author | huffman |
Sat, 27 Feb 2010 18:45:06 -0800 | |
changeset 35464 | 2ae3362ba8ee |
parent 35462 | f5461b02d754 |
child 35466 | 9fcfd5763181 |
permissions | -rw-r--r-- |
32126 | 1 |
(* Title: HOLCF/Tools/Domain/domain_theorems.ML |
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Author: David von Oheimb |
32740 | 3 |
Author: Brian Huffman |
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|
5 |
Proof generator for domain command. |
|
6 |
*) |
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||
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val HOLCF_ss = @{simpset}; |
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|
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signature DOMAIN_THEOREMS = |
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sig |
|
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val theorems: |
13 |
Domain_Library.eq * Domain_Library.eq list |
|
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-> typ * (binding * (bool * binding option * typ) list * mixfix) list |
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-> theory -> thm list * theory; |
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||
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val comp_theorems: bstring * Domain_Library.eq list -> theory -> thm list * theory; |
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val quiet_mode: bool Unsynchronized.ref; |
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val trace_domain: bool Unsynchronized.ref; |
|
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end; |
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||
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structure Domain_Theorems :> DOMAIN_THEOREMS = |
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struct |
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|
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val quiet_mode = Unsynchronized.ref false; |
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val trace_domain = Unsynchronized.ref false; |
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fun message s = if !quiet_mode then () else writeln s; |
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fun trace s = if !trace_domain then tracing s else (); |
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||
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val adm_impl_admw = @{thm adm_impl_admw}; |
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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 ch2ch_fst = @{thm ch2ch_fst}; |
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val ch2ch_snd = @{thm ch2ch_snd}; |
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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 contlub_cfun_fun = @{thm contlub_cfun_fun}; |
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val contlub_fst = @{thm contlub_fst}; |
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val contlub_snd = @{thm contlub_snd}; |
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val contlubE = @{thm contlubE}; |
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val cont_const = @{thm cont_const}; |
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val cont_id = @{thm cont_id}; |
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val cont2cont_fst = @{thm cont2cont_fst}; |
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val cont2cont_snd = @{thm cont2cont_snd}; |
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val cont2cont_Rep_CFun = @{thm cont2cont_Rep_CFun}; |
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val fix_def2 = @{thm fix_def2}; |
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val lub_equal = @{thm lub_equal}; |
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val retraction_strict = @{thm retraction_strict}; |
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val wfix_ind = @{thm wfix_ind}; |
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val iso_intro = @{thm iso.intro}; |
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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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||
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(* ----- general proof facilities ------------------------------------------- *) |
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||
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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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||
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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} = |
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rewrite_goals_tac defs THEN |
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EVERY (tacs {prems = map (rewrite_rule defs) prems, context = context}) |
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in Goal.prove_global thy [] asms prop tac end; |
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||
