The Fortress Language Specification - CiteSeerX

opr ≻(self,other: T): Boolean = (other ≺ self)
end
The trait PartialOrderBasedOnLE specifies a partial order by assuming that the “less than or equal to” predicate is
already defined and providing definitions for the comparison operator, the “less than” predicate, the equality predicate,
the “greater than or equal to” predicate, and the “greater than” predicate in terms of the “less than or equal to” predicate.
trait TotalOrderBasedOnLET extends TotalOrderBasedOnLET, ≺, , , ≻,CMP,
opr ≺,opr ,opr ,opr ≻,opr CMP
extends { TotalOrderOperatorsT, ≺, , , ≻,CMP }
opr CMP(self,other:T): TotalComparison =
if a b then (if b a then EqualTo else LessThan end) else GreaterThan end
opr ≺(self,other: T): Boolean = ¬(other self)
opr =(self,other: T): Boolean = (self other) ∧ (other self)
opr (self,other: T): Boolean = (other self)
opr ≻(self,other: T): Boolean = (other ≺ self)
end
The trait TotalOrderBasedOnLE specifies a total order by assuming that the “less than or equal to” predicate is
already defined and providing definitions for the comparison operator, the “less than” predicate, the equality predicate,
the “greater than or equal to” predicate, and the “greater than” predicate in terms of the “less than or equal to” predicate.
trait TotalOrderBasedOnLTT extends TotalOrderBasedOnLTT, ≺, , , ≻,CMP,
opr ≺,opr ,opr ,opr ≻,opr CMP
extends { TotalOrderOperatorsT, ≺, , , ≻,CMP }
opr CMP(self,other:T): TotalComparison =
if a ≺ b then LessThan elif b ≺ a then GreaterThan else EqualTo end
opr (self,other: T): Boolean = ¬(other ≺ self)
opr =(self,other: T): Boolean = (self other) ∧ (other self)
opr (self,other: T): Boolean = (other self)
opr ≻(self,other: T): Boolean = (other ≺ self)
end
The trait TotalOrderBasedOnLT specifies a total order by assuming that the “less than” predicate is already defined
and providing definitions for the comparison operator, the “less than or equal to” predicate, the equality predicate, the
“greater than or equal to” predicate, and the “greater than” predicate in terms of the “less than” predicate.
value object MaximalElementopr end
trait HasMaximalElementT extends HasMaximalElementT, ,opr
extends { PartialOrderT, }
where { T coerces MaximalElement≼ }
property ∀(a :T) a MaximalElement≼
end
The HasMaximalElement trait specifies that a partial order has a maximal element, that is, one to which every other
element is related by the ordering predicate . The maximal element may be identified by coercing the object named
MaximalElement≼ to type T .
value object MinimalElementopr end
trait HasMinimalElementT extends HasMinimalElementT, ,opr
extends { PartialOrderT, }
where { T coerces MinimalElement≼ }
property ∀(a :T) MinimalElement≼ a
end
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