Proving correctness and completeness of normal programs – a declarative approach

Drabent, Włodzimierz; Miłkowska, Mirosława

doi:10.1017/s147106840500253x

Cited by 12 publications

(17 citation statements)

References 32 publications

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“…The "completeness specification" contains what we refer to as true atoms and the "soundness specification" contains the true and inadmissible atoms. A diagram clearly shows the three truth values we use in intended interpretations and an earlier version of the paper, (Drabent and Mi lkowska 2001), stated the pair of specifications "is a formalisation of such interpretations". Each specification is simpler than our three-valued interpretations but because two specifications are always required it is more complicated overall.…”

Section: Program Verificationmentioning

confidence: 99%

A three-valued semantics for logic programmers

Naish¹

2006

Theory and Practice of Logic Programming

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This paper describes a simpler way for programmers to reason about the correctness of their code. The study of semantics of logic programs has shown strong links between the model theoretic semantics (truth and falsity of atoms in the programmer's interpretation of a program), procedural semantics (for example, SLD resolution) and fixpoint semantics (which is useful for program analysis and alternative execution mechanisms). Most of this work assumes that intended interpretations are two-valued: a ground atom is true (and should succeed according to the procedural semantics) or false (and should not succeed). In reality, intended interpretations are less precise. Programmers consider that some atoms "should not occur" or are "ill-typed" or "inadmissible". Programmers don't know and don't care whether such atoms succeed. In this paper we propose a three-valued semantics for (essentially) pure Prolog programs with (ground) negation as failure which reflects this. The semantics of Fitting is similar but only associates the third truth value with nontermination. We provide tools to reason about correctness of programs without the need for unnatural precision or undue restrictions on programming style. As well as theoretical results, we provide a programmer-oriented synopsis. This work has come out of work on declarative debugging, where it has been recognised that inadmissible calls are important. This paper has been accepted to appear in Theory and Practice of Logic Programming.

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Section: Program Verificationmentioning

confidence: 99%

A three-valued semantics for logic programmers

Naish¹

2006

Theory and Practice of Logic Programming

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“…in (Apt 1997). See (Drabent and Mi lkowska 2005;Drabent 2016a) for further comparison, examples and discussion.…”

Section: Theoremmentioning

confidence: 99%

“…See (Drabent 2016a) for an overview. We summarize the approach of (Drabent 2016a), stemming from that of (Drabent and Mi lkowska 2005). It is based on an auxiliary notion of semi-completeness.…”

Section: Reasoning About Completenessmentioning

confidence: 99%

Logic + control: On program construction and verification

Drabent

2017

Theory and Practice of Logic Programming

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This paper presents an example of formal reasoning about the semantics of a Prolog program of practical importance (the SAT solver of Howe and King). The program is treated as a definite clause logic program with added control. The logic program is constructed by means of stepwise refinement, hand in hand with its correctness and completeness proofs. The proofs are declarative -they do not refer to any operational semantics. Each step of the logic program construction follows a systematic approach to constructing programs which are provably correct and complete. We also prove that correctness and completeness of the logic program is preserved in the final Prolog program. Additionally, we prove termination, occur-check freedom and non-floundering.Our example shows how dealing with "logic" and with "control" can be separated. Most of the proofs can be done at the "logic" level, abstracting from any operational semantics.The example employs approximate specifications; they are crucial in simplifying reasoning about logic programs. It also shows that the paradigm of semantics-preserving program transformations may be not sufficient. We suggest considering transformations which preserve correctness and completeness with respect to an approximate specification.

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“…It is irrelevant whether A is an answer of the program, or not. For further discussion and examples see [Dra14,DM05], see also Ex. 4.6.…”

Section: Declarative Notions Of Correctness and Completenessmentioning

confidence: 99%

“…then H ∈ S. Deransart [Der93] attributes this method to [Cla79]. See [Dra14,DM05] for examples and discussion.…”

Section: Declarative Notions Of Correctness and Completenessmentioning

confidence: 99%

Proving completeness of logic programs with the cut

Drabent

2017

Form. Asp. Comput.

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Abstract. Completeness of a logic program means that the program produces all the answers required by its specification. The cut is an important construct of programming language Prolog. It prunes part of the search space, this may result in a loss of completeness. This paper proposes a way of proving completeness of programs with the cut. The semantics of the cut is formalized by describing how SLD-trees are pruned. A sufficient condition for completeness is presented, proved sound, and illustrated by examples.

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Proving correctness and completeness of normal programs – a declarative approach

Cited by 12 publications

References 32 publications

A three-valued semantics for logic programmers

A three-valued semantics for logic programmers

Logic + control: On program construction and verification

Proving completeness of logic programs with the cut

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