_19

Cited by 39 publications

(48 citation statements)

References 12 publications

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“…We had anticipated from the start that our framework could naturally be extended to higher-order functional programs, e.g., functional subsets of Scheme or ML. This has since been confirmed by Sereni and Jones, first reported in [19]. Sereni's Ph.D. thesis [21] develops this direction in considerably more detail with full proofs, and also investigates problems with lazy (call-by-name) languages.…”

supporting

confidence: 60%

Call-by-value Termination in the Untyped lambda-calculus

Jones¹,

Bohr²

2008

Logical Methods in Computer Science

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Abstract. A fully-automated algorithm is developed able to show that evaluation of a given untyped λ-expression will terminate under CBV (call-by-value). The "size-change principle" from first-order programs is extended to arbitrary untyped λ-expressions in two steps. The first step suffices to show CBV termination of a single, stand-alone λ-expression. The second suffices to show CBV termination of any member of a regular set of λ-expressions, defined by a tree grammar. (A simple example is a minimum function, when applied to arbitrary Church numerals.) The algorithm is sound and proven so in this paper. The Halting Problem's undecidability implies that any sound algorithm is necessarily incomplete: some λ-expressions may in fact terminate under CBV evaluation, but not be recognised as terminating.The intensional power of the termination algorithm is reasonably high. It certifies as terminating many interesting and useful general recursive algorithms including programs with mutual recursion and parameter exchanges, and Colson's "minimum" algorithm. Further, our type-free approach allows use of the Y combinator, and so can identify as terminating a substantial subset of PCF.

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supporting

confidence: 60%

Call-by-value Termination in the Untyped lambda-calculus

Jones¹,

Bohr²

2008

Logical Methods in Computer Science

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“…All are, however, related to linear computational paths and to relations among first-order values. This is in contrast to other approaches, for example Gödel's higher-order primitive recursive functions, and analyses of higher-order programs studied among others by Bohr and by Sereni [24,36,37]. In this section, we discuss qualitative differences between SCT and TI.…”

Section: Problem: Associative Closure Checking For Abstract Relationsmentioning

confidence: 91%

Size-Change Termination and Transition Invariants

2010

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Abstract. Two directions of recent work on program termination use the concepts of size-change termination resp. transition invariants. The difference in the setting has as consequence the inherent incomparability of the analysis and verification methods that result from this work. Yet, in order to facilitate the crossover of ideas and techniques in further developments, it seems interesting to identify which aspects in the respective formal foundation are related. This paper presents initial results in this direction.

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“…Lee et al prove in [20] that the problem to determine if a set of size-change graphs has the SCT property is PSPACE-complete. The size-change termination method has been successfully applied in a variety of different application areas [2,6,18,24,27,28].…”

Section: Introductionmentioning

confidence: 99%

Lazy Abstraction for Size-Change Termination

Codish

Fuhs

Giesl

et al. 2010

Logic for Programming, Artificial Intelligence, and Reasoning

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Abstract. Size-change termination is a widely used means of proving termination where source programs are first abstracted to size-change graphs which are then analyzed to determine if they satisfy the sizechange termination property. Here, the choice of the abstraction is crucial to the success of the method, and it is an open problem how to choose an abstraction such that no critical loss of precision occurs. This paper shows how to couple the search for a suitable abstraction and the test for size-change termination via an encoding to a single SAT instance. In this way, the problem of choosing the right abstraction is solved en passant by a SAT solver. We show that for the setting of term rewriting, the integration of this approach into the dependency pair framework works smoothly and gives rise to a new class of size-change reduction pairs. We implemented size-change reduction pairs in the termination prover AProVE and evaluated their usefulness in extensive experiments.

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Termination Analysis of Higher-Order Functional Programs

Cited by 39 publications

References 12 publications

Call-by-value Termination in the Untyped lambda-calculus

Call-by-value Termination in the Untyped lambda-calculus

Size-Change Termination and Transition Invariants

Lazy Abstraction for Size-Change Termination

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