Functions as Equations

• The graph representation of a function provides insight into its structure but is inconvenient to use in practice.

• add : (N x N) ? N

  • add(m, n) = m+ n

• duplicate : R ? R x R, = {1, 4, 7}

  • duplicate(r) = (r, r)

• which : (B +N) ? {isbool, isnum}

  which(m) = cases m of isB(b) ? isbool; isN(n) ? isnum end
  

• singleton : N ? P(N)

  • singleton(n) = {n}

• nothing : B N ? B

  • no equational definition (domain empty)!

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