Topic: universal data type

topics > computer science > data > Group: data type

data type as a set of values and a set of operations
data types are not needed
functional programming
lattice theory of types
list processing
object transformation language
pointer machines
primitive data type as memory
procedures as data
Thesa data model
ref_any or Object data type
type retract
uniform data model


Some high level languages are organized around a single universal type. For instance APL uses real number arrays, SNOBOL uses strings. LISP uses lists, and functional programming uses expressions. Even machine languages use memory as the universal type.

Dana Scott built a universal domain based on complete lattices, with many sub-domains corresponding to type interpretations. His universal type includes all types; this is similar to physical memory. In Thesa, the universal type is symbolic reference, and data types are self-referencing symbols. (cbb 5/80)

Subtopic: universal value domain up

Quote: assume a typeless, universal value space; no inherent meaning to values, meaning only in reference to an operation [»donaJ7_1985]
Quote: universal value space is typeless and contains all data types and computable operations [»donaJ7_1985]
Quote: resolve logical difficulties with sets by assuming a fixed, universal set [»simmGF_1963]
Quote: Scott's universal domain reflects the typelessness of computer memory [»demeA_1978]
Quote: in Scott's universal domain, an element can be a value, an argument, an integer, a function, and a combinator [»scotD9_1976]
Quote: Scott's universal domain is the set of all subsets of non-negative integers [»scotD9_1976]
Quote: a type retract defines the interpretation (value) of each element in the universal domain [»demeA_1978]

Subtopic: derived types of universal domain up

Quote: if types define subsets of a universal type, then their unions and intersections are well-defined [»reynJC9_1983]

Subtopic: other universal domains up

Quote: IBM 360 generalized machine memory as a sequence of bytes with uniform addressing independent of type [»dehnJC4_1998]
Quote: Kleisli's data exchange format is CPL values; self-describing, e.g., {| indicates a bag; no fixed schema or type declaration [»wongL9_2000]
Quote: in ATOL the fundamental data type is a string [»axfoTH3_1979]
Quote: a Red object is an atom, a sequence, or bottom [»backJ8_1978a]
QuoteRef: backJ_1973 ;;71 expression only type in a closed applicative language
QuoteRef: bellCG_1971 ;;616 takes basic logic computer units as i-unit (information is some form)

Subtopic: limitations of universal domain up

Quote: in type-free, lambda calculus, can not define a universal domain that includes all functions [»straC3_1973]
Quote: in computing, restricted data types are assumed; e.g., text editors do not work on binary files [»coxBJ7_1983]
Quote: the universal relation misses useful queries that are not based on keys [»coddEF_1990]
Quote: need sophisticated data type analysis to convert Cobol's fixed-length records into Visual Basic; can not use one type for all contexts

Related Topics up

Topic: data type as a set of values and a set of operations (16 items)
Topic: data types are not needed (8 items)
Topic: functional programming (45 items)
Topic: lattice theory of types (15 items)
Topic: list processing (15 items)
Topic: object transformation language (10 items)
Topic: pointer machines (17 items)
Topic: primitive data type as memory (29 items)
Topic: procedures as data (22 items)
Topic: Thesa data model (58 items)
Topic: ref_any or Object data type (9 items)
Topic: type retract (12 items)
Topic: uniform data model
(19 items)

Updated barberCB 3/05
Copyright © 2002-2008 by C. Bradford Barber. All rights reserved.
Thesa is a trademark of C. Bradford Barber.