Abstract
A new formalism, called Hiord, for defining type-free higher-order logic programming languages with predicate abstraction is introduced. A model theory, based on partial combinatory algebras, is presented, with respect to which the formalism is shown sound. A programming language built on a subset of Hiord, and its implementation are discussed. A new proposal for defining modules in this framework is considered, along with several examples.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Miller, D., Nadathur, G., Pfenning, F., Scedrov, A.: Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic 51, 125–157 (1991)
Nadathur, G., Miller, D.: Higher-order horn clauses. Journal of the ACM 37, 777–814 (1990)
Miller, D.: λprolog: an introduction to the language and its logic (2002), Manuscript available at http://www.cse.psu.edu/~dale
Chen, W., Kifer, M., Warren, D.S.: Hilog: JuneA Foundation for Higher-Order Logic Programming. Journal of Logic Programming (1989)
Beeson, M.: Foundations of Constructive Mathematics. Springer, Heidelberg (1985)
Lawvere, F.W.: Diagonal arguments and cartesian-closed categories. In: Category Theory, Homology Theory and their Applications. Springer, Heidelberg (1969)
Huwig, H., Poigné, A.: A Note on Inconsistencies Caused by Fixpoints in a Cartesian Closed Categories. Theoretical Computer Science 73, 101–112 (1990)
Miller, D.: A logic programming language with lambda-abstraction, function variables, and simple unification. Journal of Logic and Computation 1, 497–536 (1991)
Curry, H.B., Feys, R.: Combinatory Logic. North-Holland, Amsterdam (1958)
Cabeza, D.: An Extensible, Global Analysis Friendly Logic Programming System. PhD thesis, Dept. of Computer Science, Technical University of Madrid, Spain, Madrid, Spain (2004)
Bueno, F., Cabeza, D., Carro, M., Hermenegildo, M., López-GarcÃa, P. (eds.): G.P.: The Ciao System. Reference Manual (v1.10). The ciao system documentation series–TR, School of Computer Science, Technical University of Madrid, UPM (2002), System and on-line version of the manual, available at http://clip.dia.fi.upm.es/Software/Ciao/
Warren, D.H.: Higher-order extensions to prolog: are they needed? In: Hayes, J., Michie, D., Pao, Y.H. (eds.) Machine Intelligence 10, pp. 441–454. Ellis Horwood Ltd., Chicester (1982)
Naish, L.: Higher-order logic programming. Technical Report 96/2, Department of Computer Science, University of Melbourne, Melbourne, Australia (1996)
McDowell, R., Miller, D.: A logic for reasoning with higher-order abstract syntax. In: Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science, p. 434. IEEE Computer Society Press, Los Alamitos (1997)
Miller, D.: Abstract syntax and logic programming. In: Proceedings of the Second Russian Conference on Logic Programming. Springer, Heidelberg (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cabeza, D., Hermenegildo, M., Lipton, J. (2004). Hiord: A Type-Free Higher-Order Logic Programming Language with Predicate Abstraction. In: Maher, M.J. (eds) Advances in Computer Science - ASIAN 2004. Higher-Level Decision Making. ASIAN 2004. Lecture Notes in Computer Science, vol 3321. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30502-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-30502-6_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24087-7
Online ISBN: 978-3-540-30502-6
eBook Packages: Computer ScienceComputer Science (R0)