author | paulson |
Fri, 21 Nov 2003 11:15:40 +0100 | |
changeset 14265 | 95b42e69436c |
parent 12030 | 46d57d0290a2 |
child 14981 | e73f8140af78 |
permissions | -rw-r--r-- |
2278 | 1 |
(* Title: HOLCF/Up3.ML |
2 |
ID: $Id$ |
|
3 |
Author: Franz Regensburger |
|
12030 | 4 |
License: GPL (GNU GENERAL PUBLIC LICENSE) |
2278 | 5 |
|
9169 | 6 |
Class instance of ('a)u for class pcpo |
2278 | 7 |
*) |
8 |
||
2640 | 9 |
(* for compatibility with old HOLCF-Version *) |
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Goal "UU = Abs_Up(Inl ())"; |
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by (simp_tac (HOL_ss addsimps [UU_def,UU_up_def]) 1); |
|
12 |
qed "inst_up_pcpo"; |
|
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|
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(* -------------------------------------------------------------------------*) |
15 |
(* some lemmas restated for class pcpo *) |
|
16 |
(* ------------------------------------------------------------------------ *) |
|
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||
9169 | 18 |
Goal "~ Iup(x) << UU"; |
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by (stac inst_up_pcpo 1); |
|
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by (rtac less_up2b 1); |
|
21 |
qed "less_up3b"; |
|
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|
9169 | 23 |
Goal "Iup(x) ~= UU"; |
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by (stac inst_up_pcpo 1); |
|
25 |
by (rtac defined_Iup 1); |
|
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qed "defined_Iup2"; |
|
10230 | 27 |
AddIffs [defined_Iup2]; |
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|
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(* ------------------------------------------------------------------------ *) |
|
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(* continuity for Iup *) |
|
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(* ------------------------------------------------------------------------ *) |
|
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||
9169 | 33 |
Goal "contlub(Iup)"; |
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by (rtac contlubI 1); |
|
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by (strip_tac 1); |
|
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by (rtac trans 1); |
|
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by (rtac (thelub_up1a RS sym) 2); |
|
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by (fast_tac HOL_cs 3); |
|
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by (etac (monofun_Iup RS ch2ch_monofun) 2); |
|
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by (res_inst_tac [("f","Iup")] arg_cong 1); |
|
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by (rtac lub_equal 1); |
|
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by (atac 1); |
|
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by (rtac (monofun_Ifup2 RS ch2ch_monofun) 1); |
|
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by (etac (monofun_Iup RS ch2ch_monofun) 1); |
|
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by (asm_simp_tac Up0_ss 1); |
|
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qed "contlub_Iup"; |
|
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|
9169 | 48 |
Goal "cont(Iup)"; |
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by (rtac monocontlub2cont 1); |
|
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by (rtac monofun_Iup 1); |
|
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by (rtac contlub_Iup 1); |
|
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qed "cont_Iup"; |
|
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AddIffs [cont_Iup]; |
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|
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(* ------------------------------------------------------------------------ *) |
|
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(* continuity for Ifup *) |
|
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(* ------------------------------------------------------------------------ *) |
|
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||
9169 | 59 |
Goal "contlub(Ifup)"; |
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by (rtac contlubI 1); |
|
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by (strip_tac 1); |
|
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by (rtac trans 1); |
|
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by (rtac (thelub_fun RS sym) 2); |
|
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by (etac (monofun_Ifup1 RS ch2ch_monofun) 2); |
|
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by (rtac ext 1); |
|
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by (res_inst_tac [("p","x")] upE 1); |
|
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by (asm_simp_tac Up0_ss 1); |
|
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by (rtac (lub_const RS thelubI RS sym) 1); |
|
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by (asm_simp_tac Up0_ss 1); |
|
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by (etac contlub_cfun_fun 1); |
|
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qed "contlub_Ifup1"; |
|
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|
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||
8161 | 74 |
Goal "contlub(Ifup(f))"; |
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by (rtac contlubI 1); |
|
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by (strip_tac 1); |
|
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by (rtac disjE 1); |
|
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by (stac thelub_up1a 2); |
|
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by (atac 2); |
|
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by (atac 2); |
|
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by (asm_simp_tac Up0_ss 2); |
|
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by (stac thelub_up1b 3); |
|
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by (atac 3); |
|
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by (atac 3); |
|
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by (fast_tac HOL_cs 1); |
|
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by (asm_simp_tac Up0_ss 2); |
|
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by (rtac (chain_UU_I_inverse RS sym) 2); |
|
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by (rtac allI 2); |
|
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by (res_inst_tac [("p","Y(i)")] upE 2); |
|
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by (asm_simp_tac Up0_ss 2); |
|
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by (rtac notE 2); |
|
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by (dtac spec 2); |
|
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by (etac spec 2); |
|
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by (atac 2); |
|
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by (stac contlub_cfun_arg 1); |
|
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by (etac (monofun_Ifup2 RS ch2ch_monofun) 1); |
|
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by (rtac lub_equal2 1); |
|
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by (rtac (monofun_Rep_CFun2 RS ch2ch_monofun) 2); |
|
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by (etac (monofun_Ifup2 RS ch2ch_monofun) 2); |
|
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by (etac (monofun_Ifup2 RS ch2ch_monofun) 2); |
|
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by (rtac (chain_mono2 RS exE) 1); |
|
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by (atac 2); |
|
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by (etac exE 1); |
|
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by (etac exE 1); |
|
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by (rtac exI 1); |
|
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by (res_inst_tac [("s","Iup(x)"),("t","Y(i)")] ssubst 1); |
|
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by (atac 1); |
|
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by (rtac defined_Iup2 1); |
