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An axiomatic basis for computer programming
 COMMUNICATIONS OF THE ACM
, 1969
"... In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference w ..."
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In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference which can be used in proofs of the properties of computer programs. Examples are given of such axioms and rules, and a formal proof of a simple theorem is displayed. Finally, it is argued that important advantages, both theoretical and practical, may follow from a pursuance of these topics.
Computable total functions on metric algebras, universal algebraic specifications and dynamical systems
 THE JOURNAL OF LOGIC AND ALGEBRAIC PROGRAMMING
, 2005
"... ..."
The Logic Programming Paradigm in Numerical Computation
, 1999
"... Although CLP(R) is a promising application of the logic programming paradigm to numerical computation, it has not addressed what has long been known as ``the pitfalls of [numerical] computation''. These show that rounding errors induce a severe correctness problem wherever floatingpoint c ..."
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Cited by 1 (1 self)
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Although CLP(R) is a promising application of the logic programming paradigm to numerical computation, it has not addressed what has long been known as ``the pitfalls of [numerical] computation''. These show that rounding errors induce a severe correctness problem wherever floatingpoint computation is used. Independently of logic programming, constraint processing has been applied to problems in terms of realvalued variables. By using the techniques of interval arithmetic, constraint processing can be regarded as a computergenerated proof that a certain realvalued solution lies in a narrow interval. In this paper we propose a method for interfacing this technique with CLP(R). This is done via a realvalued analogy of Apt's prooftheoretic framework for constraint processing.
Verification of Floating Point Programs
, 2010
"... This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without proper acknowledgement. Aston University ..."
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This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with its author and that no quotation from the thesis and no information derived from it may be published without proper acknowledgement. Aston University
Formal Languages]: Mathematical Logic
"... Abstract. We give an equational specification of the field operations on the rational numbers under initial algebra semantics using just total field operations and 12 equations. A consequence of this specification is that 0−1 = 0, an interesting equation consistent with the ring axioms and many prop ..."
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Abstract. We give an equational specification of the field operations on the rational numbers under initial algebra semantics using just total field operations and 12 equations. A consequence of this specification is that 0−1 = 0, an interesting equation consistent with the ring axioms and many properties of division. The existence of an equational specification of the rationals without hidden functions was an open question. We also give an axiomatic examination of the divisibility operator, from which some interesting new axioms emerge along with equational specifications of algebras of rationals, including one with the modulus function. Finally, we state some open problems, including: Does there exist an equational specification of the field operations on the rationals without hidden functions that is a complete term rewriting system?