src/HOLCF/ccc1.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/ccc1.thy
    ID:         $Id$
    Author:     Franz Regensburger
    Copyright   1993 Technische Universitaet Muenchen

Merge Theories Cprof, Sprod, Ssum, Up, Fix and
define constants for categorical reasoning
*)

ccc1 = Cprod3 + Sprod3 + Ssum3 + Up3 + Fix + 

instance flat<chfin (flat_subclass_chfin)

consts
        ID      :: "'a -> 'a"
        cfcomp  :: "('b->'c)->('a->'b)->'a->'c"

syntax  "@oo"   :: "('b->'c)=>('a->'b)=>'a->'c" ("_ oo _" [101,100] 100)
     
translations    "f1 oo f2" == "cfcomp`f1`f2"

defs

  ID_def        "ID ==(LAM x.x)"
  oo_def        "cfcomp == (LAM f g x.f`(g`x))" 

end