src/HOLCF/One.thy

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(*  Title:      HOLCF/one.thy
    ID:         $Id$
    Author:     Franz Regensburger
    Copyright   1993 Technische Universitaet Muenchen

Introduce atomic type one = (void)u

The type is axiomatized as the least solution of a domain equation.
The functor term that specifies the domain equation is: 

  FT = <U,K_{void}>

For details see chapter 5 of:

[Franz Regensburger] HOLCF: Eine konservative Erweiterung von HOL um LCF,
                     Dissertation, Technische Universit"at M"unchen, 1994

*)

One = ccc1+

types one 0
arities one :: pcpo

consts
        abs_one         :: "(void)u -> one"
        rep_one         :: "one -> (void)u"
        one             :: "one"
        one_when        :: "'c -> one -> 'c"

rules
  abs_one_iso   "abs_one`(rep_one`u) = u"
  rep_one_iso   "rep_one`(abs_one`x) = x"

defs
  one_def       "one == abs_one`(up`UU)"
  one_when_def "one_when == (LAM c u.lift`(LAM x.c)`(rep_one`u))"

translations
  "case l of one => t1" == "one_when`t1`l"

end