An equational approach to the synthesis of functional and logic program is taken. Typically, the synthesis task involves finding equations which make the given specification an inductive theorem. To synthesize such programs, induction is necessary. We formulate efficient procedures for inductive proof as well as program synthesis using the framework of ordered rewriting. We also propose heuristics for generalizing from a sequence of equational consequences. These heuristics handle cases where the deductive process alone is not adequate to come with a program. 1
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1128
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Monads for functional programming
– Wadler
- 1992
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722
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Rewrite systems
– Dershowitz, Jouannaud
- 1990
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529
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A transformation system for developing recursive programs
– Burstall, Darlington
- 1977
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418
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Simple word problems in universal algebras
– Knuth, Bendix
- 1970
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414
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Termination of rewriting
– Dershowitz
- 1987
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237
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Orderings for term rewriting systems
– Dershowitz
- 1982
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115
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Essentials of logic programming
– Hogger
- 1990
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115
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Orderings for equational proofs
– Bachmair, Dershowitz, et al.
- 1986
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106
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Completion without failure
– Bachmair, Dershowitz, et al.
- 1989
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89
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Equations and Rewrite Rules: a Survey
– Huet, Oppen
- 1980
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73
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Proofs by induction in equational theories with constructors
– Huet, Hullot
- 1982
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66
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Logic Programming: Systematic Program Development
– Deville
- 1990
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59
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On word problems in equational theories
– Hsiang, Rusinowitch
- 1987
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54
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Procedures and Parameters: an axiomatic approach
– Hoare
- 1971
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48
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Proof by consistency in equational theories
– Bachmair
- 1988
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48
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Two generalizations of the recursive path ordering. Unpublished note
– Kamin, Levy
- 1980
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44
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A system for assisting program transformation
– Feather
- 1982
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41
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The handbook of artificial intelligence
– Barr, Feigenbaum
- 1981
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37
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Equational programming
– Dershowitz, Plaisted
- 1988
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36
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A strong restriction of the inductive completion procedure
– Fribourg
- 1986
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32
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Partial Evaluation and Mixed Computation
– Bjorner, Jones, et al.
- 1987
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32
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A completion procedure for conditional equations
– Ganzinger
- 1991
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29
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Computing with Rewrite Systems
– Dershowitz
- 1985
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20
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Completion and its applications
– Dershowitz
- 1989
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20
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Rewrite methods for clausal and non-clausal theorem proving
– Hsiang, Dershowitz
- 1983
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19
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Synthesis by completion
– Dershowitz
- 1985
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18
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LOPS - a system based on a strategical approach to program synthesis
– Bibel, Hornig
- 1984
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17
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Program transformation and rewriting
– Bellegarde
- 1991
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13
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Algorithmic learning from incomplete information: Principles and problems
– Jantke
- 1989
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11
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Applications of the Knuth-Bendix completion procedure
– Dershowitz
- 1982
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10
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A new method for establishing refutational completeness in theorem proving
– Hsiang, Rusinowitch
- 1986
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10
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Induction theorem proving using refined unfailing completion techniques
– Gramlich
- 1989
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8
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Computing ground reducibility and inductively complete positions
– Bundgen, Kuchlin
- 1989
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8
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A lemma driven automatic theorem prover for recursive function theory
– Boyer, Moore
- 1977
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8
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editors. The Handbook of Arti cial Intelligence
– Barr, Feigenbaum
- 1982
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7
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Rewrite, rewrite, rewrite, rewrite, rewrite
– Dershowitz, Kaplan
- 1989
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7
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Huet and Jean-Marie Hullot. Proofs by induction in equational theories with constructors
– G'erard
- 1982
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6
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Equations as programming language
– Dershowitz
- 1984
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5
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Towards a Set of Inference Rules for Solving Divergence in Knuth-Bendix Completion
– Lange
- 1989
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4
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Conditional rewriting in Focus
– Bronsard, Reddy
- 1991
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4
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A confluence criterion based on the generalised Newman lemma
– Kuchlin
- 1985
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3
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Proof by Consistency
– Bachmair
- 1988
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3
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A System for Developing Programs by Transformation
– Feather
- 1979
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3
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Schematization of infinite sets of rewrite rules generated by divergent completion process
– Kirchner
- 1989
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2
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The structured description of algorithm derivations
– Darlington
- 1981
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2
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A con uence criterion based on the generalised Newman lemma
– Kuchlin
- 1985
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1
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Partial Evaluation and Semantics-Based Program Manipulation
– Symp
- 1991
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1
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Bergstra and Jan Willem Klop. Conditional rewrite rules: Con uency and termination
– A
- 1986
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1
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Knuth-Bendix completion versus fold/unfold: A comparative study in program synthesis
– Fronhofer, Furbach
- 1986
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1
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Induction theorem proving using re ned unfailing completion techniques
– Gramlich
- 1989
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