author | haftmann |
Tue, 10 Jun 2008 15:31:04 +0200 | |
changeset 27112 | 661a74bafeb7 |
parent 27095 | c1c27955d7dd |
child 27131 | 9cc5964f7f3c |
permissions | -rw-r--r-- |
23152 | 1 |
(* Title: HOLCF/Tools/domain/domain_theorems.ML |
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ID: $Id$ |
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Author: David von Oheimb |
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New proofs/tactics by Brian Huffman |
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Proof generator for domain command. |
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*) |
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val HOLCF_ss = @{simpset}; |
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structure Domain_Theorems = struct |
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local |
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25805 | 15 |
val adm_impl_admw = @{thm adm_impl_admw}; |
25895
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converted adm_all and adm_ball to rule_format; cleaned up
huffman
parents:
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changeset
|
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val adm_all = @{thm adm_all}; |
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val adm_conj = @{thm adm_conj}; |
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val adm_subst = @{thm adm_subst}; |
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val antisym_less_inverse = @{thm antisym_less_inverse}; |
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val beta_cfun = @{thm beta_cfun}; |
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val cfun_arg_cong = @{thm cfun_arg_cong}; |
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val ch2ch_Rep_CFunL = @{thm ch2ch_Rep_CFunL}; |
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val ch2ch_Rep_CFunR = @{thm ch2ch_Rep_CFunR}; |
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val chain_iterate = @{thm chain_iterate}; |
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val compact_ONE = @{thm compact_ONE}; |
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val compact_sinl = @{thm compact_sinl}; |
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val compact_sinr = @{thm compact_sinr}; |
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val compact_spair = @{thm compact_spair}; |
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val compact_up = @{thm compact_up}; |
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val contlub_cfun_arg = @{thm contlub_cfun_arg}; |
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val contlub_cfun_fun = @{thm contlub_cfun_fun}; |
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val fix_def2 = @{thm fix_def2}; |
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val injection_eq = @{thm injection_eq}; |
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val injection_less = @{thm injection_less}; |
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val lub_equal = @{thm lub_equal}; |
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val monofun_cfun_arg = @{thm monofun_cfun_arg}; |
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val retraction_strict = @{thm retraction_strict}; |
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val spair_eq = @{thm spair_eq}; |
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val spair_less = @{thm spair_less}; |
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val sscase1 = @{thm sscase1}; |
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val ssplit1 = @{thm ssplit1}; |
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val strictify1 = @{thm strictify1}; |
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val wfix_ind = @{thm wfix_ind}; |
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val iso_intro = @{thm iso.intro}; |
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val iso_abs_iso = @{thm iso.abs_iso}; |
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val iso_rep_iso = @{thm iso.rep_iso}; |
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val iso_abs_strict = @{thm iso.abs_strict}; |
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val iso_rep_strict = @{thm iso.rep_strict}; |
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val iso_abs_defin' = @{thm iso.abs_defin'}; |
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val iso_rep_defin' = @{thm iso.rep_defin'}; |
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val iso_abs_defined = @{thm iso.abs_defined}; |
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val iso_rep_defined = @{thm iso.rep_defined}; |
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val iso_compact_abs = @{thm iso.compact_abs}; |
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val iso_compact_rep = @{thm iso.compact_rep}; |
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val iso_iso_swap = @{thm iso.iso_swap}; |
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val exh_start = @{thm exh_start}; |
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val ex_defined_iffs = @{thms ex_defined_iffs}; |
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val exh_casedist0 = @{thm exh_casedist0}; |
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val exh_casedists = @{thms exh_casedists}; |
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open Domain_Library; |
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infixr 0 ===>; |
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infixr 0 ==>; |
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infix 0 == ; |
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infix 1 ===; |
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infix 1 ~= ; |
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infix 1 <<; |
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infix 1 ~<<; |
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infix 9 ` ; |
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infix 9 `% ; |
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infix 9 `%%; |
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infixr 9 oo; |
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(* ----- general proof facilities ------------------------------------------- *) |
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24503 | 78 |
fun legacy_infer_term thy t = |
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let val ctxt = ProofContext.set_mode ProofContext.mode_schematic (ProofContext.init thy) |
