The Fortress Language Specification - CiteSeerX

opr ⊗,opr ⊕,opr ≈
extends { BinaryOperatorT, ⊗, BinaryOperatorT, ⊕, ReflexiveT, ≈, SymmetricT, ≈ }
property ∀(a:T, b: T, c:T) (a ⊗ (b ⊕ c)) :≈: ((a ⊗ b) ⊕ (a ⊗ c))
end
The trait ApproximatelyLeftDistributive requires the operator ⊗ to be approximately left distributive over the
operator ⊕ ; that is, the expressions a ⊗ (b ⊕ c) and (a ⊗ b) ⊕ (a ⊗ c) always produce results that are “close enough”
to each other as determined by the specified ≈ predicate.
trait LeftDistributiveT extends LeftDistributiveT, ⊗, ⊕,opr ⊗,opr ⊕
extends { ApproximatelyLeftDistributiveT, ⊗, ⊕, =, EquivalenceRelationT, = }
end
The trait LeftDistributive requires the operator ⊗ to be left distributive over the operator ⊕ ; that is, the expressions
a ⊗ (b ⊕ c) and (a ⊗ b) ⊕ (a ⊗ c) always produce equal results.
trait ApproximatelyRightDistributiveT extends ApproximatelyRightDistributiveT, ⊗, ⊕, ≈,
opr ⊗,opr ⊕,opr ≈
extends { BinaryOperatorT, ⊗, BinaryOperatorT, ⊕, ReflexiveT, ≈, SymmetricT, ≈ }
property ∀(a:T, b: T, c:T) ((a ⊕ b) ⊗ c) :≈: ((a ⊗ c) ⊕ (b ⊗ c))
end
The trait ApproximatelyRightDistributive requires the operator ⊗ to be approximately right distributive over the
operator ⊕ ; that is, the expressions (a ⊕ b) ⊗ c and (a ⊗ c) ⊕ (b ⊗ c) always produce results that are “close enough”
to each other as determined by the specified ≈ predicate.
trait RightDistributiveT extends RightDistributiveT, ⊗, ⊕,opr ⊗,opr ⊕
extends { ApproximatelyRightDistributiveT, ⊗, ⊕, =, EquivalenceRelationT, = }
end
The trait RightDistributive requires the operator ⊗ to be right distributive over the operator ⊕ ; that is, the expressions
(a ⊕ b) ⊗ c and (a ⊗ c) ⊕ (b ⊗ c) always produce equal results.
trait ApproximatelyDistributiveT extends ApproximatelyDistributiveT, ⊗, ⊕, ≈,
opr ⊗,opr ⊕,opr ≈
extends { ApproximatelyLeftDistributiveT, ⊗, ⊕, ≈,
ApproximatelyRightDistributiveT, ⊗, ⊕, ≈ }
end
The trait ApproximatelyDistributive requires the operator ⊗ to be both approximately left distributive and approximately
right distributive over the operator ⊕ .
trait DistributiveT extends DistributiveT, ⊗, ⊕,opr ⊗,opr ⊕
extends { ApproximatelyDistributiveT, ⊗, ⊕, =, LeftDistributiveT, ⊗, ⊕, RightDistributiveT, ⊗, ⊕ }
end
The trait Distributive requires the operator ⊗ to be both left distributive and right distributive over the operator ⊕ .
trait HasLeftIdentityT extends HasLeftIdentityT, ⊙,opr ⊙
extends { BinaryOperatorT, ⊙, EquivalenceRelationT, = }
isLeftIdentity():Boolean
property ∀(a:T, b: T) a.isLeftIdentity() →: ((a ⊙ b) = b)
end
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