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/Cprod1.ML
ID: $Id$
Author: Franz Regensburger
Copyright 1993 Technische Universitaet Muenchen
Lemmas for theory Cprod1.thy
*)
open Cprod1;
(* ------------------------------------------------------------------------ *)
(* less_cprod is a partial order on 'a * 'b *)
(* ------------------------------------------------------------------------ *)
qed_goal "Sel_injective_cprod" Prod.thy
"[|fst x = fst y; snd x = snd y|] ==> x = y"
(fn prems =>
[
(cut_facts_tac prems 1),
(subgoal_tac "(fst x,snd x)=(fst y,snd y)" 1),
(rotate_tac ~1 1),
(asm_full_simp_tac(HOL_ss addsimps[surjective_pairing RS sym])1),
(Asm_simp_tac 1)
]);
qed_goalw "refl_less_cprod" Cprod1.thy [less_cprod_def] "less (p::'a*'b) p"
(fn prems => [Simp_tac 1]);
qed_goalw "antisym_less_cprod" thy [less_cprod_def]
"[|less (p1::'a * 'b) p2;less p2 p1|] ==> p1=p2"
(fn prems =>
[
(cut_facts_tac prems 1),
(rtac Sel_injective_cprod 1),
(fast_tac (HOL_cs addIs [antisym_less]) 1),
(fast_tac (HOL_cs addIs [antisym_less]) 1)
]);
qed_goalw "trans_less_cprod" thy [less_cprod_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)
]);