Group:
type checking
Topic:
attribute-value pairs as information
Topic:
data type as a set of values
Topic:
elements
Topic:
integer values and operations
Topic:
kinds of numbers
Topic:
object and value equivalence
Topic:
objects as a set of attributes
Topic:
primitive data types of a language
Topic:
real numbers and floating point numbers
Topic:
science as measurement
Topic:
type checking by trademark
Topic:
type conversion
Topic:
undefined, null, and other signal values
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Summary
Units identify numerical values, for instance three apples or three feet. Numbers stated without units usually have units implicitly defined. An exception is identifying numbers such as telephone numbers. Units provide additional type information for consistency checks. They are heavily used in the physical sciences. Unit conversions can be done through linear algebra. (cbb 5/80)
Units are similar to types. They are usually composed from a small number of primitives such as meters, seconds, and grams. Are length and height different types with the same units? A unit is also like a trademark, giving the source of the value. (cbb 1/90)
Subtopic: dimensional analysis 
| Quote: pouch analysis is the same as dimensional analysis for checking units in formulas [»cleaJC_1975]
| | Quote: algorithms to convert units of measurement and perform dimensional analysis [»novaGS8_1995]
| | Quote: every quantitative expression consists of a unit or standard of reference and a magnitude [»maxwJC_1891, OK]
| | Quote: can remove the speed of light from physical equations by defining the unit of time as the time in which light travels 1cm [»einsA_1949]
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Subtopic: unit verification
| Quote: use linear algebra to tell if an expression of units is commensurate with 1; also determines the factor [»karrM5_1978]
| | Quote: with unit specifications, the compiler prevents nonsensical combinations [»cleaJC_1975]
| | Quote: specify units for data types for consistency checks; e.g., height vs. weight, radians vs. degrees [»hoarCA_1974]
| | Quote: units can be carried in calculations where they obey arithmetic laws [»karrM5_1978]
| | Quote: allowing exceptional instances can destroy type-safeness; e.g., using Canadian dollars instead of U.S. ones [»borgA10_1986]
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Subtopic: assign unit to number
| Quote: units allow programmers to distinguish different kinds of integers [»cleaJC_1975]
| | Quote: associate a quantity (a unit, e.g., volts) with a variable's value [»karrM5_1978]
| | Quote: units define equivalent values between two value sets [»chenPP3_1976]
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Subtopic: unit representation
| Quote: represented units as a vector of integral powers of a small set of primary dimensions; rules for arithmetic [»baldG8_1987]
| | Quote: use Lisp notation to specify units for literal constants, e.g., (q 2998e8 (/ meter second)) for the speed of light [»novaGS8_1995]
| | Quote: uses preals to check physical dimensions and catch errors; 32-bits for integer powers -8 to +7, or 16-bits per base dimension [»pettGW11_2001]
| | Quote: a variable and a unit should be the same; keeps manipulations visible [»karrM5_1978]
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Subtopic: trademark as unit
| Quote: can use a class or form trademark as an indication of units [»maclBJ12_1983]
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Subtopic: examples
| Quote: MicroTool supports physical units and checks for unit consistency [»elshJL1_1991]
| | Quote: MicroTool converts engineering values into computer values with a scale factor, bias, and treatment of fractional units [»elshJL1_1991]
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Subtopic: other units
| Quote: type checking can catch inappropriate indexing of arrays; like units; e.g., ArrayIndex h, ColumnIndex i, and RowIndex j [»weihK9_2002]
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Subtopic: problems with units
| Quote: if units are specified for some variables, they need to be specified for all variables; otherwise get type errors [»novaGS8_1995]
| | Quote: a problem of units is that different properties, e.g., length and height, have the same units [»parnDL3_1976]
| Quote: a state in a state machine is a unitless number
[»cbb_1980, OK]
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Related Topics
Group: type checking (12 topics, 392 quotes)
Topic: attribute-value pairs as information (57 items)
Topic: data type as a set of values (20 items)
Topic: elements (22 items)
Topic: integer values and operations (13 items)
Topic: kinds of numbers (24 items)
Topic: object and value equivalence (60 items)
Topic: objects as a set of attributes (39 items)
Topic: primitive data types of a language (31 items)
Topic: real numbers and floating point numbers (37 items)
Topic: science as measurement (36 items)
Topic: type checking by trademark (13 items)
Topic: type conversion (33 items)
Topic: undefined, null, and other signal values
(34 items)
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