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import SetCategory
import Type
import List
)abbrev category IEVALAB InnerEvalable
-- FOR THE BENEFIT OF LIBAX0 GENERATION
++ Author:
++ Date Created:
++ Date Last Updated: June 3, 1991
++ Basic Operations:
++ Related Domains:
++ Also See: Evalable
++ AMS Classifications:
++ Keywords: equation
++ Examples:
++ References:
++ Description:
++   This category provides \spadfun{eval} operations.
++   A domain may belong to this category if it is possible to make
++   ``evaluation'' substitutions.  The difference between this
++   and \spadtype{Evalable} is that the operations in this category
++   specify the substitution as a pair of arguments rather than as
++   an equation.
InnerEvalable(A:SetCategory, B:Type): Category == with
    eval: ($, A, B) -> $
       ++ eval(f, x, v) replaces x by v in f.
    eval: ($, List A, List B) -> $
       ++ eval(f, [x1,...,xn], [v1,...,vn]) replaces xi by vi in f.
 add
    eval(f:$, x:A, v:B) == eval(f, [x], [v])

import SetCategory
import InnerEvalable
import Equation
import List
)abbrev category EVALAB Evalable
++ Author:
++ Date Created:
++ Date Last Updated: June 3, 1991
++ Basic Operations:
++ Related Domains:
++ Also See: FullyEvalable
++ AMS Classifications:
++ Keywords: equation
++ Examples:
++ References:
++ Description:
++   This category provides \spadfun{eval} operations.
++   A domain may belong to this category if it is possible to make
++   ``evaluation'' substitutions.
Evalable(R:SetCategory): Category == InnerEvalable(R,R) with
    eval: ($, Equation R) -> $
       ++ eval(f,x = v) replaces x by v in f.
    eval: ($, List Equation R) -> $
       ++ eval(f, [x1 = v1,...,xn = vn]) replaces xi by vi in f.
 add
    eval(f:$, eq:Equation R) == eval(f, [eq])
    eval(f:$, xs:List R,vs:List R) == eval(f,[x=v for x in xs for v in vs])