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in singleton (Syntax.check_terms ctxt) (Sign.intern_term thy t) end; |
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fun pg'' thy defs t tacs = |
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let |
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val t' = legacy_infer_term thy t; |
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val asms = Logic.strip_imp_prems t'; |
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val prop = Logic.strip_imp_concl t'; |
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fun tac {prems, context} = |
23152 | 88 |
rewrite_goals_tac defs THEN |
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EVERY (tacs (map (rewrite_rule defs) prems)); |
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in Goal.prove_global thy [] asms prop tac end; |
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fun pg' thy defs t tacsf = |
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let |
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fun tacs [] = tacsf |
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| tacs prems = cut_facts_tac prems 1 :: tacsf; |
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in pg'' thy defs t tacs end; |
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fun case_UU_tac rews i v = |
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27095 | 99 |
DatatypePackage.case_tac (v^"=UU") i THEN |
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asm_simp_tac (HOLCF_ss addsimps rews) i; |
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val chain_tac = |
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REPEAT_DETERM o resolve_tac |
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[chain_iterate, ch2ch_Rep_CFunR, ch2ch_Rep_CFunL]; |
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(* ----- general proofs ----------------------------------------------------- *) |
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val all2E = prove_goal HOL.thy "[| !x y . P x y; P x y ==> R |] ==> R" |
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(fn prems =>[ |
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resolve_tac prems 1, |
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cut_facts_tac prems 1, |
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fast_tac HOL_cs 1]); |
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val dist_eqI = prove_goal (the_context ()) "!!x::'a::po. ~ x << y ==> x ~= y" |
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(fn prems => |
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26342 | 116 |
[blast_tac (@{claset} addDs [antisym_less_inverse]) 1]); |
23152 | 117 |
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in |
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fun theorems (((dname, _), cons) : eq, eqs : eq list) thy = |
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let |
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val dummy = writeln ("Proving isomorphism properties of domain "^dname^" ..."); |
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val pg = pg' thy; |
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(* ----- getting the axioms and definitions --------------------------------- *) |
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local |
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26343
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simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26342
diff
changeset
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fun ga s dn = PureThy.get_thm thy (dn ^ "." ^ s); |
23152 | 130 |
in |
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val ax_abs_iso = ga "abs_iso" dname; |
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val ax_rep_iso = ga "rep_iso" dname; |
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val ax_when_def = ga "when_def" dname; |
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fun get_def mk_name (con,_) = ga (mk_name con^"_def") dname; |
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val axs_con_def = map (get_def extern_name) cons; |
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val axs_dis_def = map (get_def dis_name) cons; |
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val axs_mat_def = map (get_def mat_name) cons; |
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val axs_pat_def = map (get_def pat_name) cons; |
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val axs_sel_def = |
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let |
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fun def_of_sel sel = ga (sel^"_def") dname; |
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fun def_of_arg arg = Option.map def_of_sel (sel_of arg); |
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fun defs_of_con (_, args) = List.mapPartial def_of_arg args; |
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in |
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26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
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maps defs_of_con cons |
23152 | 146 |
end; |
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val ax_copy_def = ga "copy_def" dname; |
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end; (* local *) |
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(* ----- theorems concerning the isomorphism -------------------------------- *) |
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val dc_abs = %%:(dname^"_abs"); |
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val dc_rep = %%:(dname^"_rep"); |
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val dc_copy = %%:(dname^"_copy"); |
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val x_name = "x"; |
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val iso_locale = iso_intro OF [ax_abs_iso, ax_rep_iso]; |
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val abs_strict = ax_rep_iso RS (allI RS retraction_strict); |
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val rep_strict = ax_abs_iso RS (allI RS retraction_strict); |
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val abs_defin' = iso_locale RS iso_abs_defin'; |
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val rep_defin' = iso_locale RS iso_rep_defin'; |
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val iso_rews = map standard [ax_abs_iso,ax_rep_iso,abs_strict,rep_strict]; |
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(* ----- generating beta reduction rules from definitions-------------------- *) |
