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### Strict functionals for termination proofs [chapter]

Jaco van de Pol, Helmut Schwichtenberg
1995 Lecture Notes in Computer Science
The main advantage of the method is that it makes it possible to transfer ones intuitions about why an HRS should be terminating into a proof: one has to nd a \strict" interpretation of the constants involved  ...  Its main tool is the notion of a strict functional, which is a variant of Gandy's notion of a hereditarily monotonic functional 1].  ...  The following lemma enables us to nd a lot more strict functionals: Lemma 3. For any strict functional G and monotonic functional H, the functional F de ned by F(x) := G(x) + H(x), is strict. Proof.  ...

### Proof Tool Support for Explicit Strictness [chapter]

Marko van Eekelen, Maarten de Mol
2006 Lecture Notes in Computer Science
We introduce the various ways in which strictness specific support is offered by the proof assistant Sparkle.  ...  In programs written in lazy functional languages such as for example Clean and Haskell, the programmer can choose freely whether particular subexpressions will be evaluated lazily (the default) or strictly  ...  The aim of this support is to hide the cumbersome effects of strictness to the user, allowing the same proof style and the same proof rules to be used both for the lazy and for the strict case.  ...

### Termination proofs for higher-order rewrite systems [chapter]

Jaco Pol
1994 Lecture Notes in Computer Science
The result is a proof technique for the termination of a HRS, similar to the proof technique \Termination by interpretation in a wellfounded monotone algebra", described in 8, 19] .  ...  This paper deals with termination proofs for Higher-Order Rewrite Systems (HRSs), introduced in 12].  ...  Theorem 46 suggests the following proof technique for the termination of an HRS: { Find a convenient strict interpretation J (c) for each constant symbol c 2 C. { Prove that for each rule (l !  ...

### A complexity tradeoff in ranking-function termination proofs

Amir M. Ben-Amram
2008 Acta Informatica
Our results show a tradeoff: either exponentially many local functions of certain simple forms, or an exponentially complex global function may be required for proving termination. *  ...  To prove that a program terminates, we can employ a ranking function argument, where program states are ranked so that every transition decreases the rank.  ...  Acknowledgement I am grateful to the Acta Informatica referees for their help in improving this paper.  ...

### Page 5683 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews
Thus, if the evaluation of a term ¢ does not terminate, the evaluation of a function value f(r) will not terminate. Examples of strict languages are Scheme and ML.  ...  Logics of partial terms for strict and non-strict functional programming languages. (English summary) J. Funct. Programming 8 (1998), no. 2, 97-129.  ...

### Topics in termination [chapter]

Nachum Dershowitz, Charles Hoot
1993 Lecture Notes in Computer Science
We look at methods for proving termination of orthogonal systems and give a new solution to a problem of Zantema's.  ...  In fact, we must combine termination with the semantics (f(x) = x), as one must for the functional proof. 2.  ...  The path ordering satisfies lhe strict subterm property f(. . . , st,...) ~ si, for all i. Proof. By (1) f( .... si,...) ~_ si, but si ~ f(...  ...

### Automated termination proofs with measure functions [chapter]

Jürgen Giesl
1995 Lecture Notes in Computer Science
This paper deals with the automation of termination proofs for recursively de ned algorithms (i.e. algorithms in a pure functional language).  ...  To overcome these drawbacks we introduce a calculus for automated termination proofs which is able to handle arbitrary measure functions based on polynomial norms.  ...  Acknowledgements I would like to thank J urgen Brauburger, Stefan Gerberding, Thomas Kolbe, Martin Protzen, Christoph Walther and the referees for helpful comments.  ...

### Strict Linearizability and Abstract Atomicity [article]

Tangliu Wen
2018 arXiv   pre-print
We also investigate its relationship with strict linearizability.  ...  We also investigate several important properties of strict linearizability.  ...  : Since Z is strict linearizable. 2.2 There exists a sequential and terminating execution ϕ of A such that H(ϕ ) = H(ϕ ). proof: by the 1.1. 2.3 Q.E.D. proof: By 2.1 and 2.2, for any execution ϕ of Z starting  ...

### Certification extends Termination Techniques [article]

Christian Sternagel, René Thiemann
2012 arXiv   pre-print
There are termination proofs that are produced by termination tools for which certifiers are not powerful enough. However, a similar situation also occurs in the other direction.  ...  We have formalized termination techniques in a more general setting as they have been introduced. Hence, we can certify proofs using techniques that no termination tool supports so far.  ...  Moreover, monotone reduction pairs can be used for direct termination proofs or rule removal [3, 9, 14] .  ...

### Strictness and totality analysis with conjunction [chapter]

Kirsten Lackner Solberg
1995 Lecture Notes in Computer Science
We prove the strictness and totality analysis correct with respect to a denotational semantics and finally construct an algorithm for inferring the strictness and totality properties.  ...  We extend the strictness and totality analysis of  by allowing conjunction at all levels rather than at the top-level.  ...  As an example a function may have the annotated type (n Int ~ n Int) A (b Int ~ b Ine) which means that given a terminating argument the function will definitely terminate and given a non-terminating argument  ...

### Combining Proofs and Programs [chapter]

Stephanie Weirich
2011 Lecture Notes in Computer Science
We call this principle freedom of speech: whereas proofs themselves must terminate, they must be allowed to reason about any function a programmer might write.  ...  These languages trade termination obligations for more limited correctness assurances. In this talk, I present a work-in-progress overview of the Trellys project.  ...  We call this principle freedom of speech: whereas proofs themselves must terminate, they must be allowed to reason about any function a programmer might write.  ...

### Elementary strong functional programming [chapter]

D. A. Turner
1995 Lecture Notes in Computer Science
What we should be doing is strong (or total) functional programming -in which all computations terminate. We propose an elementary discipline of strong functional programming.  ...  Functional programming is a good idea, but we haven't got it quite right yet. What we have been doing up to now is weak (or partial) functional programming.  ...  I am grateful to the audience at that symposium for a number of comments.  ...

### Universal extensions to simulate specifications

2008 Information and Computation
The proofs have been verified with the theorem prover PVS. The methodology of using eternity extensions in correctness proofs is briefly discussed.  ...  Proof. Since K is never-terminating, the successor function s of K satisfies s k+1 (z) / = s k (z) for all k.  ...  Then z = xs(0) satisfies z = q(xs(i)) for all i. Therefore, f • xs = h(z) • c • xs. Since K is never-terminating, xs does not terminate. By Lemma 5.1, c • xs is a stutter function.  ...

### An Improved General Path Order

A. Geser
1996 Applicable Algebra in Engineering, Communication and Computing
We define a strong and versatile termination order for term rewriting systems, called the Improved General Path Order, which simplifies and strengthens Dershowitz/Hoot's General Path Order.  ...  We demonstrate the power of the Improved General Path Order by proofs of termination of non-trivial examples, among them a medium-scale term rewriting system that models a lift control.  ...  I also wish to thank Nachum Dershowitz for a number of discussions about the general path order, and Joachim Steinbach for pointing to interesting examples.  ...

### TEA: Automatically proving termination of programs in a non-strict higher-order functional language [chapter]

Sven Eric Panitz, Manfred Schmidt-Schauß
1997 Lecture Notes in Computer Science
We present TEA, a tool that is able to detect termination of functions written in a non-strict high-level functional programming language like Haskell.  ...  Since almost every compiler for lazy functional languages transforms programs into a functional core language, we use such a core language as the source language for the analysis.  ...  Acknowledgment We would like to thank Marko Sch utz for his helpful remarks in discussions.  ...
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