src/HOLCF/Sprod1.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/Sprod1.ML
    ID:         $Id$
    Author:     Franz Regensburger
    Copyright   1993  Technische Universitaet Muenchen

Lemmas for theory Sprod1.thy
*)

open Sprod1;

(* ------------------------------------------------------------------------ *)
(* less_sprod is a partial order on Sprod                                   *)
(* ------------------------------------------------------------------------ *)

qed_goalw "refl_less_sprod" thy [less_sprod_def]"less (p::'a ** 'b) p"
(fn prems => [(fast_tac (HOL_cs addIs [refl_less]) 1)]);

qed_goalw "antisym_less_sprod" thy [less_sprod_def]
        "[|less (p1::'a ** 'b) p2;less p2 p1|] ==> p1=p2"
(fn prems =>
        [
        (cut_facts_tac prems 1),
        (rtac Sel_injective_Sprod 1),
        (fast_tac (HOL_cs addIs [antisym_less]) 1),
        (fast_tac (HOL_cs addIs [antisym_less]) 1)
        ]);

qed_goalw "trans_less_sprod" thy [less_sprod_def]
        "[|less (p1::'a**'b) p2;less p2 p3|] ==> less p1 p3"
(fn prems =>
        [
        (cut_facts_tac prems 1),
        (rtac conjI 1),
        (fast_tac (HOL_cs addIs [trans_less]) 1),
        (fast_tac (HOL_cs addIs [trans_less]) 1)
        ]);