VDM-10 Language Manual

Chapter 3. Data Type Definitions
total function type = discretionary type, ‘+>’, type ;
discretionary type = type | ‘(’,‘)’ ;
Equation: F = A +> B 7 or F = A -> B
Constructors: In addition to the traditional function definitions the only way to construct functions
is by the lambda expression: lambda pat1 : T1, ..., patn : Tn &
body where the patj are patterns, the Tj are type expressions, and body is the body
expression which may use the pattern identifiers from all the patterns.
Operators:
The syntax and semantics for the lambda expression are given in section 6.16.
Operator Name Type
f(a1,...,an) Function apply A1 * · · · * An → B
f1 comp f2 Function composition (B → C) * (A → B) → (A → C)
f ** n Function iteration (A → A) * nat → (A → A)
t1 = t2 Equality A * A → bool
t1 t2 Inequality A * A → bool
Note that equality and inequality between type values should be used with great care. In
VDM languages this corresponds to the mathematical equality (and inequality) which is not
computable for infinite values like general functions. Thus, in the interpreter the equality is
on the abstract syntax of the function value (see inc1 and inc2 below).
Semantics of Operators:
Operator Name
Function apply
Function composition
Function iteration
Semantics Description
yields the result of applying the function f to the values
of a j . See the definition of apply expressions in
Section 6.12.
it yields the function equivalent to applying first f2
and then applying f1 to the result. f1, but not f2
may be Curried.
yields the funciton equivalent to applying f n times.
n=0 yields the identity function which just returns the
value of its parameter; n=1 yields the function itself.
For n>1, the result of f must be contained in its parameter
type.
7 Note that the total function arrow can only be used in signatures of totally defined functions and thus not in a type
definition.
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