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local |
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fun arglist (Const _ $ Abs (s, _, t)) = |
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let |
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val (vars,body) = arglist t; |
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in (s :: vars, body) end |
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| arglist t = ([], t); |
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fun bind_fun vars t = Library.foldr mk_All (vars, t); |
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fun bound_vars 0 = [] |
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| bound_vars i = Bound (i-1) :: bound_vars (i - 1); |
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in |
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fun appl_of_def def = |
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let |
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val (_ $ con $ lam) = concl_of def; |
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val (vars, rhs) = arglist lam; |
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val lhs = list_ccomb (con, bound_vars (length vars)); |
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val appl = bind_fun vars (lhs == rhs); |
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val cs = ContProc.cont_thms lam; |
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val betas = map (fn c => mk_meta_eq (c RS beta_cfun)) cs; |
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in pg (def::betas) appl [rtac reflexive_thm 1] end; |
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end; |
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val when_appl = appl_of_def ax_when_def; |
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val con_appls = map appl_of_def axs_con_def; |
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local |
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fun arg2typ n arg = |
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let val t = TVar (("'a", n), pcpoS) |
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in (n + 1, if is_lazy arg then mk_uT t else t) end; |
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fun args2typ n [] = (n, oneT) |
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| args2typ n [arg] = arg2typ n arg |
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| args2typ n (arg::args) = |
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let |
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val (n1, t1) = arg2typ n arg; |
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val (n2, t2) = args2typ n1 args |
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in (n2, mk_sprodT (t1, t2)) end; |
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fun cons2typ n [] = (n,oneT) |
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| cons2typ n [con] = args2typ n (snd con) |
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| cons2typ n (con::cons) = |
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let |
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val (n1, t1) = args2typ n (snd con); |
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val (n2, t2) = cons2typ n1 cons |
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in (n2, mk_ssumT (t1, t2)) end; |
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in |
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fun cons2ctyp cons = ctyp_of thy (snd (cons2typ 1 cons)); |
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end; |
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local |
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val iso_swap = iso_locale RS iso_iso_swap; |
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fun one_con (con, args) = |
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let |
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val vns = map vname args; |
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val eqn = %:x_name === con_app2 con %: vns; |
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val conj = foldr1 mk_conj (eqn :: map (defined o %:) (nonlazy args)); |
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in Library.foldr mk_ex (vns, conj) end; |
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||
23894
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23152
diff
changeset
|
223 |
val conj_assoc = @{thm conj_assoc}; |
23152 | 224 |
val exh = foldr1 mk_disj ((%:x_name === UU) :: map one_con cons); |
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val thm1 = instantiate' [SOME (cons2ctyp cons)] [] exh_start; |
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val thm2 = rewrite_rule (map mk_meta_eq ex_defined_iffs) thm1; |
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25805 | 227 |
val thm3 = rewrite_rule [mk_meta_eq @{thm conj_assoc}] thm2; |
23152 | 228 |
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(* first 3 rules replace "x = UU \/ P" with "rep$x = UU \/ P" *) |
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val tacs = [ |
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rtac disjE 1, |
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etac (rep_defin' RS disjI1) 2, |
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etac disjI2 2, |
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rewrite_goals_tac [mk_meta_eq iso_swap], |
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rtac thm3 1]; |
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in |
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val exhaust = pg con_appls (mk_trp exh) tacs; |
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val casedist = |
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standard (rewrite_rule exh_casedists (exhaust RS exh_casedist0)); |
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end; |
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local |
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fun bind_fun t = Library.foldr mk_All (when_funs cons, t); |
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fun bound_fun i _ = Bound (length cons - i); |
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val when_app = list_ccomb (%%:(dname^"_when"), mapn bound_fun 1 cons); |
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in |
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val when_strict = |
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let |
