--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
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--Copyright (C) 2007-2008, Gabriel Dos Reis.
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)abbrev category TYPE Type
++ Author: Richard Jenks
++ Date Created: 14 May 1992
++ Date Last Updated: February 12, 2012
++ Description: The fundamental Type;
Type(): Category == Join()

)abbrev category UTYPE UnionType
++ Author: Gabriel Dos Reis
++ Date Created: December 17, 2007
++ Date Last Modified: December 17, 2007
++ Description: The category of domains that act like unions.
++ UnionType, like Type or Category, acts mostly as a take that
++ communicates `union-like' intended semantics to the compiler.
++ A domain D that satifies UnionType should provide definitions
++ for `case' operators, with corresponding `autoCoerce' operators.
UnionType(): Category == with nil
)abbrev category KOERCE CoercibleTo
++ Category for coerce
++ Author: Manuel Bronstein
++ Date Created: ???
++ Date Last Updated: 14 May 1991
++ Description:
++ A is coercible to B means any element of A can automatically be
++ converted into an element of B by the interpreter.
CoercibleTo(S:Type): Category == with
    coerce: % -> S
      ++ coerce(a) transforms a into an element of S.

)abbrev category KRCFROM CoercibleFrom
++ Author: Gabriel Dos Reis
++ Date Create: November 19, 2008
++ Date Last Modified: November 19, 2008
++ See Also: CoercibleTo
++ Description:
++   A is coercible from B iff any element of domain B can be
++   automically converted into an element of domain A. 
CoercibleFrom(S: Type): Category == with
  coerce: S -> %
    ++ coerce(s) transforms `s' into an element of `%'.

)abbrev category HOMOTOP HomotopicTo
++ Author: Gabriel Dos Reis
++ Date Create: November 19, 2008
++ Date Last Modified: November 19, 2008
++ See Also: CoercibleTo, CoercibleFrom
++ Description:
++   A is homotopic to B iff any element of domain B can be
++   automically converted into an element of domain B, and nay
++   element of domain B can be automatically converted into an A.
HomotopicTo(S: Type): Category ==  Join(CoercibleTo S, CoercibleFrom S)


)abbrev category KONVERT ConvertibleTo
++ Category for convert
++ Author: Manuel Bronstein
++ Date Created: ???
++ Date Last Updated: 14 May 1991
++ Description:
++ A is convertible to B means any element of A
++ can be converted into an element of B,
++ but not automatically by the interpreter.
ConvertibleTo(S:Type): Category == with
    convert: % -> S
      ++ convert(a) transforms a into an element of S.

)abbrev category KVTFROM ConvertibleFrom
++ Author: Gabriel Dos Reis
++ Date Create: November 19, 2008
++ Date Last Modified: November 19, 2008
++ See Also: ConvertibleTo
++ Description:
++   A is convertible from B iff any element of domain B can be
++   explicitly converted into an element of domain A. 
ConvertibleFrom(S: Type): Category == with
  convert: S -> %
    ++ convert(s) transforms `s' into an element of `%'.

)abbrev category RETRACT RetractableTo
++ Category for retract
++ Author: ???
++ Date Created: ???
++ Date Last Updated: November 19, 2008
++ Related Constructor: CoercibleFrom
++ Description:
++ A is retractable to B means that some elementsif A can be converted
++ into elements of B and any element of B can be converted into an
++ element of A.
RetractableTo(S: Type): Category == CoercibleFrom S with
    retractIfCan: % -> Union(S,"failed")
      ++ retractIfCan(a) transforms a into an element of S if possible.
      ++ Returns "failed" if a cannot be made into an element of S.
    retract:      % -> S
      ++ retract(a) transforms a into an element of S if possible.
      ++ Error: if a cannot be made into an element of S.
  add
    retract(s) ==
      (u:=retractIfCan s) case "failed" => error "not retractable"
      u

