149 ;;Quote: data type is poorly defined as syntax (i.e., declaration), value space, value space and its operations, representation, representation and operations

149;;Quote: a data type is an equivalence class of variables with the same permitted contexts

150;;Quote: an abstraction is a concept with more than one possible realization; solving a problem as an abstraction, solves many problems at once

150+;;Quote: user-defined data types are abstractions; e.g., structured programming, stepwise refinement, and information hiding

150;;Quote: a data type provides information about the intended use of data, restricting its meaningful operations

150+;;Quote: data types increase reliability and reduce development costs; compile-time checking and redundancy

150 ;;Quote: with user-defined data types, programs are shorter; easier to write, understand, prove correct, modify

150 ;;Quote: data abstraction allows abbreviation, code sharing, and reuse; like subroutines

150 ;;Quote: user-defined data types improve data portability between systems; helps reduce the amount of program rewriting

150 ;;Quote: self-describing data may be completely determined only at the time of actual processing; needs an extensible language

150 ;;Quote: a problem of units is that different properties, e.g., length and height, have the same units

150 ;;Quote: data type abstraction allows one variable to be substituted for another without making the program illegal or meaningless

150 ;;Quote: variables have the same mode if they have the same data representation and data access; can freely substitute variables or generate code

151 ;;Quote: a data type is a class of variables that can be substituted in some restricted context; hence, a class of modes

151 ;;Quote: automatic type conversion does not work as intended; i.e., perform intended conversions while refusing to perform other conversions

151 ;;Quote: an abstract data type is a class of modes that specifies the permissible operands for its operators; can use any member of the mode class

151+;;Quote: a programming language should be able to group modes into abstract types almost arbitrarily

151 ;;Quote: spec-types have different representations but the same set of operators; operators are generic

151+;;Quote: if can prove a program correct according to its specifications, can then replace spec-types with other variables of the same type, but different modes

151 ;;Quote: a rep-type is the set of modes with the same representation; explicitly declared, includes operations

152 ;;Quote: a param-type is a set of possible assignments to parameterized modes; e.g., all arrays of varying element types and bounds

152 ;;Quote: variant-type -- a type could be all data structures that contain name and birth-date fields

152 ;;Quote: a variable could belong to many types; may be difficult to understand

152+;;Quote: should control any dependencies on representation and machine details; better than dirty tricks

153 ;;Quote: a spec-type either branches on the actual mode or its variables carry its procedures