|
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by (rtac exI 1); |
|
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by (strip_tac 1); |
|
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by (res_inst_tac [("p","Y(i)")] upE 1); |
|
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by (asm_simp_tac Up0_ss 2); |
|
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by (res_inst_tac [("P","Y(i) = UU")] notE 1); |
|
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by (fast_tac HOL_cs 1); |
|
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by (stac inst_up_pcpo 1); |
|
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by (atac 1); |
|
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qed "contlub_Ifup2"; |
|
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|
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Goal "cont(Ifup)"; |
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by (rtac monocontlub2cont 1); |
|
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by (rtac monofun_Ifup1 1); |
|
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by (rtac contlub_Ifup1 1); |
|
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qed "cont_Ifup1"; |
|
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|
9169 | 125 |
Goal "cont(Ifup(f))"; |
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by (rtac monocontlub2cont 1); |
|
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by (rtac monofun_Ifup2 1); |
|
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by (rtac contlub_Ifup2 1); |
|
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qed "cont_Ifup2"; |
|
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|
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||
132 |
(* ------------------------------------------------------------------------ *) |
|
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(* continuous versions of lemmas for ('a)u *) |
|
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(* ------------------------------------------------------------------------ *) |
|
135 |
||
10834 | 136 |
Goalw [up_def] "z = UU | (EX x. z = up$x)"; |
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by (simp_tac (Up0_ss addsimps [cont_Iup]) 1); |
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by (stac inst_up_pcpo 1); |
|
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by (rtac Exh_Up 1); |
|
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qed "Exh_Up1"; |
|
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|
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Goalw [up_def] "up$x=up$y ==> x=y"; |
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by (rtac inject_Iup 1); |
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by Auto_tac; |
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qed "inject_up"; |
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|
10834 | 147 |
Goalw [up_def] " up$x ~= UU"; |
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by Auto_tac; |
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qed "defined_up"; |
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|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9245
diff
changeset
|
151 |
val prems = Goalw [up_def] |
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"[| p=UU ==> Q; !!x. p=up$x==>Q|] ==>Q"; |
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by (rtac upE 1); |
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by (resolve_tac prems 1); |
|
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by (etac (inst_up_pcpo RS ssubst) 1); |
|
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by (resolve_tac (tl prems) 1); |
|
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by (asm_simp_tac (Up0_ss addsimps [cont_Iup]) 1); |
|
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qed "upE1"; |
|
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|
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val tac = (simp_tac (simpset() addsimps [cont_Iup,cont_Ifup1, |
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cont_Ifup2,cont2cont_CF1L]) 1); |
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|
10834 | 163 |
Goalw [up_def,fup_def] "fup$f$UU=UU"; |
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by (stac inst_up_pcpo 1); |
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by (stac beta_cfun 1); |
|
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by tac; |
|
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by (stac beta_cfun 1); |
|
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by tac; |
|
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by (simp_tac (Up0_ss addsimps [cont_Iup,cont_Ifup1,cont_Ifup2]) 1); |
|
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qed "fup1"; |
|
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|
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Goalw [up_def,fup_def] "fup$f$(up$x)=f$x"; |
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by (stac beta_cfun 1); |
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by (rtac cont_Iup 1); |
|
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by (stac beta_cfun 1); |
|
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by tac; |
|
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by (stac beta_cfun 1); |
|
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by (rtac cont_Ifup2 1); |
|
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by (simp_tac (Up0_ss addsimps [cont_Iup,cont_Ifup1,cont_Ifup2]) 1); |
|
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qed "fup2"; |
|
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|
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Goalw [up_def,fup_def] "~ up$x << UU"; |
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by (simp_tac (Up0_ss addsimps [cont_Iup]) 1); |
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by (rtac less_up3b 1); |
|
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qed "less_up4b"; |
|
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|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9245
diff
changeset
|
187 |
Goalw [up_def,fup_def] |
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"(up$x << up$y) = (x<<y)"; |
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by (simp_tac (Up0_ss addsimps [cont_Iup]) 1); |
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by (rtac less_up2c 1); |
|
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qed "less_up4c"; |
|
2278 | 192 |
|
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9245
diff
changeset
|
193 |
Goalw [up_def,fup_def] |
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"[| chain(Y); EX i x. Y(i) = up$x |] ==>\ |
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\ lub(range(Y)) = up$(lub(range(%i. fup$(LAM x. x)$(Y i))))"; |
|
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by (stac beta_cfun 1); |
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by tac; |
|
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by (stac beta_cfun 1); |
|
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by tac; |
|
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by (stac (beta_cfun RS ext) 1); |
|
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by tac; |
|
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by (rtac thelub_up1a 1); |
|
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by (atac 1); |
|
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by (etac exE 1); |
|
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by (etac exE 1); |
|
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by (rtac exI 1); |
|
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by (rtac exI 1); |
|
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by (etac box_equals 1); |
|
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by (rtac refl 1); |
|
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by (simp_tac (Up0_ss addsimps [cont_Iup]) 1); |
|
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qed "thelub_up2a"; |
|
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|
213 |
||
214 |
||
9248
e1dee89de037
massive tidy-up: goal -> Goal, remove use of prems, etc.
