author | paulson |
Mon, 11 Mar 1996 14:16:35 +0100 | |
changeset 1566 | a203d206fab7 |
parent 1461 | 6bcb44e4d6e5 |
child 1675 | 36ba4da350c3 |
permissions | -rw-r--r-- |
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(* Title: HOLCF/cfun3.ML |
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ID: $Id$ |
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Author: Franz Regensburger |
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Copyright 1993 Technische Universitaet Muenchen |
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*) |
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open Cfun3; |
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(* ------------------------------------------------------------------------ *) |
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(* the contlub property for fapp its 'first' argument *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "contlub_fapp1" Cfun3.thy "contlub(fapp)" |
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(fn prems => |
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[ |
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(rtac contlubI 1), |
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(strip_tac 1), |
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(rtac (expand_fun_eq RS iffD2) 1), |
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(strip_tac 1), |
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(rtac (thelub_cfun RS ssubst) 1), |
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(atac 1), |
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(rtac (Cfunapp2 RS ssubst) 1), |
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(etac cont_lubcfun 1), |
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(rtac (thelub_fun RS ssubst) 1), |
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(etac (monofun_fapp1 RS ch2ch_monofun) 1), |
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(rtac refl 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* the cont property for fapp in its first argument *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "cont_fapp1" Cfun3.thy "cont(fapp)" |
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(fn prems => |
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[ |
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(rtac monocontlub2cont 1), |
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(rtac monofun_fapp1 1), |
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(rtac contlub_fapp1 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* contlub, cont properties of fapp in its first argument in mixfix _[_] *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "contlub_cfun_fun" Cfun3.thy |
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"is_chain(FY) ==>\ |
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\ lub(range FY)`x = lub(range (%i.FY(i)`x))" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac trans 1), |
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(etac (contlub_fapp1 RS contlubE RS spec RS mp RS fun_cong) 1), |
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(rtac (thelub_fun RS ssubst) 1), |
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(etac (monofun_fapp1 RS ch2ch_monofun) 1), |
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(rtac refl 1) |
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]); |
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qed_goal "cont_cfun_fun" Cfun3.thy |
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"is_chain(FY) ==>\ |
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\ range(%i.FY(i)`x) <<| lub(range FY)`x" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac thelubE 1), |
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(etac ch2ch_fappL 1), |
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(etac (contlub_cfun_fun RS sym) 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* contlub, cont properties of fapp in both argument in mixfix _[_] *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "contlub_cfun" Cfun3.thy |
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"[|is_chain(FY);is_chain(TY)|] ==>\ |
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\ (lub(range FY))`(lub(range TY)) = lub(range(%i.FY(i)`(TY i)))" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac contlub_CF2 1), |
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(rtac cont_fapp1 1), |
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(rtac allI 1), |
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(rtac cont_fapp2 1), |
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(atac 1), |
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(atac 1) |
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]); |
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qed_goal "cont_cfun" Cfun3.thy |
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"[|is_chain(FY);is_chain(TY)|] ==>\ |
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\ range(%i.(FY i)`(TY i)) <<| (lub (range FY))`(lub(range TY))" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac thelubE 1), |
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(rtac (monofun_fapp1 RS ch2ch_MF2LR) 1), |
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(rtac allI 1), |
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(rtac monofun_fapp2 1), |
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(atac 1), |
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(atac 1), |
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(etac (contlub_cfun RS sym) 1), |
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(atac 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* cont2cont lemma for fapp *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "cont2cont_fapp" Cfun3.thy |
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"[|cont(%x.ft x);cont(%x.tt x)|] ==> cont(%x. (ft x)`(tt x))" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac cont2cont_app2 1), |
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(rtac cont2cont_app2 1), |
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(rtac cont_const 1), |
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(rtac cont_fapp1 1), |
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(atac 1), |
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(rtac cont_fapp2 1), |
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(atac 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* cont2mono Lemma for %x. LAM y. c1(x)(y) *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "cont2mono_LAM" Cfun3.thy |
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"[|!x.cont(c1 x); !y.monofun(%x.c1 x y)|] ==>\ |
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\ monofun(%x. LAM y. c1 x y)" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac monofunI 1), |
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(strip_tac 1), |
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(rtac (less_cfun RS ssubst) 1), |
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(rtac (less_fun RS ssubst) 1), |
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(rtac allI 1), |
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(rtac (beta_cfun RS ssubst) 1), |
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(etac spec 1), |
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(rtac (beta_cfun RS ssubst) 1), |
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(etac spec 1), |
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(etac ((hd (tl prems)) RS spec RS monofunE RS spec RS spec RS mp) 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* cont2cont Lemma for %x. LAM y. c1 x y) *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "cont2cont_LAM" Cfun3.thy |
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"[| !x.cont(c1 x); !y.cont(%x.c1 x y) |] ==> cont(%x. LAM y. c1 x y)" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(rtac monocontlub2cont 1), |
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(etac cont2mono_LAM 1), |
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(rtac (cont2mono RS allI) 1), |
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(etac spec 1), |
