The Fortress Language Specification - CiteSeerX

Chapter 35
Dimensions and Units Declarations
Syntax:
DimUnitDecl ::= dim Id [ = DimRef ] [default Unit]
| (unit | SI unit ) Id + [ : DimRef ] [ = Expr]
| dim Id [ = DimRef ] (unit | SI unit ) Id + [ = Expr]
35.1 Dimensions Declarations
Dimensions may be explicitly declared; every declared dimension must be declared at the top level of a program
component, not within a block expression or trait. Other dimensions may be constructed by multiplying and dividing
other dimensions, as described in Chapter 18. An explicitly declared dimension may be a base dimension (with no
definition specified) or a derived dimension (with a definition specified in the form of an initialization expression).
The set of all dimensions has the algebraic structure of a free abelian group. The identity element of this group is the
dimension Unity, which represents dimensionlessness.
For every two dimensions D and E , there is a dimension DE (which may also be written D · E ), corresponding to
the product of the dimensions D and E and a dimension D/E , corresponding to the quotient of the dimensions D
and E . The syntactic sugar 1/D is equivalent to Unity/D for all dimensions D . A dimension can be raised to a
rational power where both the numerator and the denominator of the rational power must be a valid nat parameter
instantiation (as described in Section 11.2); D 0 is the same as Unity, D 1 is the same as D , and D m+n is the same
as D m D n . The syntactic sugar D −n is the same as Unity/D n .
Here are some examples of base dimension declarations:
dim Length
dim Mass
dim Time
dim ElectricCurrent
Here are some examples of computed dimensions:
Length/Time
Velocity/Time
Length · Mass/Time 2
Length Mass Time −2
ElectricCurrent/Length 2 236