paulson
parents:
9245
diff
changeset
|
215 |
Goalw [up_def,fup_def] |
10834 | 216 |
"[| chain(Y); ! i x. Y(i) ~= up$x |] ==> lub(range(Y)) = UU"; |
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by (stac inst_up_pcpo 1); |
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by (rtac thelub_up1b 1); |
|
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by (atac 1); |
|
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by (strip_tac 1); |
|
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by (dtac spec 1); |
|
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by (dtac spec 1); |
|
10230 | 223 |
by (asm_full_simp_tac (Up0_ss addsimps [cont_Iup]) 1); |
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qed "thelub_up2b"; |
2278 | 225 |
|
226 |
||
10834 | 227 |
Goal "(EX x. z = up$x) = (z~=UU)"; |
9169 | 228 |
by (rtac iffI 1); |
229 |
by (etac exE 1); |
|
230 |
by (hyp_subst_tac 1); |
|
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by (rtac defined_up 1); |
|
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by (res_inst_tac [("p","z")] upE1 1); |
|
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by (etac notE 1); |
|
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by (atac 1); |
|
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by (etac exI 1); |
|
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qed "up_lemma2"; |
|
2278 | 237 |
|
238 |
||
10834 | 239 |
Goal "[| chain(Y); lub(range(Y)) = up$x |] ==> EX i x. Y(i) = up$x"; |
9169 | 240 |
by (rtac exE 1); |
241 |
by (rtac chain_UU_I_inverse2 1); |
|
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by (rtac (up_lemma2 RS iffD1) 1); |
|
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by (etac exI 1); |
|
244 |
by (rtac exI 1); |
|
245 |
by (rtac (up_lemma2 RS iffD2) 1); |
|
246 |
by (atac 1); |
|
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qed "thelub_up2a_rev"; |
|
2278 | 248 |
|
10834 | 249 |
Goal "[| chain(Y); lub(range(Y)) = UU |] ==> ! i x. Y(i) ~= up$x"; |
10230 | 250 |
by (blast_tac (claset() addSDs [chain_UU_I RS spec, |
251 |
exI RS (up_lemma2 RS iffD1)]) 1); |
|
9169 | 252 |
qed "thelub_up2b_rev"; |
2278 | 253 |
|
254 |
||
9169 | 255 |
Goal "chain(Y) ==> lub(range(Y)) = UU | \ |
10834 | 256 |
\ lub(range(Y)) = up$(lub(range(%i. fup$(LAM x. x)$(Y i))))"; |
9169 | 257 |
by (rtac disjE 1); |
258 |
by (rtac disjI1 2); |
|
259 |
by (rtac thelub_up2b 2); |
|
260 |
by (atac 2); |
|
261 |
by (atac 2); |
|
262 |
by (rtac disjI2 2); |
|
263 |
by (rtac thelub_up2a 2); |
|
264 |
by (atac 2); |
|
265 |
by (atac 2); |
|
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by (fast_tac HOL_cs 1); |
|
267 |
qed "thelub_up3"; |
|
2278 | 268 |
|
10834 | 269 |
Goal "fup$up$x=x"; |
9169 | 270 |
by (res_inst_tac [("p","x")] upE1 1); |
271 |
by (asm_simp_tac ((simpset_of Cfun3.thy) addsimps [fup1,fup2]) 1); |
|
272 |
by (asm_simp_tac ((simpset_of Cfun3.thy) addsimps [fup1,fup2]) 1); |
|
273 |
qed "fup3"; |
|
2278 | 274 |
|
275 |
(* ------------------------------------------------------------------------ *) |
|
276 |
(* install simplifier for ('a)u *) |
|
277 |
(* ------------------------------------------------------------------------ *) |
|
278 |
||
3327 | 279 |
Addsimps [fup1,fup2,defined_up]; |