Expressions

• An ``expression'' is an array expression.

  An expression node may correspond to a complete temporary array constructed at run-time, or through some process of interpretation (akin to interpretation of the mooted of forall scripts) it may simply correspond to a scalar temporary inside a loop in some ``node code''.

  The classes for expressions parallel the classes for arrays:

       ExprInt, ExprFloat, ExprDouble, ...
  

• The shape and mapping of an expression are defined by an unordered set of orthogonal index ranges.
• An array is an expression. It's shape and mapping are defined by the set of ranges of the array.
• A range is an integer expression. It's shape and mapping are defined by the singleton set containing the range itself.
• Members on the expression class provide arithmetic, eg

       b.plus(c)
  

  corresponds to the array expression

       b + c
  

  The shape of the result is the union of the shape of the addend and the argument. The operation is illegal if this union contains any non-orthogonal range pairs.

  Certain arithmetic coercions can be defined by overloading plus, eg

       ExprInt   ExprInt :: plus(ExprInt) ;
  
       ExprFloat ExprInt :: plus(ExprFloat) ;
  
       ExprFloat ExprFloat :: plus(ExprFloat) ;
  
       ExprFloat ExprFloat :: plus(ExprInt) ;
  

  Other analogous members (times, if, and so on) are provided.