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val axs = [when_appl, mk_meta_eq rep_strict]; |
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val goal = bind_fun (mk_trp (strict when_app)); |
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val tacs = [resolve_tac [sscase1, ssplit1, strictify1] 1]; |
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in pg axs goal tacs end; |
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val when_apps = |
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let |
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fun one_when n (con,args) = |
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let |
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val axs = when_appl :: con_appls; |
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val goal = bind_fun (lift_defined %: (nonlazy args, |
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mk_trp (when_app`(con_app con args) === |
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list_ccomb (bound_fun n 0, map %# args)))); |
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val tacs = [asm_simp_tac (HOLCF_ss addsimps [ax_abs_iso]) 1]; |
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in pg axs goal tacs end; |
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in mapn one_when 1 cons end; |
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end; |
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val when_rews = when_strict :: when_apps; |
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||
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(* ----- theorems concerning the constructors, discriminators and selectors - *) |
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||
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local |
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fun dis_strict (con, _) = |
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let |
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val goal = mk_trp (strict (%%:(dis_name con))); |
|
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in pg axs_dis_def goal [rtac when_strict 1] end; |
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||
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fun dis_app c (con, args) = |
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let |
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val lhs = %%:(dis_name c) ` con_app con args; |
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26012 | 279 |
val rhs = if con = c then TT else FF; |
23152 | 280 |
val goal = lift_defined %: (nonlazy args, mk_trp (lhs === rhs)); |
281 |
val tacs = [asm_simp_tac (HOLCF_ss addsimps when_rews) 1]; |
|
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in pg axs_dis_def goal tacs end; |
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283 |
||
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
284 |
val dis_apps = maps (fn (c,_) => map (dis_app c) cons) cons; |
23152 | 285 |
|
286 |
fun dis_defin (con, args) = |
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287 |
let |
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val goal = defined (%:x_name) ==> defined (%%:(dis_name con) `% x_name); |
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289 |
val tacs = |
|
290 |
[rtac casedist 1, |
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291 |
contr_tac 1, |
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292 |
DETERM_UNTIL_SOLVED (CHANGED |
|
293 |
(asm_simp_tac (HOLCF_ss addsimps dis_apps) 1))]; |
|
294 |
in pg [] goal tacs end; |
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295 |
||
296 |
val dis_stricts = map dis_strict cons; |
|
297 |
val dis_defins = map dis_defin cons; |
|
298 |
in |
|
299 |
val dis_rews = dis_stricts @ dis_defins @ dis_apps; |
|
300 |
end; |
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301 |
||
302 |
local |
|
303 |
fun mat_strict (con, _) = |
|
304 |
let |
|
305 |
val goal = mk_trp (strict (%%:(mat_name con))); |
|
306 |
val tacs = [rtac when_strict 1]; |
|
307 |
in pg axs_mat_def goal tacs end; |
|
308 |
||
309 |
val mat_stricts = map mat_strict cons; |
|
310 |
||
311 |
fun one_mat c (con, args) = |
|
312 |
let |
|
313 |
val lhs = %%:(mat_name c) ` con_app con args; |
|
314 |
val rhs = |
|
315 |
if con = c |
|
26012 | 316 |
then mk_return (mk_ctuple (map %# args)) |
317 |
else mk_fail; |
|
23152 | 318 |
val goal = lift_defined %: (nonlazy args, mk_trp (lhs === rhs)); |
319 |
val tacs = [asm_simp_tac (HOLCF_ss addsimps when_rews) 1]; |
|
320 |
in pg axs_mat_def goal tacs end; |
|
321 |
||
322 |
val mat_apps = |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
323 |
maps (fn (c,_) => map (one_mat c) cons) cons; |
23152 | 324 |
in |
325 |
val mat_rews = mat_stricts @ mat_apps; |
|
326 |
end; |
|
327 |
||
328 |
local |
|
329 |
fun ps args = mapn (fn n => fn _ => %:("pat" ^ string_of_int n)) 1 args; |
|
330 |
||
26012 | 331 |
fun pat_lhs (con,args) = mk_branch (list_comb (%%:(pat_name con), ps args)); |
23152 | 332 |
|
26012 | 333 |
fun pat_rhs (con,[]) = mk_return ((%:"rhs") ` HOLogic.unit) |
23152 | 334 |
| pat_rhs (con,args) = |
26012 | 335 |
(mk_branch (mk_ctuple_pat (ps args))) |
23152 | 336 |
`(%:"rhs")`(mk_ctuple (map %# args)); |
337 |
||
338 |
fun pat_strict c = |
|
339 |
let |
|
25132 | 340 |
val axs = @{thm branch_def} :: axs_pat_def; |
23152 | 341 |
val goal = mk_trp (strict (pat_lhs c ` (%:"rhs"))); |
342 |
val tacs = [simp_tac (HOLCF_ss addsimps [when_strict]) 1]; |
|
343 |
in pg axs goal tacs end; |
|
344 |
||
345 |
fun pat_app c (con, args) = |
|
346 |
let |
|
25132 | 347 |
val axs = @{thm branch_def} :: axs_pat_def; |
23152 | 348 |
val lhs = (pat_lhs c)`(%:"rhs")`(con_app con args); |
26012 | 349 |
val rhs = if con = fst c then pat_rhs c else mk_fail; |
23152 | 350 |
val goal = lift_defined %: (nonlazy args, mk_trp (lhs === rhs)); |
351 |
val tacs = [asm_simp_tac (HOLCF_ss addsimps when_rews) 1]; |
|
352 |
in pg axs goal tacs end; |
|
353 |
||
354 |
val pat_stricts = map pat_strict cons; |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
355 |
val pat_apps = maps (fn c => map (pat_app c) cons) cons; |
23152 | 356 |
in |
357 |
val pat_rews = pat_stricts @ pat_apps; |
|
358 |
end; |
|
359 |
||
360 |
local |
|
23894
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23152
diff
changeset
|
361 |
val rev_contrapos = @{thm rev_contrapos}; |
23152 | 362 |
fun con_strict (con, args) = |
363 |
let |
|
364 |
fun one_strict vn = |
|
365 |
let |
|
366 |
fun f arg = if vname arg = vn then UU else %# arg; |
|
367 |
