Open AccessA Programming Language for the Inductive Sets, and Applications
Author(s) -
David Harel,
Dexter Kozen
Publication year - 1982
Publication title -
daimi pb
Language(s) - English
Resource type - Journals
eISSN - 2245-9316
pISSN - 0105-8517
DOI - 10.7146/dpb.v11i143.7418
Subject(s) - programming language , computer science , logic programming , inductive logic programming , datalog , turing , set (abstract data type) , turing machine , first order logic , theoretical computer science , computation
We introduce a programming language IND that generalizes alternating Turing machines to arbitrary first-order structures. We show that IND programs (respectively, everywhere-halting IND programs, loop-free IND programs) accept precisely the inductively definable (respectively, hyperelementary, elementary) relations. We give several examples showing how the language provides a robust and computational approach to the theory of first-order inductive definability. We then show: (1) on all acceptable structures (in the sense of Moschovakis), r.e. Dynamic Logic is more expressive than finite-test Dynamic Logic. This refines a separation result of Meyer and Parikh; (2) IND provides a natural query language for the set of fixpoint queries over a relational database, answering a question of Chandra and Harel.