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fun pg' thy defs t tacsf = |
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let |
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fun tacs {prems, context} = |
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if null prems then tacsf context |
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else cut_facts_tac prems 1 :: tacsf context; |
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in pg'' thy defs t tacs end; |
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||
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(* FIXME!!!!!!!!! *) |
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(* We should NEVER re-parse variable names as strings! *) |
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(* The names can conflict with existing constants or other syntax! *) |
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fun case_UU_tac ctxt rews i v = |
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InductTacs.case_tac ctxt (v^"=UU") i THEN |
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asm_simp_tac (HOLCF_ss addsimps rews) i; |
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||
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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, ch2ch_fst, ch2ch_snd]; |
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|
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(* ----- general proofs ----------------------------------------------------- *) |
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||
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val all2E = @{lemma "!x y . P x y ==> (P x y ==> R) ==> R" by simp} |
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|
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fun theorems |
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(((dname, _), cons) : eq, eqs : eq list) |
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(dom_eqn : typ * (binding * (bool * binding option * typ) list * mixfix) list) |
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(thy : theory) = |
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let |
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||
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val _ = message ("Proving isomorphism properties of domain "^dname^" ..."); |
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val map_tab = Domain_Isomorphism.get_map_tab thy; |
114 |
||
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|
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(* ----- getting the axioms and definitions --------------------------------- *) |
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||
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local |
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fun ga s dn = PureThy.get_thm thy (dn ^ "." ^ s); |
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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_pat_def = map (get_def pat_name) cons; |
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val ax_copy_def = ga "copy_def" dname; |
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end; (* local *) |
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||
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(* ----- define constructors ------------------------------------------------ *) |
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val lhsT = fst dom_eqn; |
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val rhsT = |
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let |
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fun mk_arg_typ (lazy, sel, T) = if lazy then mk_uT T else T; |
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fun mk_con_typ (bind, args, mx) = |
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if null args then oneT else foldr1 mk_sprodT (map mk_arg_typ args); |
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fun mk_eq_typ (_, cons) = foldr1 mk_ssumT (map mk_con_typ cons); |
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in |
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mk_eq_typ dom_eqn |
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end; |
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||
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val rep_const = Const(dname^"_rep", lhsT ->> rhsT); |
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val abs_const = Const(dname^"_abs", rhsT ->> lhsT); |
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val (result, thy) = |
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Domain_Constructors.add_domain_constructors |
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(Long_Name.base_name dname) dom_eqn |
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(rep_const, abs_const) (ax_rep_iso, ax_abs_iso) ax_when_def thy; |
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val con_appls = #con_betas result; |
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val {exhaust, casedist, ...} = result; |
