src/HOLCF/Lift1.ML

Changes of HOLCF from Oscar Slotosch:

1. axclass instead of class
* less instead of
less_fun,
less_cfun,
less_sprod,
less_cprod,
less_ssum,
less_up,
less_lift
* @x.!y.x<<y instead of UUU instead of
UU_fun, UU_cfun, ...
* no witness type void needed (eliminated Void.thy.Void.ML)
* inst_<typ>_<class> derived as theorems

2. improved some proves on less_sprod and less_cprod
* eliminated the following theorems
Sprod1.ML: less_sprod1a
Sprod1.ML: less_sprod1b
Sprod1.ML: less_sprod2a
Sprod1.ML: less_sprod2b
Sprod1.ML: less_sprod2c
Sprod2.ML: less_sprod3a
Sprod2.ML: less_sprod3b
Sprod2.ML: less_sprod4b
Sprod2.ML: less_sprod4c
Sprod3.ML: less_sprod5b
Sprod3.ML: less_sprod5c
Cprod1.ML: less_cprod1b
Cprod1.ML: less_cprod2a
Cprod1.ML: less_cprod2b
Cprod1.ML: less_cprod2c
Cprod2.ML: less_cprod3a
Cprod2.ML: less_cprod3b

3. new classes:
* cpo<po,
* chfin<pcpo,
* flat<pcpo,
* derived: flat<chfin
to do: show instances for lift

4. Data Type One
* Used lift for the definition: one = unit lift
* Changed the constant one into ONE

5. Data Type Tr
* Used lift for the definition: tr = bool lift
* adopted definitions of if,andalso,orelse,neg
* only one theory Tr.thy,Tr.ML instead of
Tr1.thy,Tr1.ML, Tr2.thy,Tr2.ML
* reintroduced ceils for =TT,=FF

6. typedef
* Using typedef instead of faking type definitions
to do: change fapp, fabs from Cfun1 to Rep_Cfun, Abs_Cfun

7. adopted examples and domain construct to theses changes

These changes eliminated all rules and arities from HOLCF

(*  Title:      HOLCF/Lift1.ML
    ID:         $Id$
    Author:     Olaf Mueller, Robert Sandner
    Copyright   1996 Technische Universitaet Muenchen

Theorems for Lift1.thy
*)


open Lift1;

(* ------------------------------------------------------------------------ *)
(* less_lift is a partial order on type 'a -> 'b                            *)
(* ------------------------------------------------------------------------ *)

goalw thy [less_lift_def] "less (x::'a lift) x";
by (fast_tac HOL_cs 1);
qed"refl_less_lift";

val prems = goalw thy [less_lift_def] 
  "[|less (x1::'a lift) x2; less x2 x1|] ==> x1 = x2";
by (cut_facts_tac prems 1);
by (fast_tac HOL_cs 1);
qed"antisym_less_lift";

val prems = goalw Lift1.thy [less_lift_def] 
  "[|less (x1::'a lift) x2; less x2 x3|] ==> less x1 x3";
by (cut_facts_tac prems 1);
by (fast_tac HOL_cs 1);
qed"trans_less_lift";