VDM-10 Language Manual

Chapter 6. Expressions
where bd is either a set bind or a type bind, and e is a boolean expression involving the
pattern identifiers of bd. The iota operator can only be used if a unique value exists which
matches the bind and makes the body expression e yield true (i.e. exists1 bd & e
must be true). The semantics of the iota expression is such that it returns the unique value
which satisfies the body expression (e).
Examples: Using the values sc1,...,sc4 defined by
✞
✡✝
sc1 = mk_Score (, 3, 0, 0, 9);
sc2 = mk_Score (, 1, 1, 1, 4);
sc3 = mk_Score (, 0, 2, 1, 2);
sc4 = mk_Score (, 0, 1, 2, 1);
✆
we have
iota x in set {sc1,sc2,sc3,sc4} & x.team = ≡ sc1
iota x in set {sc1,sc2,sc3,sc4} & x.points > 3 ≡ ⊥
iota x : Score & x.points < x.won ≡ ⊥
Notice that the last example cannot be executed and that the last two expressions are undefined
- in the former case because there is more than value satisfying the expression, and in
the latter because no value satisfies the expression.
6.7 Set Expressions
Syntax: expression = . . .
| set enumeration
| set comprehension
| set range expression
| . . . ;
set enumeration = ‘{’, [ expression list ], ‘}’ ;
expression list = expression, { ‘,’, expression } ;
set comprehension = ‘{’, expression, ‘|’, bind list,
[ ‘&’, expression ], ‘}’ ;
set range expression = ‘{’, expression, ‘,’, ‘...’, ‘,’,
expression, ‘}’ ;
Semantics: A Set enumeration has the form:
✞
{e1, e2, e3, ..., en}
✡✝
✆
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