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val {con_compacts, con_rews, inverts, injects, dist_les, dist_eqs, ...} = result; |
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val {sel_rews, ...} = result; |
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val when_rews = #cases result; |
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val when_strict = hd when_rews; |
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move proofs of dis_rews to domain_constructors.ML; change dis_defins to iff-style
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val dis_rews = #dis_rews result; |
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val axs_mat_def = #match_rews result; |
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|
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(* ----- theorems concerning the isomorphism -------------------------------- *) |
162 |
||
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val pg = pg' thy; |
164 |
||
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val dc_copy = %%:(dname^"_copy"); |
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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 iso_rews = map Drule.export_without_context [ax_abs_iso, ax_rep_iso, abs_strict, rep_strict]; |
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|
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(* ----- theorems concerning the constructors, discriminators and selectors - *) |
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||
173 |
local |
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fun mat_strict (con, _, _) = |
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let |
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val goal = mk_trp (%%:(mat_name con) ` UU ` %:"rhs" === UU); |
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val tacs = [asm_simp_tac (HOLCF_ss addsimps [when_strict]) 1]; |
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in pg axs_mat_def goal (K tacs) end; |
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|
29402 | 180 |
val _ = trace " Proving mat_stricts..."; |
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val mat_stricts = map mat_strict cons; |
182 |
||
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fun one_mat c (con, _, args) = |
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let |
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val lhs = %%:(mat_name c) ` con_app con args ` %:"rhs"; |
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val rhs = |
187 |
if con = c |
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then list_ccomb (%:"rhs", map %# args) |
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else mk_fail; |
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val goal = lift_defined %: (nonlazy args, mk_trp (lhs === rhs)); |
191 |
val tacs = [asm_simp_tac (HOLCF_ss addsimps when_rews) 1]; |
|
27208
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192 |
in pg axs_mat_def goal (K tacs) end; |
23152 | 193 |
|
29402 | 194 |
val _ = trace " Proving mat_apps..."; |
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val mat_apps = |
35288 | 196 |
maps (fn (c,_,_) => map (one_mat c) cons) cons; |
23152 | 197 |
in |
198 |
val mat_rews = mat_stricts @ mat_apps; |
|
199 |
end; |
|
200 |
||
201 |
local |
|
202 |
fun ps args = mapn (fn n => fn _ => %:("pat" ^ string_of_int n)) 1 args; |
|
203 |
||
35288 | 204 |
fun pat_lhs (con,_,args) = mk_branch (list_comb (%%:(pat_name con), ps args)); |
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|
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fun pat_rhs (con,_,[]) = mk_return ((%:"rhs") ` HOLogic.unit) |
207 |
| pat_rhs (con,_,args) = |
|
26012 | 208 |
(mk_branch (mk_ctuple_pat (ps args))) |
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`(%:"rhs")`(mk_ctuple (map %# args)); |
210 |
||
211 |
fun pat_strict c = |
|
212 |
let |
|
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val axs = @{thm branch_def} :: axs_pat_def; |
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val goal = mk_trp (strict (pat_lhs c ` (%:"rhs"))); |
215 |
val tacs = [simp_tac (HOLCF_ss addsimps [when_strict]) 1]; |
|
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parents:
27153
diff
changeset
|
216 |
in pg axs goal (K tacs) end; |
23152 | 217 |
|
35288 | 218 |
fun pat_app c (con, _, args) = |
23152 | 219 |
let |
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val axs = @{thm branch_def} :: axs_pat_def; |
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val lhs = (pat_lhs c)`(%:"rhs")`(con_app con args); |
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val rhs = if con = first c then pat_rhs c else mk_fail; |
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val goal = lift_defined %: (nonlazy args, mk_trp (lhs === rhs)); |
224 |
val tacs = [asm_simp_tac (HOLCF_ss addsimps when_rews) 1]; |
|
27208
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wenzelm
parents:
27153
diff
changeset
