The Fortress Language Specification - CiteSeerX

for tokens.
For readability, plural forms of the unit names are defined as equivalent to the corresponding singular forms; thus one
can write meters per second , for example. Standard SI prefixes may be used on both the name and the symbol, so
that nanometer and nm are also units of the dimension named Length, related to meter and m by a conversion
factor of 10 −9 .
Every dimension may have a default unit that is used for representing values of quantities of that dimension if no unit
is specified explicitly. The Fortress standard libraries define these default dimensions and units:
Length meter MagneticFlux weber
Mass kilogram MagneticFluxDensity tesla
Time second Inductance henry
Frequency hertz Velocity meters per second
Force newton Acceleration meters per second squared
Pressure pascal Angle radian
Energy joule SolidAngle steradian
Power watt LuminousIntensity candela
Temperature kelvin LuminousFlux lumen
Area square meter Illuminance lux
Volume cubic meter RadionuclideActivity becquerel
ElectricCurrent ampere AbsorbedDose gray
ElectricCharge coulomb DoseEquivalent sievert
ElectricPotential volt AmountOfSubstance mole
Capacitance farad CatalyticActivity katal
Resistance ohm MassDensity kilograms per cubic meter
Conductance siemens
In addition, the Fortress standard libraries define the dimension Information with units bit and byte (and the plurals
bits and bytes), a byte being equal to 8 bits. To avoid confusion, SI prefixes are not provided for these units; instead,
programmers must use appropriate powers of 2 or 10, for example 10 6 bits or 2 20 bits .
Here are some examples of the use of dimensions and units:
x: R64 Length = 1.3 m
t: R64 Time = 5 s
v: R64 Velocity = x/t
w: R64 Velocity in nm/s = 17 nm/s
x: R64 Velocity in furlongs per fortnight = v in furlongs per fortnight
Dimensions and units can be multiplied, divided, and raised to rational powers to produce new dimensions and units.
Both the numerator and the denominator of a rational power of a dimension or a unit must be a valid nat parameter
instantiation (as described in Section 11.2). Multiplication can be expressed using juxtaposition or · ; division can be
expressed using / or per. The syntactic operators square and cubic may be applied to a dimension or unit in order
to raise it to the second power, third power, respectively; the special postfix syntactic operators squared and cubed
may be used for the same purpose. The syntactic operator inverse may be applied to a dimension or unit to divide it
into 1. All of these syntactic operators are merely syntactic sugar, expanded before type checking.
grams per cubic centimeter
meter per second squared
inverse ohms
One can also write 1/X as a synonym for X −1 if X is either a dimension or a unit.
Most numerical values in Fortress are dimensionless quantity values. Multiplying or dividing a dimensionless value
by a unit produces a dimensioned value; thus 5 s is the dimensioned value equal to five seconds, which has numerical
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