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Fundamentals Of Deductive Program Synthesis
 IEEE Transactions on Software Engineering
, 1992
"... An informal tutorial is presented for program synthesis, with an emphasis on deductive methods. According to this approach, to construct a program meeting a given specification, we prove the existence of an object meeting the specified conditions. The proof is restricted to be sufficiently construct ..."
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An informal tutorial is presented for program synthesis, with an emphasis on deductive methods. According to this approach, to construct a program meeting a given specification, we prove the existence of an object meeting the specified conditions. The proof is restricted to be sufficiently constructive, in the sense that, in establishing the existence of the desired output, the proof is forced to indicate a computational method for finding it. That method becomes the basis for a program that can be extracted from the proof. The exposition is based on the deductivetableau system, a theoremproving framework particularly suitable for program synthesis. The system includes a nonclausal resolution rule, facilities for reasoning about equality, and a wellfounded induction rule. INTRODUCTION This is an introduction to program synthesis, the derivation of a program to meet a given specification. It focuses on the deductive approach, in which the derivation task is regarded as a problem of ...
Generalisation for Induction
, 1993
"... Proof by induction plays a central role in showing that recursive programs satisfy their specification. Sometimes a key step is to generalise a lemma so that its inductive proof is easier. This report examines existing heuristics for generalisation for induction. We first examine the applicabil ..."
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Cited by 2 (1 self)
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Proof by induction plays a central role in showing that recursive programs satisfy their specification. Sometimes a key step is to generalise a lemma so that its inductive proof is easier. This report examines existing heuristics for generalisation for induction. We first examine the applicability of heuristics for generalisation and then develop a new approach for a class of problems for which the existing methods fail. Unlike the existing methods, we give the conditions under which our method guarantees a valid generalisation.
Two Formal Theories of Strings
, 2002
"... In this thesis we present two axiomatic theories in higherorder logic, either of which can be thought of as a formalization of string theory. One theory, called ST Theory, is a product of our own devising. The second theory, called WM Theory, is taken, with modification, from chapter 7 in the first ..."
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In this thesis we present two axiomatic theories in higherorder logic, either of which can be thought of as a formalization of string theory. One theory, called ST Theory, is a product of our own devising. The second theory, called WM Theory, is taken, with modification, from chapter 7 in the first edition of Manna and Waldinger's text book The Logical Basis for Computer Programming, AddisonWesley, 1985. We show that the two theories are equivalent in the sense that they are mutually interpretable. This means roughly that the axioms of one theory are theorems of the other theory, and vice versa. The entire formalization and analysis is performed in the IMPS Interactive Mathematical Proof System.
Review of heuristics for generalisation
"... Proof by induction plays a central role in showing that recursive programs satisfy their specification. Sometimes a key step is to generalise a lemma so that its inductive proof is easier. Existing heuristics for generalisation for induction are examined. The applicability of heuristics for generali ..."
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Proof by induction plays a central role in showing that recursive programs satisfy their specification. Sometimes a key step is to generalise a lemma so that its inductive proof is easier. Existing heuristics for generalisation for induction are examined. The applicability of heuristics for generalisation is also examined, and it is shown that the kind of examples on which some of the heuristics work best form a well defined class of problems. A class of generalisation problems is identified for which none of the methods work, and directions for future research are provided. 1 Introduction to generalisation 1.1