The Fortress Language Specification - CiteSeerX

Chapter 37
Algebraic Constraints
The traits in this component are used to describe properties of traits and their associated operators. These traits provide
very few concrete methods, but specify abstract methods and property declarations. For this reason, the complete
code for these traits is presented here, rather than just the APIs.
37.1 Predicates and Equivalence Relations
A predicate is an operator that produces a boolean result. A binary predicate may be identified with a mathematical
relation, where the predicate returns true in exactly those cases that its two operands satisfy the relation; therefore we
use the mathematical terminology usually associated with relations to describe the properties of binary predicates.
trait UnaryPredicateT extends UnaryPredicateT, ∼,opr ∼
opr ∼(self): Boolean
end
A unary predicate is a prefix operator that takes one argument and returns a boolean value (true or false ). Note that
∼ is a static parameter, used here as a “variable” name for an operator.
trait BinaryPredicateT extends BinaryPredicateT, ∼,opr ∼
opr ∼(self,other: T): Boolean
end
A binary predicate is an infix operator that takes two arguments and returns a boolean value. Thus, for example, any
trait T that extends BinaryPredicateT, ⊏ necessarily has an infix method for the operator ⊏ , and that operator
returns a boolean value.
trait ReflexiveT extends ReflexiveT, ∼,opr ∼
extends { BinaryPredicateT, ∼ }
property ∀(a:T) (a ∼ a)
end
A reflexive predicate always returns true when its operands are the same. Because this fact is expressed as a property
declaration, the behavior of such an operator can be checked for correctness by unit testing.
trait IrreflexiveT extends IrreflexiveT, ∼,opr ∼
extends { BinaryPredicateT, ∼ }
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