Lexical Scoping as Universal Quantification

Loading...
Thumbnail Image
Penn collection
Technical Reports (CIS)
Degree type
Discipline
Subject
Funder
Grant number
License
Copyright date
Distributor
Related resources
Author
Miller, Dale
Contributor
Abstract

A universally quantified goal can be interpreted intensionally, that is, the goal ∀x.G(x) succeeds if for some new constant c, the goal G(c) succeeds. The constant c is, in a sense, given a scope: it is introduced to solve this goal and is "discharged" after the goal succeeds or fails. This interpretation is similar to the interpretation of implicational goals: the goal D ⊃ G should succeed if when D is assumed, the goal G succeeds. The assumption D is discharged after G succeeds or fails. An interpreter for a logic programming language containing both universal quantifiers and implications in goals and the body of clauses is described. In its non-deterministic form, this interpreter is sound and complete for intuitionistic logic. Universal quantification can provide lexical scoping of individual, function, and predicate constants. Several examples are presented to show how such scoping can be used to provide a Prolog-like language with facilities for local definition of programs, local declarations in modules, abstract data types, and encapsulation of state.

Advisor
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
1989-03-01
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-89-23.
Recommended citation
Collection