Proving Correctness and Completeness of Normal Programs — A Declarative Approach

Drabent, Włodzimierz; Miłkowska, Mirosława

doi:10.1007/3-540-45635-x_27

Cited by 6 publications

(4 citation statements)

References 16 publications

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“…The paper is concluded by a section on related work. A preliminary and abridged version of this paper appeared as (Drabent and Mi lkowska 2001).…”

Section: Introductionmentioning

confidence: 99%

Proving correctness and completeness of normal programs – a declarative approach

Drabent¹,

Miłkowska²

2005

Theory and Practice of Logic Programming

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We advocate a declarative approach to proving properties of logic programs. Total correctness can be separated into correctness, completeness and clean termination; the latter includes non-floundering. Only clean termination depends on the operational semantics, in particular on the selection rule. We show how to deal with correctness and completeness in a declarative way, treating programs only from the logical point of view. Specifications used in this approach are interpretations (or theories). We point out that specifications for correctness may differ from those for completeness, as usually there are answers which are neither considered erroneous nor required to be computed.We present proof methods for correctness and completeness for definite programs and generalize them to normal programs. For normal programs we use the 3-valued completion semantics; this is a standard semantics corresponding to negation as finite failure. The proof methods employ solely the classical 2-valued logic. We use a 2-valued characterization of the 3-valued completion semantics, which may be of separate interest.The method of proving correctness of definite programs is not new and can be traced back to the work of Clark in 1979. However a more complicated approach using operational semantics was proposed by some authors. We show that it is not stronger than the declarative one, as far as properties of program answers are concerned. For a corresponding operational approach to normal programs, we show that it is (strictly) weaker than our method. We also employ the ideas of this work to generalize a known method of proving termination of normal programs.

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“…The paper is concluded by a section on related work. A preliminary and abridged version of this paper appeared as (Drabent and Mi lkowska 2001).…”

Section: Introductionmentioning

confidence: 99%

Proving correctness and completeness of normal programs – a declarative approach

Drabent¹,

Miłkowska²

2005

Theory and Practice of Logic Programming

Self Cite

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“…In this paper, the treatment of specifications and reasoning about correctness and completeness follows that of Drabent (2016); missing proofs and further explanations can be found there. For further discussion, examples and references, see also Drabent (2018) and Drabent and Mi lkowska (2005).…”

Section: Preliminariesmentioning

confidence: 99%

“…The choice of an approximate specification depends on the properties of interest. See for instance Drabent (2019) or Drabent and Mi lkowska (2005) for various specifications for append describing various properties of the program.…”

Section: Preliminariesmentioning

confidence: 99%

On Correctness and Completeness of an n Queens Program

Drabent

2021

Theory and Practice of Logic Programming

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Thom Frühwirth presented a short, elegant, and efficient Prolog program for the n queens problem. However, the program may be seen as rather tricky and one may not be convinced about its correctness. This paper explains the program in a declarative way and provides proofs of its correctness and completeness. The specification and the proofs are declarative, that is they abstract from any operational semantics. The specification is approximate, it is unnecessary to describe the program’s semantics exactly. Despite the program works on non-ground terms, this work employs the standard semantics, based on logical consequence and Herbrand interpretations. Another purpose of the paper is to present an example of precise declarative reasoning about the semantics of a logic program.

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“…To assess programming assignments, usually understanding the code semantically is required, and for a machine it would essentially mean determining the functional equivalence of a reference solution and the student solution, which is theoretically hard -deciding functional equivalence of two programs in general is NP-complete [19], and only in limited instances and for special classes of programs we are able to do so [20], [21]. Undeterred by this weakness, researchers took a different route and tried to assess correctness of programs by various means so that the method can be used in learning exercises and online settings [22] but faced complexity barriers of a different nature [23]. Other approaches used test data to assess correctness [24], [25] to match with known outcomes and "assume" correctness.…”

Section: Related Researchmentioning

confidence: 99%

Smart Assessment of and Tutoring for Computational Thinking MOOC Assignments using MindReader

Jamil¹

2017

Preprint

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One of the major hurdles toward automatic semantic understanding of computer programs is the lack of knowledge about what constitutes functional equivalence of code segments. We postulate that a sound knowledgebase can be used to deductively understand code segments in a hierarchical fashion by first de-constructing a code and then reconstructing it from elementary knowledge and equivalence rules of elementary code segments. The approach can also be engineered to produce computable programs from conceptual and abstract algorithms as an inverse function. In this paper, we introduce the core idea behind the MindReader online assessment system that is able to understand a wide variety of elementary algorithms students learn in their entry level programming classes such as Java, C++ and Python. The MindReader system is able to assess student assignments and guide them how to develop correct and better code in real time without human assistance.

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Proving Correctness and Completeness of Normal Programs — A Declarative Approach

Cited by 6 publications

References 16 publications

Proving correctness and completeness of normal programs – a declarative approach

Proving correctness and completeness of normal programs – a declarative approach

On Correctness and Completeness of an n Queens Program

Smart Assessment of and Tutoring for Computational Thinking MOOC Assignments using MindReader

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