val goal = mk_trp (con_app2 con f args === UU); |
|
368 |
val tacs = [asm_simp_tac (HOLCF_ss addsimps [abs_strict]) 1]; |
|
369 |
in pg con_appls goal tacs end; |
|
370 |
in map one_strict (nonlazy args) end; |
|
371 |
||
372 |
fun con_defin (con, args) = |
|
373 |
let |
|
374 |
val concl = mk_trp (defined (con_app con args)); |
|
375 |
val goal = lift_defined %: (nonlazy args, concl); |
|
376 |
val tacs = [ |
|
25805 | 377 |
rtac @{thm rev_contrapos} 1, |
23152 | 378 |
eres_inst_tac [("f",dis_name con)] cfun_arg_cong 1, |
379 |
asm_simp_tac (HOLCF_ss addsimps dis_rews) 1]; |
|
380 |
in pg [] goal tacs end; |
|
381 |
in |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
382 |
val con_stricts = maps con_strict cons; |
23152 | 383 |
val con_defins = map con_defin cons; |
384 |
val con_rews = con_stricts @ con_defins; |
|
385 |
end; |
|
386 |
||
387 |
local |
|
388 |
val rules = |
|
389 |
[compact_sinl, compact_sinr, compact_spair, compact_up, compact_ONE]; |
|
390 |
fun con_compact (con, args) = |
|
391 |
let |
|
26012 | 392 |
val concl = mk_trp (mk_compact (con_app con args)); |
393 |
val goal = lift (fn x => mk_compact (%#x)) (args, concl); |
|
23152 | 394 |
val tacs = [ |
395 |
rtac (iso_locale RS iso_compact_abs) 1, |
|
396 |
REPEAT (resolve_tac rules 1 ORELSE atac 1)]; |
|
397 |
in pg con_appls goal tacs end; |
|
398 |
in |
|
399 |
val con_compacts = map con_compact cons; |
|
400 |
end; |
|
401 |
||
402 |
local |
|
403 |
fun one_sel sel = |
|
404 |
pg axs_sel_def (mk_trp (strict (%%:sel))) |
|
405 |
[simp_tac (HOLCF_ss addsimps when_rews) 1]; |
|
406 |
||
407 |
fun sel_strict (_, args) = |
|
408 |
List.mapPartial (Option.map one_sel o sel_of) args; |
|
409 |
in |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
410 |
val sel_stricts = maps sel_strict cons; |
23152 | 411 |
end; |
412 |
||
413 |
local |
|
414 |
fun sel_app_same c n sel (con, args) = |
|
415 |
let |
|
416 |
val nlas = nonlazy args; |
|
417 |
val vns = map vname args; |
|
418 |
val vnn = List.nth (vns, n); |
|
419 |
val nlas' = List.filter (fn v => v <> vnn) nlas; |
|
420 |
val lhs = (%%:sel)`(con_app con args); |
|
421 |
val goal = lift_defined %: (nlas', mk_trp (lhs === %:vnn)); |
|
422 |
val tacs1 = |
|
423 |
if vnn mem nlas |
|
424 |
then [case_UU_tac (when_rews @ con_stricts) 1 vnn] |
|
425 |
else []; |
|
426 |
val tacs2 = [asm_simp_tac (HOLCF_ss addsimps when_rews) 1]; |
|
427 |
in pg axs_sel_def goal (tacs1 @ tacs2) end; |
|
428 |
||
429 |
fun sel_app_diff c n sel (con, args) = |
|
430 |
let |
|
431 |
val nlas = nonlazy args; |
|
432 |
val goal = mk_trp (%%:sel ` con_app con args === UU); |
|
433 |
val tacs1 = map (case_UU_tac (when_rews @ con_stricts) 1) nlas; |
|
434 |
val tacs2 = [asm_simp_tac (HOLCF_ss addsimps when_rews) 1]; |
|
435 |
in pg axs_sel_def goal (tacs1 @ tacs2) end; |
|
436 |
||
437 |
fun sel_app c n sel (con, args) = |
|
438 |
if con = c |
|
439 |
then sel_app_same c n sel (con, args) |
|
440 |
else sel_app_diff c n sel (con, args); |
|
441 |
||
442 |
fun one_sel c n sel = map (sel_app c n sel) cons; |
|
443 |
fun one_sel' c n arg = Option.map (one_sel c n) (sel_of arg); |
|
444 |
fun one_con (c, args) = |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
445 |
flat (map_filter I (mapn (one_sel' c) 0 args)); |
23152 | 446 |
in |
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
447 |
val sel_apps = maps one_con cons; |
23152 | 448 |
end; |
449 |
||
450 |
local |
|
451 |
fun sel_defin sel = |
|
452 |
let |
|
453 |
val goal = defined (%:x_name) ==> defined (%%:sel`%x_name); |
|
454 |
val tacs = [ |
|
455 |
rtac casedist 1, |
|
456 |
contr_tac 1, |
|
457 |
DETERM_UNTIL_SOLVED (CHANGED |
|
458 |
(asm_simp_tac (HOLCF_ss addsimps sel_apps) 1))]; |
|
459 |
in pg [] goal tacs end; |
|
460 |
in |
|
461 |
val sel_defins = |
|
462 |
if length cons = 1 |
|
463 |
then List.mapPartial (fn arg => Option.map sel_defin (sel_of arg)) |
|
464 |
(filter_out is_lazy (snd (hd cons))) |
|
465 |
else []; |
|
466 |
end; |
|
467 |
||
468 |
val sel_rews = sel_stricts @ sel_defins @ sel_apps; |
|
23894
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23152
diff
changeset
|
469 |
val rev_contrapos = @{thm rev_contrapos}; |
23152 | 470 |
|
471 |
val distincts_le = |
|
472 |
let |
|
473 |
fun dist (con1, args1) (con2, args2) = |
|
474 |
let |
|
475 |
val goal = lift_defined %: (nonlazy args1, |
|
476 |
mk_trp (con_app con1 args1 ~<< con_app con2 args2)); |
|
477 |
val tacs = [ |
|
25805 | 478 |
rtac @{thm rev_contrapos} 1, |
23152 | 479 |
eres_inst_tac [("f", dis_name con1)] monofun_cfun_arg 1] |
480 |
@ map (case_UU_tac (con_stricts @ dis_rews) 1) (nonlazy args2) |
|
481 |
@ [asm_simp_tac (HOLCF_ss addsimps dis_rews) 1]; |
|
482 |
in pg [] goal tacs end; |
|
483 |
||
484 |
fun distinct (con1, args1) (con2, args2) = |
|
485 |
let |
|
486 |
val arg1 = (con1, args1); |
|
487 |
val arg2 = |
|
488 |
(con2, ListPair.map (fn (arg,vn) => upd_vname (K vn) arg) |
|
489 |
(args2, Name.variant_list (map vname args1) (map vname args2))); |
|
490 |
in [dist arg1 arg2, dist arg2 arg1] end; |
|
491 |
fun distincts [] = [] |
|
492 |
| distincts (c::cs) = (map (distinct c) cs) :: distincts cs; |
|
493 |
in distincts cons end; |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
494 |
val dist_les = flat (flat distincts_le); |
23152 | 495 |
val dist_eqs = |
496 |
let |
|
497 |
fun distinct (_,args1) ((_,args2), leqs) = |
|
498 |
let |
|
499 |
val (le1,le2) = (hd leqs, hd(tl leqs)); |
|
500 |
val (eq1,eq2) = (le1 RS dist_eqI, le2 RS dist_eqI) |
|
501 |
in |
|
502 |
if nonlazy args1 = [] then [eq1, eq1 RS not_sym] else |
|
503 |
if nonlazy args2 = [] then [eq2, eq2 RS not_sym] else |
|
504 |
[eq1, eq2] |
|
505 |
end; |
|
506 |
fun distincts [] = [] |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
507 |
| distincts ((c,leqs)::cs) = flat |
23152 | 508 |
(ListPair.map (distinct c) ((map #1 cs),leqs)) @ |
509 |
distincts cs; |
|
510 |
in map standard (distincts (cons ~~ distincts_le)) end; |
|
511 |
||
512 |
local |
|
513 |
fun pgterm rel con args = |
|
514 |
let |
|
515 |
fun append s = upd_vname (fn v => v^s); |
|
516 |
val (largs, rargs) = (args, map (append "'") args); |
|
517 |
val concl = |
|
518 |
foldr1 mk_conj (ListPair.map rel (map %# largs, map %# rargs)); |
|
519 |
val prem = rel (con_app con largs, con_app con rargs); |
|
520 |
val sargs = case largs of [_] => [] | _ => nonlazy args; |
|
521 |
val prop = lift_defined %: (sargs, mk_trp (prem === concl)); |
|
522 |
in pg con_appls prop end; |
|
523 |
val cons' = List.filter (fn (_,args) => args<>[]) cons; |
|
524 |
in |
|
525 |
val inverts = |