|
225 |
in pg axs goal (K tacs) end; |
23152 | 226 |
|
29402 | 227 |
val _ = trace " Proving pat_stricts..."; |
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val pat_stricts = map pat_strict cons; |
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val _ = trace " Proving pat_apps..."; |
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230 |
val pat_apps = maps (fn c => map (pat_app c) cons) cons; |
23152 | 231 |
in |
232 |
val pat_rews = pat_stricts @ pat_apps; |
|
233 |
end; |
|
234 |
||
235 |
(* ----- theorems concerning one induction step ----------------------------- *) |
|
236 |
||
237 |
val copy_strict = |
|
238 |
let |
|
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239 |
val _ = trace " Proving copy_strict..."; |
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val goal = mk_trp (strict (dc_copy `% "f")); |
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val rules = [abs_strict, rep_strict] @ @{thms domain_map_stricts}; |
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242 |
val tacs = [asm_simp_tac (HOLCF_ss addsimps rules) 1]; |
35058
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|
243 |
in |
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|
244 |
SOME (pg [ax_copy_def] goal (K tacs)) |
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245 |
handle |
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|
246 |
THM (s, _, _) => (trace s; NONE) |
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247 |
| ERROR s => (trace s; NONE) |
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|
248 |
end; |
23152 | 249 |
|
250 |
local |
|
35288 | 251 |
fun copy_app (con, _, args) = |
23152 | 252 |
let |
253 |
val lhs = dc_copy`%"f"`(con_app con args); |
|
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|
254 |
fun one_rhs arg = |
33971 | 255 |
if Datatype_Aux.is_rec_type (dtyp_of arg) |
33801 | 256 |
then Domain_Axioms.copy_of_dtyp map_tab |
257 |
(proj (%:"f") eqs) (dtyp_of arg) ` (%# arg) |
|
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|
258 |
else (%# arg); |
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|
259 |
val rhs = con_app2 con one_rhs args; |
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|
260 |
fun is_rec arg = Datatype_Aux.is_rec_type (dtyp_of arg); |
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|
261 |
fun is_nonlazy_rec arg = is_rec arg andalso not (is_lazy arg); |
acbc346e5310
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diff
changeset
|
262 |
fun nonlazy_rec args = map vname (filter is_nonlazy_rec args); |
23152 | 263 |
val goal = lift_defined %: (nonlazy_rec args, mk_trp (lhs === rhs)); |
33317 | 264 |
val args' = filter_out (fn a => is_rec a orelse is_lazy a) args; |
33504
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map functions for various types, with ep_pair/deflation/finite_deflation lemmas
huffman
parents:
33427
diff
changeset
|
265 |
val stricts = abs_strict :: rep_strict :: @{thms domain_map_stricts}; |
35443
2e0f9516947e
change domain package's treatment of variable names in theorems to be like datatype package
huffman
parents:
35288
diff
changeset
|
266 |
(* FIXME! case_UU_tac *) |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
267 |
fun tacs1 ctxt = map (case_UU_tac ctxt stricts 1 o vname) args'; |
33504
b4210cc3ac97
map functions for various types, with ep_pair/deflation/finite_deflation lemmas
huffman
parents:
33427
diff
changeset
|
268 |
val rules = [ax_abs_iso] @ @{thms domain_map_simps}; |
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
269 |
val tacs2 = [asm_simp_tac (HOLCF_ss addsimps rules) 1]; |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
270 |
in pg (ax_copy_def::con_appls) goal (fn ctxt => (tacs1 ctxt @ tacs2)) end; |
23152 | 271 |
in |
29402 | 272 |
val _ = trace " Proving copy_apps..."; |
23152 | 273 |
val copy_apps = map copy_app cons; |
274 |
end; |
|
275 |
||
276 |
local |
|
35288 | 277 |
fun one_strict (con, _, args) = |
23152 | 278 |
let |
279 |
val goal = mk_trp (dc_copy`UU`(con_app con args) === UU); |
|
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changeset
|
280 |
val rews = the_list copy_strict @ copy_apps @ con_rews; |
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|
281 |
(* FIXME! case_UU_tac *) |
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changeset
|
282 |
fun tacs ctxt = map (case_UU_tac ctxt rews 1) (nonlazy args) @ |
23152 | 283 |
[asm_simp_tac (HOLCF_ss addsimps rews) 1]; |
35058
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|
284 |
in |
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|
285 |
SOME (pg [] goal tacs) |
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|
286 |
handle |
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|
287 |
THM (s, _, _) => (trace s; NONE) |
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|
288 |
| ERROR s => (trace s; NONE) |
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|
289 |
end; |
23152 | 290 |
|
35288 | 291 |
fun has_nonlazy_rec (_, _, args) = exists is_nonlazy_rec args; |
