)abbrev category TYPE Type
++ The new fundamental Type
++ Author: Richard Jenks
++ Date Created: 14 May 1992
++ Description: The fundamental Type;
Type() : Category == with ()

)abbrev category KOERCE CoercibleTo
++ Category for coerce
++ Author: Manuel Bronstein
++ 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 KOERCEF CoercibleFrom
++ Category for coerce
++ Description:
++ A is coercible to B means any element of A can automatically be
++ converted into an element of B by the interpreter.
CoercibleFrom(S : Type) : Category == with
    coerce : S -> %
      ++ coerce(a) transforms a into an element of %.


)abbrev category KONVERT ConvertibleTo
++ Category for convert
++ Author: Manuel Bronstein
++ 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 KONVERF ConvertibleFrom
++ Category for convert
++ Author: Manuel Bronstein
++ 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.
ConvertibleFrom(S : Type) : Category == with
    convert : S -> %
      ++ convert(a) transforms a into element of %.


)abbrev category RETRACT RetractableTo
++ Category for retract
++ Author: ???
++ Description:
++ A is retractable to B means that some elements of 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


)abbrev category RETFROM RetractableFrom
++ Category for retract
++ Author: Johannes Grabmeier
++ Date Created: 25.09.2010
++ Description:
++ B is retractable from A means that some elements in A can be converted
++ into elements of B and any element of B can be converted into an
++ element of A.
RetractableFrom(S : Type) : Category == CoercibleTo(S) with
    retractIfCan : S -> Union(%,"failed")
      ++ retractIfCan(a) transforms a into an element of % if possible.
      ++ Returns "failed" if a cannot be made into an element of %.
    retract :      S -> %
      ++ retract(a) transforms a into an element of % if possible.
      ++ Error: if a cannot be made into an element of %.
  add
    retract(s) ==
      (u := retractIfCan s) case "failed" => error "not retractable"
      u

--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
--    - Redistributions of source code must retain the above copyright
--      notice, this list of conditions and the following disclaimer.
--
--    - Redistributions in binary form must reproduce the above copyright
--      notice, this list of conditions and the following disclaimer in
--      the documentation and/or other materials provided with the
--      distribution.
--
--    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
--      names of its contributors may be used to endorse or promote products
--      derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