|
526 |
let |
|
527 |
val abs_less = ax_abs_iso RS (allI RS injection_less); |
|
528 |
val tacs = |
|
529 |
[asm_full_simp_tac (HOLCF_ss addsimps [abs_less, spair_less]) 1]; |
|
530 |
in map (fn (con, args) => pgterm (op <<) con args tacs) cons' end; |
|
531 |
||
532 |
val injects = |
|
533 |
let |
|
534 |
val abs_eq = ax_abs_iso RS (allI RS injection_eq); |
|
535 |
val tacs = [asm_full_simp_tac (HOLCF_ss addsimps [abs_eq, spair_eq]) 1]; |
|
536 |
in map (fn (con, args) => pgterm (op ===) con args tacs) cons' end; |
|
537 |
end; |
|
538 |
||
539 |
(* ----- theorems concerning one induction step ----------------------------- *) |
|
540 |
||
541 |
val copy_strict = |
|
542 |
let |
|
543 |
val goal = mk_trp (strict (dc_copy `% "f")); |
|
544 |
val tacs = [asm_simp_tac (HOLCF_ss addsimps [abs_strict, when_strict]) 1]; |
|
545 |
in pg [ax_copy_def] goal tacs end; |
|
546 |
||
547 |
local |
|
548 |
fun copy_app (con, args) = |
|
549 |
let |
|
550 |
val lhs = dc_copy`%"f"`(con_app con args); |
|
551 |
val rhs = con_app2 con (app_rec_arg (cproj (%:"f") eqs)) args; |
|
552 |
val goal = lift_defined %: (nonlazy_rec args, mk_trp (lhs === rhs)); |
|
553 |
val args' = List.filter (fn a => not (is_rec a orelse is_lazy a)) args; |
|
554 |
val stricts = abs_strict::when_strict::con_stricts; |
|
555 |
val tacs1 = map (case_UU_tac stricts 1 o vname) args'; |
|
556 |
val tacs2 = [asm_simp_tac (HOLCF_ss addsimps when_apps) 1]; |
|
557 |
in pg [ax_copy_def] goal (tacs1 @ tacs2) end; |
|
558 |
in |
|
559 |
val copy_apps = map copy_app cons; |
|
560 |
end; |
|
561 |
||
562 |
local |
|
563 |
fun one_strict (con, args) = |
|
564 |
let |
|
565 |
val goal = mk_trp (dc_copy`UU`(con_app con args) === UU); |
|
566 |
val rews = copy_strict :: copy_apps @ con_rews; |
|
567 |
val tacs = map (case_UU_tac rews 1) (nonlazy args) @ |
|
568 |
[asm_simp_tac (HOLCF_ss addsimps rews) 1]; |
|
569 |
in pg [] goal tacs end; |
|
570 |
||
571 |
fun has_nonlazy_rec (_, args) = exists is_nonlazy_rec args; |
|
572 |
in |
|
573 |
val copy_stricts = map one_strict (List.filter has_nonlazy_rec cons); |
|
574 |
end; |
|
575 |
||
576 |
val copy_rews = copy_strict :: copy_apps @ copy_stricts; |
|
577 |
||
578 |
in |
|
579 |
thy |
|
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24503
diff
changeset
|
580 |
|> Sign.add_path (Sign.base_name dname) |
23152 | 581 |
|> (snd o (PureThy.add_thmss (map Thm.no_attributes [ |
582 |
("iso_rews" , iso_rews ), |
|
583 |
("exhaust" , [exhaust] ), |
|
584 |
("casedist" , [casedist]), |
|
585 |
("when_rews", when_rews ), |
|
586 |
("compacts", con_compacts), |
|
587 |
("con_rews", con_rews), |
|
588 |
("sel_rews", sel_rews), |
|
589 |
("dis_rews", dis_rews), |
|
590 |
("pat_rews", pat_rews), |
|
591 |
("dist_les", dist_les), |
|
592 |
("dist_eqs", dist_eqs), |
|
593 |
("inverts" , inverts ), |
|
594 |
("injects" , injects ), |
|
595 |
("copy_rews", copy_rews)]))) |
|
596 |
|> (snd o PureThy.add_thmss |
|
597 |
[(("match_rews", mat_rews), [Simplifier.simp_add])]) |
|
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24503
diff
changeset
|
598 |
|> Sign.parent_path |
23152 | 599 |
|> rpair (iso_rews @ when_rews @ con_rews @ sel_rews @ dis_rews @ |
600 |
pat_rews @ dist_les @ dist_eqs @ copy_rews) |
|
601 |
end; (* let *) |
|
602 |
||
603 |
fun comp_theorems (comp_dnam, eqs: eq list) thy = |
|
604 |
let |
|
605 |
val dnames = map (fst o fst) eqs; |
|
606 |
val conss = map snd eqs; |
|
607 |
val comp_dname = Sign.full_name thy comp_dnam; |
|
608 |
||
609 |
val d = writeln("Proving induction properties of domain "^comp_dname^" ..."); |
|
610 |
val pg = pg' thy; |
|
611 |
||
612 |
(* ----- getting the composite axiom and definitions ------------------------ *) |
|
613 |
||
614 |
local |
|
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26342
diff
changeset
|
615 |
fun ga s dn = PureThy.get_thm thy (dn ^ "." ^ s); |
23152 | 616 |
in |
617 |
val axs_reach = map (ga "reach" ) dnames; |
|
618 |
val axs_take_def = map (ga "take_def" ) dnames; |
|
619 |
val axs_finite_def = map (ga "finite_def") dnames; |
|
620 |
val ax_copy2_def = ga "copy_def" comp_dnam; |
|
621 |
val ax_bisim_def = ga "bisim_def" comp_dnam; |
|
622 |
end; |
|
623 |
||
624 |
local |
|
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26342
diff
changeset
|
625 |
fun gt s dn = PureThy.get_thm thy (dn ^ "." ^ s); |
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26342
diff
changeset
|
626 |
fun gts s dn = PureThy.get_thms thy (dn ^ "." ^ s); |
23152 | 627 |
in |
628 |
val cases = map (gt "casedist" ) dnames; |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
629 |
val con_rews = maps (gts "con_rews" ) dnames; |
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
630 |
val copy_rews = maps (gts "copy_rews") dnames; |
23152 | 631 |
end; |
632 |
||
633 |
fun dc_take dn = %%:(dn^"_take"); |
|
634 |
val x_name = idx_name dnames "x"; |
|
635 |
val P_name = idx_name dnames "P"; |
|
636 |
val n_eqs = length eqs; |
|
637 |
||
638 |
(* ----- theorems concerning finite approximation and finite induction ------ *) |
|
639 |
||
640 |
local |
|
26342 | 641 |
val iterate_Cprod_ss = simpset_of @{theory Fix}; |
23152 | 642 |
val copy_con_rews = copy_rews @ con_rews; |
643 |
val copy_take_defs = |
|
644 |
(if n_eqs = 1 then [] else [ax_copy2_def]) @ axs_take_def; |
|
645 |
val take_stricts = |
|
646 |
let |
|
647 |
fun one_eq ((dn, args), _) = strict (dc_take dn $ %:"n"); |
|
648 |
val goal = mk_trp (foldr1 mk_conj (map one_eq eqs)); |
|
649 |
val tacs = [ |
|
27112 | 650 |
DatatypePackage.induct_tac @{context} "n" 1, |
23152 | 651 |
simp_tac iterate_Cprod_ss 1, |
652 |
asm_simp_tac (iterate_Cprod_ss addsimps copy_rews) 1]; |
|
653 |
in pg copy_take_defs goal tacs end; |
|
654 |
||
655 |
val take_stricts' = rewrite_rule copy_take_defs take_stricts; |
|
656 |
fun take_0 n dn = |
|
657 |
let |
|
658 |
val goal = mk_trp ((dc_take dn $ %%:"HOL.zero") `% x_name n === UU); |
|
659 |
in pg axs_take_def goal [simp_tac iterate_Cprod_ss 1] end; |
|
660 |
val take_0s = mapn take_0 1 dnames; |
|
661 |
val c_UU_tac = case_UU_tac (take_stricts'::copy_con_rews) 1; |
|
662 |
val take_apps = |
|
663 |
let |
|
664 |
fun mk_eqn dn (con, args) = |
|
665 |
let |
|
666 |
fun mk_take n = dc_take (List.nth (dnames, n)) $ %:"n"; |
|
667 |
val lhs = (dc_take dn $ (%%:"Suc" $ %:"n"))`(con_app con args); |
|
668 |
val rhs = con_app2 con (app_rec_arg mk_take) args; |
|
669 |
in Library.foldr mk_all (map vname args, lhs === rhs) end; |
|
670 |
fun mk_eqns ((dn, _), cons) = map (mk_eqn dn) cons; |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