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(rtac contlubI 1), |
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(strip_tac 1), |
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(rtac (thelub_cfun RS ssubst) 1), |
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(rtac (cont2mono_LAM RS ch2ch_monofun) 1), |
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(atac 1), |
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(rtac (cont2mono RS allI) 1), |
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(etac spec 1), |
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(atac 1), |
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(res_inst_tac [("f","fabs")] arg_cong 1), |
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(rtac ext 1), |
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(rtac (beta_cfun RS ext RS ssubst) 1), |
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(etac spec 1), |
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(rtac (cont2contlub RS contlubE |
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RS spec RS mp ) 1), |
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(etac spec 1), |
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(atac 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* elimination of quantifier in premisses of cont2cont_LAM yields good *) |
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(* lemma for the cont tactic *) |
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(* ------------------------------------------------------------------------ *) |
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val cont2cont_LAM2 = (allI RSN (2,(allI RS cont2cont_LAM))); |
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(* |
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[| !!x. cont (?c1.0 x); |
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!!y. cont (%x. ?c1.0 x y) |] ==> cont (%x. LAM y. ?c1.0 x y) |
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*) |
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(* ------------------------------------------------------------------------ *) |
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(* cont2cont tactic *) |
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(* ------------------------------------------------------------------------ *) |
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val cont_lemmas = [cont_const, cont_id, cont_fapp2, |
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cont2cont_fapp,cont2cont_LAM2]; |
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val cont_tac = (fn i => (resolve_tac cont_lemmas i)); |
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val cont_tacR = (fn i => (REPEAT (cont_tac i))); |
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(* ------------------------------------------------------------------------ *) |
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(* function application _[_] is strict in its first arguments *) |
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(* ------------------------------------------------------------------------ *) |
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qed_goal "strict_fapp1" Cfun3.thy "(UU::'a->'b)`x = (UU::'b)" |
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(fn prems => |
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[ |
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(rtac (inst_cfun_pcpo RS ssubst) 1), |
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(rewtac UU_cfun_def), |
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(rtac (beta_cfun RS ssubst) 1), |
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(cont_tac 1), |
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(rtac refl 1) |
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]); |
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(* ------------------------------------------------------------------------ *) |
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(* results about strictify *) |
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(* ------------------------------------------------------------------------ *) |
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|
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qed_goalw "Istrictify1" Cfun3.thy [Istrictify_def] |
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"Istrictify(f)(UU)= (UU)" |
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(fn prems => |
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[ |
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(Simp_tac 1) |
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]); |
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|
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qed_goalw "Istrictify2" Cfun3.thy [Istrictify_def] |
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"~x=UU ==> Istrictify(f)(x)=f`x" |
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(fn prems => |
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[ |
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(cut_facts_tac prems 1), |
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(Asm_simp_tac 1) |
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]); |
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qed_goal "monofun_Istrictify1" Cfun3.thy "monofun(Istrictify)" |
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(fn prems => |
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[ |
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(rtac monofunI 1), |
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(strip_tac 1), |
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(rtac (less_fun RS iffD2) 1), |
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(strip_tac 1), |
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(res_inst_tac [("Q","xa=UU")] (excluded_middle RS disjE) 1), |
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(rtac (Istrictify2 RS ssubst) 1), |
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(atac 1), |
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(rtac (Istrictify2 RS ssubst) 1), |
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(atac 1), |
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(rtac monofun_cfun_fun 1), |
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(atac 1), |
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(hyp_subst_tac 1), |
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(rtac (Istrictify1 RS ssubst) 1), |
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(rtac (Istrictify1 RS ssubst) 1), |
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(rtac refl_less 1) |
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]); |
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qed_goal "monofun_Istrictify2" Cfun3.thy "monofun(Istrictify(f))" |
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(fn prems => |
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[ |
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(rtac monofunI 1), |
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(strip_tac 1), |
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(res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1), |
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(rtac (Istrictify2 RS ssubst) 1), |
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(etac notUU_I 1), |
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(atac 1), |
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(rtac (Istrictify2 RS ssubst) 1), |
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(atac 1), |
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(rtac monofun_cfun_arg 1), |
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(atac 1), |
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(hyp_subst_tac 1), |
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(rtac (Istrictify1 RS ssubst) 1), |
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(rtac minimal 1) |
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]); |
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qed_goal "contlub_Istrictify1" Cfun3.thy "contlub(Istrictify)" |
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(fn prems => |
