Type-based termination of generic programs

Abel, Andreas

doi:10.1016/j.scico.2008.01.004

Cited by 9 publications

(6 citation statements)

References 25 publications

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“…But since the size j of the rose argument is present, we can verify termination. 3 This is usually a severe problem for untyped termination checkers. The current solution in Coq requires Rose and List to be defined mutually, destroying important modularity in library development.…”

Section: Data List ++(A : Set) : Set { Nil : List a ; Cons : A -> Lismentioning

confidence: 99%

MiniAgda: Integrating Sized and Dependent Types

Abel

2010

Electron. Proc. Theor. Comput. Sci.

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Sized types are a modular and theoretically well-understood tool for checking termination of recursive and productivity of corecursive definitions. The essential idea is to track structural descent and guardedness in the type system to make termination checking robust and suitable for strong abstractions like higher-order functions and polymorphism. To study the application of sized types to proof assistants and programming languages based on dependent type theory, we have implemented a core language, MiniAgda, with explicit handling of sizes. New considerations were necessary to soundly integrate sized types with dependencies and pattern matching, which was made possible by modern concepts such as inaccessible patterns and parametric function spaces. This paper provides an introduction to MiniAgda by example and informal explanations of the underlying principles.

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Section: Data List ++(A : Set) : Set { Nil : List a ; Cons : A -> Lismentioning

confidence: 99%

MiniAgda: Integrating Sized and Dependent Types

Abel

2010

Electron. Proc. Theor. Comput. Sci.

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“…For example, adding μ-reduction is not sufficient to check the guardedness of coinductive proofs computed by proof specialization, although it is not clear at this point what is stopping the guardedness checker from unrolling the proof sufficiently. Ultimately, a semantic approach, possibly type based (Abel 2006(Abel , 2009, would be preferable but such approaches are not currently available for Coq.…”

Section: Reflectionmentioning

confidence: 99%

Formal polytypic programs and proofs

2010

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The aim of our work is to be able to do fully formal, machine-verified proofs over Generic Haskell-style polytypic programs. In order to achieve this goal, we embed polytypic programming in the proof assistantCoqand provide an infrastructure for polytypic proofs. Polytypic functions are reified within Coq as a datatype and they can then be specialized by applying a dependently typed term specialization function. Polytypic functions are thus first-class citizens and can be passed as arguments or returned as results. Likewise, we reify polytypic proofs as a datatype and provide a lemma that a polytypic proof can be specialized to any datatype in the universe. The correspondence between polytypic functions and their polytypic proofs is very clear: programmers need to give proofs for, and only for, the same cases that they need to give instances for when they define the polytypic function itself. Finally, we discuss how to write (co)recursive functions and do (co)recursive proofs in a similar way that recursion is handled in Generic Haskell.

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“…[62,22] address termination analysis for higher-order functional programs; it may be possible to extend these systems with awareness for onelayer traversal and generic functions for traversal. [2] addresses termination analysis for generic functional programs of the kind of Generic Haskell [25]; the approach is based on type-based termination and exploits the fact that generic functions are defined by induction on types, which is not directly the case for traversal strategies, though.…”

Section: Simplified Traversal Programmingmentioning

confidence: 99%

Programming Errors in Traversal Programs Over Structured Data

Laemmel

Thompson

Kaiser

2009

Electronic Notes in Theoretical Computer Science

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Traversal strategiesà la Stratego (alsoà la Strafunski and 'Scrap Your Boilerplate') provide an exceptionally versatile and uniform means of querying and transforming deeply nested and heterogeneously structured data including terms in functional programming and rewriting, objects in OO programming, and XML documents in XML programming.However, the resulting traversal programs are prone to programming errors. We are specifically concerned with errors that go beyond conservative type errors; examples we examine include divergent traversals, prematurely terminated traversals, and traversals with dead code.Based on an inventory of possible programming errors we explore options of static typing and static analysis so that some categories of errors can be avoided. This exploration generates suggestions for improvements to strategy libraries as well as their underlying programming languages. Haskell is used for illustrations and specifications with sufficient explanations to make the presentation comprehensible to the non-specialist. The overall ideas are language-agnostic and they are summarized accordingly. by ENTCS. The present paper is generally more detailed and updated, but its distinctive contribution is research on static program analysis for traversal strategies in §5; only one of the analyses was sketched briefly in the short version. The present paper also takes advantage of other previously published work by two of the present authors in so far that some of the strategy properties discovered by [30] help steering research on programming errors in the present paper. Programming errors are not systematically discussed in [30]. Also, type systems and static program analysis played no substantial role in said work. Instead, the focus was on demonstrating the potential of theorem proving in the context of traversal strategies.

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Type-based termination of generic programs

Cited by 9 publications

References 25 publications

MiniAgda: Integrating Sized and Dependent Types

MiniAgda: Integrating Sized and Dependent Types

Formal polytypic programs and proofs

Programming Errors in Traversal Programs Over Structured Data

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