671 |
val goal = mk_trp (foldr1 mk_conj (maps mk_eqns eqs)); |
23152 | 672 |
val simps = List.filter (has_fewer_prems 1) copy_rews; |
673 |
fun con_tac (con, args) = |
|
674 |
if nonlazy_rec args = [] |
|
675 |
then all_tac |
|
676 |
else EVERY (map c_UU_tac (nonlazy_rec args)) THEN |
|
677 |
asm_full_simp_tac (HOLCF_ss addsimps copy_rews) 1; |
|
678 |
fun eq_tacs ((dn, _), cons) = map con_tac cons; |
|
679 |
val tacs = |
|
680 |
simp_tac iterate_Cprod_ss 1 :: |
|
27112 | 681 |
DatatypePackage.induct_tac @{context} "n" 1 :: |
23152 | 682 |
simp_tac (iterate_Cprod_ss addsimps copy_con_rews) 1 :: |
683 |
asm_full_simp_tac (HOLCF_ss addsimps simps) 1 :: |
|
684 |
TRY (safe_tac HOL_cs) :: |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
685 |
maps eq_tacs eqs; |
23152 | 686 |
in pg copy_take_defs goal tacs end; |
687 |
in |
|
688 |
val take_rews = map standard |
|
689 |
(atomize take_stricts @ take_0s @ atomize take_apps); |
|
690 |
end; (* local *) |
|
691 |
||
692 |
local |
|
693 |
fun one_con p (con,args) = |
|
694 |
let |
|
695 |
fun ind_hyp arg = %:(P_name (1 + rec_of arg)) $ bound_arg args arg; |
|
696 |
val t1 = mk_trp (%:p $ con_app2 con (bound_arg args) args); |
|
697 |
val t2 = lift ind_hyp (List.filter is_rec args, t1); |
|
698 |
val t3 = lift_defined (bound_arg (map vname args)) (nonlazy args, t2); |
|
699 |
in Library.foldr mk_All (map vname args, t3) end; |
|
700 |
||
701 |
fun one_eq ((p, cons), concl) = |
|
702 |
mk_trp (%:p $ UU) ===> Logic.list_implies (map (one_con p) cons, concl); |
|
703 |
||
704 |
fun ind_term concf = Library.foldr one_eq |
|
705 |
(mapn (fn n => fn x => (P_name n, x)) 1 conss, |
|
706 |
mk_trp (foldr1 mk_conj (mapn concf 1 dnames))); |
|
707 |
val take_ss = HOL_ss addsimps take_rews; |
|
708 |
fun quant_tac i = EVERY |
|
709 |
(mapn (fn n => fn _ => res_inst_tac [("x", x_name n)] spec i) 1 dnames); |
|
710 |
||
711 |
fun ind_prems_tac prems = EVERY |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
712 |
(maps (fn cons => |
23152 | 713 |
(resolve_tac prems 1 :: |
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
714 |
maps (fn (_,args) => |
23152 | 715 |
resolve_tac prems 1 :: |
716 |
map (K(atac 1)) (nonlazy args) @ |
|
717 |
map (K(atac 1)) (List.filter is_rec args)) |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
718 |
cons)) |
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
719 |
conss); |
23152 | 720 |
local |
721 |
(* check whether every/exists constructor of the n-th part of the equation: |
|
722 |
it has a possibly indirectly recursive argument that isn't/is possibly |
|
723 |
indirectly lazy *) |
|
724 |
fun rec_to quant nfn rfn ns lazy_rec (n,cons) = quant (exists (fn arg => |
|
725 |
is_rec arg andalso not(rec_of arg mem ns) andalso |
|
726 |
((rec_of arg = n andalso nfn(lazy_rec orelse is_lazy arg)) orelse |
|
727 |
rec_of arg <> n andalso rec_to quant nfn rfn (rec_of arg::ns) |
|
728 |
(lazy_rec orelse is_lazy arg) (n, (List.nth(conss,rec_of arg)))) |
|
729 |
) o snd) cons; |
|
730 |
fun all_rec_to ns = rec_to forall not all_rec_to ns; |
|
731 |
fun warn (n,cons) = |
|
732 |
if all_rec_to [] false (n,cons) |
|
733 |
then (warning ("domain "^List.nth(dnames,n)^" is empty!"); true) |
|
734 |
else false; |
|
735 |
fun lazy_rec_to ns = rec_to exists I lazy_rec_to ns; |
|
736 |
||
737 |
in |
|
738 |
val n__eqs = mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs; |
|
739 |
val is_emptys = map warn n__eqs; |
|
740 |
val is_finite = forall (not o lazy_rec_to [] false) n__eqs; |
|
741 |
end; |
|
742 |
in (* local *) |
|
743 |
val finite_ind = |
|
744 |
let |
|
745 |
fun concf n dn = %:(P_name n) $ (dc_take dn $ %:"n" `%(x_name n)); |
|
746 |
val goal = ind_term concf; |
|
747 |
||
748 |
fun tacf prems = |
|
749 |
let |
|
750 |
val tacs1 = [ |
|
751 |
quant_tac 1, |
|
752 |
simp_tac HOL_ss 1, |
|
27112 | 753 |
DatatypePackage.induct_tac @{context} "n" 1, |
23152 | 754 |
simp_tac (take_ss addsimps prems) 1, |
755 |
TRY (safe_tac HOL_cs)]; |
|
756 |
fun arg_tac arg = |
|
757 |
case_UU_tac (prems @ con_rews) 1 |
|
758 |
(List.nth (dnames, rec_of arg) ^ "_take n$" ^ vname arg); |
|
759 |
fun con_tacs (con, args) = |
|
760 |
asm_simp_tac take_ss 1 :: |
|
761 |
map arg_tac (List.filter is_nonlazy_rec args) @ |
|
762 |
[resolve_tac prems 1] @ |
|
763 |
map (K (atac 1)) (nonlazy args) @ |
|
764 |
map (K (etac spec 1)) (List.filter is_rec args); |
|
765 |
fun cases_tacs (cons, cases) = |
|
766 |
res_inst_tac [("x","x")] cases 1 :: |
|
767 |
asm_simp_tac (take_ss addsimps prems) 1 :: |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
768 |
maps con_tacs cons; |
23152 | 769 |
in |
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
770 |
tacs1 @ maps cases_tacs (conss ~~ cases) |
23152 | 771 |
end; |
772 |
in pg'' thy [] goal tacf end; |
|
773 |
||
774 |
val take_lemmas = |
|
775 |
let |
|
776 |
fun take_lemma n (dn, ax_reach) = |
|
777 |
let |
|
778 |
val lhs = dc_take dn $ Bound 0 `%(x_name n); |
|
779 |
val rhs = dc_take dn $ Bound 0 `%(x_name n^"'"); |
|
780 |
val concl = mk_trp (%:(x_name n) === %:(x_name n^"'")); |
|
781 |
val goal = mk_All ("n", mk_trp (lhs === rhs)) ===> concl; |
|
782 |
fun tacf prems = [ |
|
783 |
res_inst_tac [("t", x_name n )] (ax_reach RS subst) 1, |
|
784 |
res_inst_tac [("t", x_name n^"'")] (ax_reach RS subst) 1, |
|
785 |
stac fix_def2 1, |
|
786 |
REPEAT (CHANGED |
|
787 |
(rtac (contlub_cfun_arg RS ssubst) 1 THEN chain_tac 1)), |
|
788 |
stac contlub_cfun_fun 1, |
|
789 |
stac contlub_cfun_fun 2, |
|
790 |
rtac lub_equal 3, |
|
791 |
chain_tac 1, |
|
792 |
rtac allI 1, |
|
793 |
resolve_tac prems 1]; |
|
794 |
in pg'' thy axs_take_def goal tacf end; |
|
795 |
in mapn take_lemma 1 (dnames ~~ axs_reach) end; |
|
796 |
||
797 |
(* ----- theorems concerning finiteness and induction ----------------------- *) |
|
798 |
||
799 |
val (finites, ind) = |
|
800 |
if is_finite |
|
801 |
then (* finite case *) |
|
802 |
let |
|
803 |
fun take_enough dn = mk_ex ("n",dc_take dn $ Bound 0 ` %:"x" === %:"x"); |
|
804 |
fun dname_lemma dn = |
|
805 |
let |
|
806 |
val prem1 = mk_trp (defined (%:"x")); |
|
807 |
val disj1 = mk_all ("n", dc_take dn $ Bound 0 ` %:"x" === UU); |
|
808 |
val prem2 = mk_trp (mk_disj (disj1, take_enough dn)); |
|
809 |
val concl = mk_trp (take_enough dn); |
|
810 |
val goal = prem1 ===> prem2 ===> concl; |
|
811 |
val tacs = [ |
|
812 |
etac disjE 1, |
|
813 |
etac notE 1, |
|
814 |
resolve_tac take_lemmas 1, |
|
815 |
asm_simp_tac take_ss 1, |
|
816 |
atac 1]; |
|
817 |
in pg [] goal tacs end; |
|
818 |
val finite_lemmas1a = map dname_lemma dnames; |
