Termination checking with types

Abel, Andreas

doi:10.1051/ita:2004015

Cited by 42 publications

(54 citation statements)

References 28 publications

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“…In this section, we define the type interpretation and prove its correctness. Our proof follows the pattern of [1]. We interpret types by saturated sets.…”

Section: Definition 322 (Interpretation Of Stages)mentioning

confidence: 99%

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A Tutorial on Type-Based Termination

Barthe

Grégoire

Riba

2009

Language Engineering and Rigorous Software Development

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Abstract. Type-based termination is a method to enforce termination of recursive definitions through a non-standard type system that introduces a notion of size for inhabitants of inductively defined types. The purpose of this tutorial is to provide a gentle introduction to a polymorphically typed λ-calculus with type-based termination, and to the size inference algorithm which is used to guarantee automatically termination of recursive definitions.

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“…In this section, we define the type interpretation and prove its correctness. Our proof follows the pattern of [1]. We interpret types by saturated sets.…”

Section: Definition 322 (Interpretation Of Stages)mentioning

confidence: 99%

“…X → (X → X) → X Moreover, Z : N Ch and S : N Ch → N Ch . Iteration can be typed as follows: 1. Typing rules of System F Some important properties.…”

Section: Computations In Polymorphic Type Systemsmentioning

confidence: 99%

A Tutorial on Type-Based Termination

Barthe

Grégoire

Riba

2009

Language Engineering and Rigorous Software Development

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“…For instance, dead-code elimination, strictness analysis [17] or termination checking [1,2] are known procedures for functional programs, perhaps even generic functional programs. We hope to exploit this body of knowledge in the future.…”

Section: Related Workmentioning

confidence: 99%

Programming errors in traversal programs over structured data

Lämmel

Thompson

Kaiser

2013

Science of Computer Programming

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Traversal strategies provide an established means of describing automated queries, analyses, transformations, and other non-trivial computations on deeply structured data (including, most notably, data representations of software artifacts such as programs). The resulting traversal programs are prone to programming errors. We are specifically concerned with errors that go beyond classic type errors, in particular: (i) divergence of traversal, (ii) unintentional extent of traversal into data, (iii) trivial traversal results, (iv) inapplicability of the constituents of a traversal program along traversal. We deliver a taxonomy of programming errors, and start attacking some of them by refinements of traversal programming.

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“…In our approach we build upon the method of [12], but we adapt it in order to make TRS-techniques applicable. 1 We recapitulate Haskell in Sect. 2 and introduce our notion of "termination".…”

Section: Introductionmentioning

confidence: 99%

“…Methods for first-order languages with strict evaluation strategy were developed in [5,11,17]. For higher-order languages, [1,3,18] study how to ensure termination by typing and [16] defines a restricted language where all evaluations terminate. A successful approach for automated termination proofs for a small Haskell-like language was developed in [12].…”

Section: Introductionmentioning

confidence: 99%

Automated Termination Analysis for Haskell: From Term Rewriting to Programming Languages

Giesl

Swiderski

Schneider–Kamp

et al. 2006

Lecture Notes in Computer Science

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Abstract. There are many powerful techniques for automated termination analysis of term rewriting. However, up to now they have hardly been used for real programming languages. We present a new approach which permits the application of existing techniques from term rewriting in order to prove termination of programs in the functional language Haskell. In particular, we show how termination techniques for ordinary rewriting can be used to handle those features of Haskell which are missing in term rewriting (e.g., lazy evaluation, polymorphic types, and higherorder functions). We implemented our results in the termination prover AProVE and successfully evaluated them on existing Haskell-libraries.

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Termination checking with types

Cited by 42 publications

References 28 publications

A Tutorial on Type-Based Termination

A Tutorial on Type-Based Termination

Programming errors in traversal programs over structured data

Automated Termination Analysis for Haskell: From Term Rewriting to Programming Languages

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