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Semantic Algebras

Format for presenting semantic domains

Rational Numbers

Domain Rat = (Z × Z)_{_|_}

Operations

makerat: Z => (Z => Rat)

makerat = lambda p.lambda q.(q=0) => _|_ [] (p,q)

addrat: Rat => (Rat => Rat)

addrat = lambda (p₁,q₁).lambda (p₂,q₂). ((p₁*q₂)+(p₂*q₁), q1*q2)

multrat: Rat => (Rat => Rat)

multrat = lambda (p₁,q₁).lambda (p₂,q₂). (p₁*p₂,q₁*q₂)

Choice function e₁ => e₂ [] e₃
=> e₂, if e₁ = true
=> e₃, if e₁ = false