|
819 |
||
820 |
val finite_lemma1b = |
|
821 |
let |
|
822 |
fun mk_eqn n ((dn, args), _) = |
|
823 |
let |
|
824 |
val disj1 = dc_take dn $ Bound 1 ` Bound 0 === UU; |
|
825 |
val disj2 = dc_take dn $ Bound 1 ` Bound 0 === Bound 0; |
|
826 |
in |
|
827 |
mk_constrainall |
|
828 |
(x_name n, Type (dn,args), mk_disj (disj1, disj2)) |
|
829 |
end; |
|
830 |
val goal = |
|
831 |
mk_trp (mk_all ("n", foldr1 mk_conj (mapn mk_eqn 1 eqs))); |
|
832 |
fun arg_tacs vn = [ |
|
833 |
eres_inst_tac [("x", vn)] all_dupE 1, |
|
834 |
etac disjE 1, |
|
835 |
asm_simp_tac (HOL_ss addsimps con_rews) 1, |
|
836 |
asm_simp_tac take_ss 1]; |
|
837 |
fun con_tacs (con, args) = |
|
838 |
asm_simp_tac take_ss 1 :: |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
839 |
maps arg_tacs (nonlazy_rec args); |
23152 | 840 |
fun foo_tacs n (cons, cases) = |
841 |
simp_tac take_ss 1 :: |
|
842 |
rtac allI 1 :: |
|
843 |
res_inst_tac [("x",x_name n)] cases 1 :: |
|
844 |
asm_simp_tac take_ss 1 :: |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
845 |
maps con_tacs cons; |
23152 | 846 |
val tacs = |
847 |
rtac allI 1 :: |
|
27112 | 848 |
DatatypePackage.induct_tac @{context} "n" 1 :: |
23152 | 849 |
simp_tac take_ss 1 :: |
850 |
TRY (safe_tac (empty_cs addSEs [conjE] addSIs [conjI])) :: |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
851 |
flat (mapn foo_tacs 1 (conss ~~ cases)); |
23152 | 852 |
in pg [] goal tacs end; |
853 |
||
854 |
fun one_finite (dn, l1b) = |
|
855 |
let |
|
856 |
val goal = mk_trp (%%:(dn^"_finite") $ %:"x"); |
|
857 |
val tacs = [ |
|
858 |
case_UU_tac take_rews 1 "x", |
|
859 |
eresolve_tac finite_lemmas1a 1, |
|
860 |
step_tac HOL_cs 1, |
|
861 |
step_tac HOL_cs 1, |
|
862 |
cut_facts_tac [l1b] 1, |
|
863 |
fast_tac HOL_cs 1]; |
|
864 |
in pg axs_finite_def goal tacs end; |
|
865 |
||
866 |
val finites = map one_finite (dnames ~~ atomize finite_lemma1b); |
|
867 |
val ind = |
|
868 |
let |
|
869 |
fun concf n dn = %:(P_name n) $ %:(x_name n); |
|
870 |
fun tacf prems = |
|
871 |
let |
|
872 |
fun finite_tacs (finite, fin_ind) = [ |
|
873 |
rtac(rewrite_rule axs_finite_def finite RS exE)1, |
|
874 |
etac subst 1, |
|
875 |
rtac fin_ind 1, |
|
876 |
ind_prems_tac prems]; |
|
877 |
in |
|
878 |
TRY (safe_tac HOL_cs) :: |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
879 |
maps finite_tacs (finites ~~ atomize finite_ind) |
23152 | 880 |
end; |
881 |
in pg'' thy [] (ind_term concf) tacf end; |
|
882 |
in (finites, ind) end (* let *) |
|
883 |
||
884 |
else (* infinite case *) |
|
885 |
let |
|
886 |
fun one_finite n dn = |
|
887 |
read_instantiate_sg thy |
|
888 |
[("P",dn^"_finite "^x_name n)] excluded_middle; |
|
889 |
val finites = mapn one_finite 1 dnames; |
|
890 |
||
891 |
val goal = |
|
892 |
let |
|
26012 | 893 |
fun one_adm n _ = mk_trp (mk_adm (%:(P_name n))); |
23152 | 894 |
fun concf n dn = %:(P_name n) $ %:(x_name n); |
895 |
in Logic.list_implies (mapn one_adm 1 dnames, ind_term concf) end; |
|
896 |
fun tacf prems = |
|
897 |
map (fn ax_reach => rtac (ax_reach RS subst) 1) axs_reach @ [ |
|
898 |
quant_tac 1, |
|
899 |
rtac (adm_impl_admw RS wfix_ind) 1, |
|
25895
0eaadfa8889e
converted adm_all and adm_ball to rule_format; cleaned up
huffman
parents:
25805
diff
changeset
|
900 |
REPEAT_DETERM (rtac adm_all 1), |
23152 | 901 |
REPEAT_DETERM ( |
902 |
TRY (rtac adm_conj 1) THEN |
|
903 |
rtac adm_subst 1 THEN |
|
904 |
cont_tacR 1 THEN resolve_tac prems 1), |
|
905 |
strip_tac 1, |
|
906 |
rtac (rewrite_rule axs_take_def finite_ind) 1, |
|
907 |
ind_prems_tac prems]; |
|
908 |
val ind = (pg'' thy [] goal tacf |
|
909 |
handle ERROR _ => |
|
910 |
(warning "Cannot prove infinite induction rule"; refl)); |
|
911 |
in (finites, ind) end; |
|
912 |
end; (* local *) |
|
913 |
||
914 |
(* ----- theorem concerning coinduction ------------------------------------- *) |
|
915 |
||
916 |
local |
|
917 |
val xs = mapn (fn n => K (x_name n)) 1 dnames; |
|
918 |
fun bnd_arg n i = Bound(2*(n_eqs - n)-i-1); |
|
919 |
val take_ss = HOL_ss addsimps take_rews; |
|
920 |
val sproj = prj (fn s => K("fst("^s^")")) (fn s => K("snd("^s^")")); |
|
921 |
val coind_lemma = |
|
922 |
let |
|
923 |
fun mk_prj n _ = proj (%:"R") eqs n $ bnd_arg n 0 $ bnd_arg n 1; |
|
924 |
fun mk_eqn n dn = |
|
925 |
(dc_take dn $ %:"n" ` bnd_arg n 0) === |
|
926 |
(dc_take dn $ %:"n" ` bnd_arg n 1); |
|
927 |
fun mk_all2 (x,t) = mk_all (x, mk_all (x^"'", t)); |
|
928 |
val goal = |
|
929 |
mk_trp (mk_imp (%%:(comp_dname^"_bisim") $ %:"R", |
|
930 |
Library.foldr mk_all2 (xs, |
|
931 |
Library.foldr mk_imp (mapn mk_prj 0 dnames, |
|
932 |
foldr1 mk_conj (mapn mk_eqn 0 dnames))))); |
|
933 |
fun x_tacs n x = [ |
|
934 |
rotate_tac (n+1) 1, |
|
935 |
etac all2E 1, |
|
936 |
eres_inst_tac [("P1", sproj "R" eqs n^" "^x^" "^x^"'")] (mp RS disjE) 1, |
|
937 |
TRY (safe_tac HOL_cs), |
|
938 |
REPEAT (CHANGED (asm_simp_tac take_ss 1))]; |
|
939 |
val tacs = [ |
|
940 |
rtac impI 1, |
|
27112 | 941 |
DatatypePackage.induct_tac @{context} "n" 1, |
23152 | 942 |
simp_tac take_ss 1, |
943 |
safe_tac HOL_cs] @ |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
944 |
flat (mapn x_tacs 0 xs); |
23152 | 945 |
in pg [ax_bisim_def] goal tacs end; |
946 |
in |
|
947 |
val coind = |
|
948 |
let |
|
949 |
fun mk_prj n x = mk_trp (proj (%:"R") eqs n $ %:x $ %:(x^"'")); |
|
950 |
fun mk_eqn x = %:x === %:(x^"'"); |
|
951 |
val goal = |
|
952 |
mk_trp (%%:(comp_dname^"_bisim") $ %:"R") ===> |
|
953 |
Logic.list_implies (mapn mk_prj 0 xs, |
|
954 |
mk_trp (foldr1 mk_conj (map mk_eqn xs))); |
|
955 |
val tacs = |
|
956 |
TRY (safe_tac HOL_cs) :: |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
957 |
maps (fn take_lemma => [ |
23152 | 958 |
rtac take_lemma 1, |
959 |
cut_facts_tac [coind_lemma] 1, |
|
960 |
fast_tac HOL_cs 1]) |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
961 |
take_lemmas; |
23152 | 962 |
in pg [] goal tacs end; |
963 |
end; (* local *) |
|
964 |
||
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24503
diff
changeset
|
965 |
in thy |> Sign.add_path comp_dnam |
23152 | 966 |
|> (snd o (PureThy.add_thmss (map Thm.no_attributes [ |
967 |
("take_rews" , take_rews ), |
|
968 |
("take_lemmas", take_lemmas), |
|
969 |
("finites" , finites ), |
|
970 |
("finite_ind", [finite_ind]), |
|
971 |
("ind" , [ind ]), |
|
972 |
("coind" , [coind ])]))) |
|
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24503
diff
changeset
|
973 |
|> Sign.parent_path |> rpair take_rews |
23152 | 974 |
end; (* let *) |
975 |
end; (* local *) |
|
976 |
end; (* struct *) |