VDM-10 Language Manual

Chapter 3. Data Type Definitions
Operator Name Type
-x Unary minus real → real
abs x Absolute value real → real
floor x Floor real → int
x + y Sum real * real → real
x - y Difference real * real → real
x * y Product real * real → real
x / y Division real * real → real
x div y Integer division int * int → int
x rem y Remainder int * int → int
x mod y Modulus int * int → int
x**y Power real * real → real
x < y Less than real * real → bool
x > y Greater than real * real → bool
x = y Greater or equal real * real → bool
x = y Equal real * real → bool
x y Not equal real * real → bool
The types stated for operands are the most general types allowed. This means for instance
that unary minus works for operands of all five types (nat1, nat, int rat and real).
Semantics of Operators: The operators Unary minus, Sum, Difference, Product, Division, Less
than, Greater than, Less or equal, Greater or equal, Equal and Not equal have the usual
semantics of such operators.
Operator Name Semantics Description
Floor
yields the greatest integer which is equal to or smaller
than x.
Absolute value yields the absolute value of x, i.e. x itself if x >= 0
and -x if x < 0.
Power
yields x raised to the y’th power.
There is often confusion on how integer division, remainder and modulus work on negative
numbers. In fact, there are two valid answers to -14 div 3: either (the intuitive) -4 as in
the Toolbox, or -5 as in e.g. Standard ML [Paulson91]. It is therefore appropriate to explain
these operations in some detail.
Integer division is defined using floor and real number division:
✞
✡✝
x/y < 0: x div y = -floor(abs(-x/y))
x/y >= 0: x div y = floor(abs(x/y))
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