The Fortress Language Specification - CiteSeerX

end
extends { ApproximateCommutativeRingT, ⊕, ⊖, ⊗, =,
RingT, ⊕, ⊖, ⊗,
CommutativeT, ⊗ }
A commutative ring is a ring for which the binary operator ⊗ is also commutative.
trait ApproximateDivisionRing T extends ApproximateDivisionRingT, U, ⊕, ⊖, ⊗, ⊘, ≈,
U extends T,
opr ⊕,opr ⊖,opr ⊗,opr ⊘,opr ≈
extends { ApproximateRingT, ⊕, ⊖, ⊗, ≈,
ApproximateGroupU, ⊗, ⊘, ≈ }
property ¬ instanceOf U(castT(Zero⊕))
property ∀(a:T) a ≠ Zero⊕ → instanceOf U(a)
An approximate division ring is an approximate ring for which the binary operator ⊗ also has approximate inverses,
so that the values other than the zero of ⊗ form an approximate group with ⊗ and ⊘ .
trait DivisionRing T extends DivisionRingT, U, ⊕, ⊖, ⊗, ⊘,
U extends T,
opr ⊕,opr ⊖,opr ⊗,opr ⊘
extends { ApproximateDivisionRingT, U, ⊕, ⊖, ⊗, ⊘, =,
RingT, ⊕, ⊖, ⊗,
GroupU, ⊗, ⊘ }
end
A division ring is a ring for which the binary operator ⊗ also has inverses, so that the values other than the zero of ⊗
form a group with ⊗ and ⊘ .
trait ApproximateField T extends ApproximateFieldT, U, ⊕, ⊖, ⊗, ⊘, ≈,
U extends T,
opr ⊕,opr ⊖,opr ⊗,opr ⊘,opr ≈
extends { ApproximateCommutativeRingT, ⊕, ⊖, ⊗, ≈,
ApproximateDivisionRingT, U, ⊕, ⊖, ⊗, ⊘, ≈ }
end
An approximate field is an approximate commutative ring that is also an approximate division ring: the binary operator
⊗ is approximately commutative and also has approximate inverses, so that the values other than the zero of ⊗ form
an approximate Abelian group with ⊗ and ⊘ .
trait FieldT extends FieldT, U, ⊕, ⊖, ⊗, ⊘, U extends T,opr ⊕,opr ⊖,opr ⊗,opr ⊘
extends { ApproximateFieldT, U, ⊕, ⊖, ⊗, ⊘, =,
CommutativeRingT, ⊕, ⊖, ⊗,
DivisionRingT, U, ⊕, ⊖, ⊗, ⊘ }
end
A field is a commutative ring that is also a division ring: the binary operator ⊗ is commutative and also has inverses,
so that the values other than the zero of ⊗ form an Abelian group with ⊗ and ⊘ .
37.5 Boolean Algebras
value object ComplementBoundopr ⊙ end
trait HasComplementsT extends HasComplementsT, ⊙, ∼,opr ⊙,opr ∼
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