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[ |
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(rtac contlubI 1), |
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(strip_tac 1), |
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(rtac (expand_fun_eq RS iffD2) 1), |
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(strip_tac 1), |
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(rtac (thelub_fun RS ssubst) 1), |
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(etac (monofun_Istrictify1 RS ch2ch_monofun) 1), |
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(res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1), |
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(rtac (Istrictify2 RS ssubst) 1), |
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(atac 1), |
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(rtac (Istrictify2 RS ext RS ssubst) 1), |
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(atac 1), |
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(rtac (thelub_cfun RS ssubst) 1), |
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(atac 1), |
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(rtac (beta_cfun RS ssubst) 1), |
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(rtac cont_lubcfun 1), |
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(atac 1), |
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(rtac refl 1), |
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(hyp_subst_tac 1), |
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(rtac (Istrictify1 RS ssubst) 1), |
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(rtac (Istrictify1 RS ext RS ssubst) 1), |
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(rtac (chain_UU_I_inverse RS sym) 1), |
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(rtac (refl RS allI) 1) |
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]); |
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qed_goal "contlub_Istrictify2" Cfun3.thy "contlub(Istrictify(f::'a -> 'b))" |
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(fn prems => |
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[ |
307 |
(rtac contlubI 1), |
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(strip_tac 1), |
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(res_inst_tac [("Q","lub(range(Y))=(UU::'a)")] classical2 1), |
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(res_inst_tac [("t","lub(range(Y))")] subst 1), |
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(rtac sym 1), |
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(atac 1), |
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(rtac (Istrictify1 RS ssubst) 1), |
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(rtac sym 1), |
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(rtac chain_UU_I_inverse 1), |
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(strip_tac 1), |
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(res_inst_tac [("t","Y(i)"),("s","UU::'a")] subst 1), |
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(rtac sym 1), |
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(rtac (chain_UU_I RS spec) 1), |
|
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(atac 1), |
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(atac 1), |
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(rtac Istrictify1 1), |
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(rtac (Istrictify2 RS ssubst) 1), |
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(atac 1), |
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(res_inst_tac [("s","lub(range(%i. f`(Y i)))")] trans 1), |
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(rtac contlub_cfun_arg 1), |
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(atac 1), |
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(rtac lub_equal2 1), |
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(rtac (chain_mono2 RS exE) 1), |
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(atac 2), |
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331 |
(rtac chain_UU_I_inverse2 1), |
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(atac 1), |
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333 |
(rtac exI 1), |
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334 |
(strip_tac 1), |
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(rtac (Istrictify2 RS sym) 1), |
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(fast_tac HOL_cs 1), |
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(rtac ch2ch_monofun 1), |
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338 |
(rtac monofun_fapp2 1), |
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(atac 1), |
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(rtac ch2ch_monofun 1), |
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(rtac monofun_Istrictify2 1), |
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(atac 1) |
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]); |
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val cont_Istrictify1 = (contlub_Istrictify1 RS |
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(monofun_Istrictify1 RS monocontlub2cont)); |
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val cont_Istrictify2 = (contlub_Istrictify2 RS |
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(monofun_Istrictify2 RS monocontlub2cont)); |
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qed_goalw "strictify1" Cfun3.thy [strictify_def] |
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"strictify`f`UU=UU" |
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(fn prems => |
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[ |
357 |
(rtac (beta_cfun RS ssubst) 1), |
|
358 |
(cont_tac 1), |
|
359 |
(rtac cont_Istrictify2 1), |
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360 |
(rtac cont2cont_CF1L 1), |
|
361 |
(rtac cont_Istrictify1 1), |
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362 |
(rtac (beta_cfun RS ssubst) 1), |
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(rtac cont_Istrictify2 1), |
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(rtac Istrictify1 1) |
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365 |
]); |
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qed_goalw "strictify2" Cfun3.thy [strictify_def] |
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"~x=UU ==> strictify`f`x=f`x" |
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(fn prems => |
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[ |
371 |
(rtac (beta_cfun RS ssubst) 1), |
|
372 |
(cont_tac 1), |
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373 |
(rtac cont_Istrictify2 1), |
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374 |
(rtac cont2cont_CF1L 1), |
|
375 |
(rtac cont_Istrictify1 1), |
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376 |
(rtac (beta_cfun RS ssubst) 1), |
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377 |
(rtac cont_Istrictify2 1), |
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(rtac Istrictify2 1), |
|
379 |
(resolve_tac prems 1) |
|
380 |
]); |
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(* ------------------------------------------------------------------------ *) |
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(* Instantiate the simplifier *) |
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(* ------------------------------------------------------------------------ *) |
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Addsimps [minimal,refl_less,beta_cfun,strict_fapp1,strictify1, strictify2]; |
388 |
||
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(* ------------------------------------------------------------------------ *) |
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(* use cont_tac as autotac. *) |
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(* ------------------------------------------------------------------------ *) |
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simpset := !simpset setsolver |
395 |
(fn thms => (resolve_tac (TrueI::refl::thms)) ORELSE' atac ORELSE' |
|
396 |
(fn i => DEPTH_SOLVE_1 (cont_tac i)) |
|
397 |
); |