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- No more "and", "or", "implies", "iff", and "~".
  Use "/\", "\/", "->", "<->", and "not" instead.

- No more "logic". Use "function" or "predicate".

new theory number for... number theory

  in the logic language into (more or less) higher-order style.
  For example,

    logic func (x : int, y : int, 'a list) : (int, 'a) map list

    logic pred (bool, int * real)

  is now written:
    
    logic func (x y : int) (list 'a) : list (map int 'a)

    logic pred bool (int, real)

  Note that types use prefix notation (as in Coq) and the types
  of tuples are now written as (type1, type2, ..., typeN).

- Use the same syntax of type expressions in the program language.

- Allow binders of the form (x y:int) in the program language.
  

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