src/HOLCF/Porder0.thy

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/Porder0.thy
    ID:         $Id$
    Author:     Franz Regensburger
    Copyright   1993 Technische Universitaet Muenchen

Definition of class porder (partial order)

*)

Porder0 = Nat +

(* first the global constant for HOLCF type classes *)
consts
  "less"        :: "['a,'a] => bool" (infixl "\\<sqsubseteq>\\<sqsubseteq>" 55)

axclass po < term
        (* class axioms: *)
ax_refl_less       "less x x"        
ax_antisym_less    "[|less x y; less y x |] ==> x = y"    
ax_trans_less      "[|less x y; less y z |] ==> less x z"
 
	(* characteristic constant << on po *)
consts
  "<<"          :: "['a,'a::po] => bool"        (infixl 55)

syntax (symbols)
  "op <<"       :: "['a,'a::po] => bool"        (infixl "\\<sqsubseteq>" 55)

defs
po_def             "(op <<) == less"
end