Results 1 
7 of
7
InductiveDataType Systems
, 2002
"... In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schem ..."
Abstract

Cited by 821 (23 self)
 Add to MetaCart
In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schema", whichgeneral39I theusual recursor definitions fornatural numbers and simil9 "basic inductive types". This combined lmbined was shown to bestrongl normalIk39f The purpose of this paper is toreformul33 and extend theGeneral Schema in order to make it easil extensibl3 to capture a more general cler of inductive types, cals, "strictly positive", and to ease the strong normalgAg9Ik proof of theresulGGg system. Thisresul provides a computation model for the combination of anal"DAfGI specification language based on abstract data types and of astrongl typed functional language with strictly positive inductive types.
Inductive synthesis of equational programs
 In Eighth National Conf. on Arti cial Intelligence
, 1990
"... An equational approach to the synthesis of functional and logic program is taken. In this context, the synthesis task involves nding executable equations such that the given speci cation holds in their standard model. Hence, to synthesize such programs, induction is necessary.We formulate procedures ..."
Abstract

Cited by 27 (3 self)
 Add to MetaCart
An equational approach to the synthesis of functional and logic program is taken. In this context, the synthesis task involves nding executable equations such that the given speci cation holds in their standard model. Hence, to synthesize such programs, induction is necessary.We formulate procedures for inductiveproof,aswell as for 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 inadequate for coming up with a program. 1.
LOGIC PROGRAMMING cum APPLICATIVE PROGRAMMING* ABSTRACT
"... Conditional (directed) equations provid' ~ a paradigm of computation that combines the cl(',, ~ svntax and semantics of both PROLOGlike logic p'rogra~ming and (firstorder) LIsPlike applicative (functional) programming in a uniform manner. For applicative programming, equations are ..."
Abstract
 Add to MetaCart
Conditional (directed) equations provid' ~ a paradigm of computation that combines the cl(',, ~ svntax and semantics of both PROLOGlike logic p'rogra~ming and (firstorder) LIsPlike applicative (functional) programming in a uniform manner. For applicative programming, equations are used as conditional rewrite rules; for logic programming, the same equations are employed for "conditional narrowing". Increased expressive power is obtainable by combining both paradigms in one program. 1.
Inductive Synt quat ional
"... An equational approach to the synthesis of functional and logic programs is taken. Typically, a target program contains equations that are only true in the standard model of the given domain rules. To synthesize such programs, induction is necessary. We propose heuristics for generalizing from a s ..."
Abstract
 Add to MetaCart
(Show Context)
An equational approach to the synthesis of functional and logic programs is taken. Typically, a target program contains equations that are only true in the standard model of the given domain rules. To synthesize such programs, induction is necessary. We propose heuristics for generalizing from a sequence of deductive consequences. These are combined with rewritebased methods of inductive proof to derive provably correct programs. a survey of rewriting, see (Dershowitz & Jouannaud 1990); for completion and its applications, see (Dershowitz 1989). Consider the following toy system S for addition and doubling (d) of natural numbers in unary notation: x+0 + x x + S(Y) + s(x+y) d(x) + x+x