VDM-10 Language Manual

Chapter 6. Expressions
Semantics: Assuming e is of function type the expression pre (e,e1,...,en) is true if and
only if the pre-condition of e is true for arguments e1,...,em where m is the arity of the
pre-condition of e. If e is not a function or m > n then the result is true. If e has no
pre-condition then the expression equals true.
Examples: Consider the functions f and g defined below
✞
f : nat * nat -> nat
f(m,n) == m div n
pre n 0;
✡✝
g (n: nat) sqrt: nat
pre n >= 0
post sqrt * sqrt n
✆
Then the expression
✞
✡✝
pre_(let h in set {f,g,lambda mk_(x,y): nat * nat & x div y}
in h, 1,0,-1)
✆
is equal to
• false if h is bound to f since this equates to pre f(1,0);
• true if h is bound to g since this equates to pre g(1);
• true if h is bound to lambda mk (x,y):nat * nat & x div y since there is
no pre-condition defined for this function.
Note that however h is bound, the last argument (-1) is never used.
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