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)abbrev category FEVALAB FullyEvalableOver
++ Date Last Updated: June 3, 1991
++ Description:
++ This category provides a selection of evaluation operations
++ depending on what the argument type R provides.

FullyEvalableOver(R) : Category == SIG where
  R : SetCategory

  SIG ==> with

    map : (R -> R, $) -> $
      ++ map(f, ex) evaluates ex, applying f to values of type R in ex.

    if R has Eltable(R, R) then Eltable(R, $)

    if R has Evalable(R) then Evalable(R)

    if R has InnerEvalable(Symbol, R) then InnerEvalable(Symbol, R)

   add

     if R has Eltable(R, R) then

       elt(x:$, r:R) == map(y +-> y(r), x)

     if R has Evalable(R) then

       eval(x:$, l:List Equation R) == map(y +-> eval(y, l), x)

     if R has InnerEvalable(Symbol, R) then

       eval(x:$, ls:List Symbol, lv:List R) == map(y +-> eval(y, ls, lv), x)