Type Systems

Example ?-calculus language:

• C = I ? F where

  I = {…, -2, -1, 0, 1, 2 …}
  
  F = {+, -, *, / }

• V = {a, b, … z, aa, … }

• B = {int}

• ?(i) = int for i ? I; ?(f) = int ? (int ? int)

• What is type of (?f: int ? int (?g: int ? int (?x: int (f (g x)))))?

  (int ? int) ? ((int ? int) ? (int ? int))
  
  which is the “curried” form of
  (int ? int) ? (int ? int) ? (int ? int)

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