Type

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• Type Theory
  • Type theory is the study of types.
• A type has normal form
  • In Pie a Type has a normal form just like any other expression would. A type is the same as another type if they share the same normal form.
• A type describes a set of possible values
  • In type theory, a type describes a set of possible values. This is usually used to declare what is possible to exist within a variable.
• A type is the same as another type if they share a normal form
  • In Pie, any two Types which share the same normal form are the same type. They are effectively isomorphic. Therefore
• The normal form of an expression is determined by the type of the expression
  • Because the normal form of an expression has a constructor for a type on top, asking for the normal form of an expression without a Type is meaningless in Pie. It isn't possible to normalise anything without type information.