23152 | 292 |
in |
29402 | 293 |
val _ = trace " Proving copy_stricts..."; |
35058
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changeset
|
294 |
val copy_stricts = map_filter one_strict (filter has_nonlazy_rec cons); |
23152 | 295 |
end; |
296 |
||
35058
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changeset
|
297 |
val copy_rews = the_list copy_strict @ copy_apps @ copy_stricts; |
23152 | 298 |
|
299 |
in |
|
300 |
thy |
|
30364
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diff
changeset
|
301 |
|> Sign.add_path (Long_Name.base_name dname) |
31004 | 302 |
|> snd o PureThy.add_thmss [ |
303 |
((Binding.name "iso_rews" , iso_rews ), [Simplifier.simp_add]), |
|
304 |
((Binding.name "exhaust" , [exhaust] ), []), |
|
305 |
((Binding.name "casedist" , [casedist] ), [Induct.cases_type dname]), |
|
306 |
((Binding.name "when_rews" , when_rews ), [Simplifier.simp_add]), |
|
307 |
((Binding.name "compacts" , con_compacts), [Simplifier.simp_add]), |
|
33427 | 308 |
((Binding.name "con_rews" , con_rews ), |
309 |
[Simplifier.simp_add, Fixrec.fixrec_simp_add]), |
|
31004 | 310 |
((Binding.name "sel_rews" , sel_rews ), [Simplifier.simp_add]), |
311 |
((Binding.name "dis_rews" , dis_rews ), [Simplifier.simp_add]), |
|
312 |
((Binding.name "pat_rews" , pat_rews ), [Simplifier.simp_add]), |
|
313 |
((Binding.name "dist_les" , dist_les ), [Simplifier.simp_add]), |
|
314 |
((Binding.name "dist_eqs" , dist_eqs ), [Simplifier.simp_add]), |
|
315 |
((Binding.name "inverts" , inverts ), [Simplifier.simp_add]), |
|
316 |
((Binding.name "injects" , injects ), [Simplifier.simp_add]), |
|
317 |
((Binding.name "copy_rews" , copy_rews ), [Simplifier.simp_add]), |
|
33427 | 318 |
((Binding.name "match_rews", mat_rews ), |
319 |
[Simplifier.simp_add, Fixrec.fixrec_simp_add])] |
|
24712
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changeset
|
320 |
|> Sign.parent_path |
28536 | 321 |
|> pair (iso_rews @ when_rews @ con_rews @ sel_rews @ dis_rews @ |
23152 | 322 |
pat_rews @ dist_les @ dist_eqs @ copy_rews) |
323 |
end; (* let *) |
|
324 |
||
325 |
fun comp_theorems (comp_dnam, eqs: eq list) thy = |
|
326 |
let |
|
27232 | 327 |
val global_ctxt = ProofContext.init thy; |
33801 | 328 |
val map_tab = Domain_Isomorphism.get_map_tab thy; |
27232 | 329 |
|
23152 | 330 |
val dnames = map (fst o fst) eqs; |
331 |
val conss = map snd eqs; |
|
28965 | 332 |
val comp_dname = Sign.full_bname thy comp_dnam; |
23152 | 333 |
|
29402 | 334 |
val _ = message ("Proving induction properties of domain "^comp_dname^" ..."); |
23152 | 335 |
val pg = pg' thy; |
336 |
||
337 |
(* ----- getting the composite axiom and definitions ------------------------ *) |
|
338 |
||
339 |
local |
|
26343
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diff
changeset
|
340 |
fun ga s dn = PureThy.get_thm thy (dn ^ "." ^ s); |
23152 | 341 |
in |
342 |
val axs_reach = map (ga "reach" ) dnames; |
|
343 |
val axs_take_def = map (ga "take_def" ) dnames; |
|
344 |
val axs_finite_def = map (ga "finite_def") dnames; |
|
345 |
val ax_copy2_def = ga "copy_def" comp_dnam; |
|
35444 | 346 |
(* TEMPORARILY DISABLED |
23152 | 347 |
val ax_bisim_def = ga "bisim_def" comp_dnam; |
35444 | 348 |
TEMPORARILY DISABLED *) |
23152 | 349 |
end; |
350 |
||
351 |
local |
|
26343
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diff
changeset
|
352 |
fun gt s dn = PureThy.get_thm thy (dn ^ "." ^ s); |
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parents:
26342
diff
changeset
|
353 |
fun gts s dn = PureThy.get_thms thy (dn ^ "." ^ s); |
23152 | 354 |
in |
355 |
val cases = map (gt "casedist" ) dnames; |
|
26336
a0e2b706ce73
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wenzelm
parents:
26012
diff
changeset
|
356 |
val con_rews = maps (gts "con_rews" ) dnames; |
a0e2b706ce73
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wenzelm
parents:
26012
diff
changeset
|
357 |
val copy_rews = maps (gts "copy_rews") dnames; |
23152 | 358 |
end; |
359 |
||
360 |
fun dc_take dn = %%:(dn^"_take"); |
|
361 |
val x_name = idx_name dnames "x"; |
|
362 |
val P_name = idx_name dnames "P"; |
|
363 |
val n_eqs = length eqs; |
|
364 |
||
365 |
(* ----- theorems concerning finite approximation and finite induction ------ *) |
|
366 |
||
367 |
local |
|
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32126
diff
changeset
|
368 |
val iterate_Cprod_ss = global_simpset_of @{theory Fix}; |
23152 | 369 |
val copy_con_rews = copy_rews @ con_rews; |
370 |
val copy_take_defs = |
|
371 |
(if n_eqs = 1 then [] else [ax_copy2_def]) @ axs_take_def; |
|
29402 | 372 |
val _ = trace " Proving take_stricts..."; |
35057 | 373 |
fun one_take_strict ((dn, args), _) = |
23152 | 374 |
let |
35057 | 375 |
val goal = mk_trp (strict (dc_take dn $ %:"n")); |
376 |
val rules = [ |
|
377 |
@{thm monofun_fst [THEN monofunE]}, |
|
378 |
@{thm monofun_snd [THEN monofunE]}]; |
|
379 |
val tacs = [ |
|
380 |
rtac @{thm UU_I} 1, |
|
381 |
rtac @{thm below_eq_trans} 1, |
|
382 |
resolve_tac axs_reach 2, |
|
383 |
rtac @{thm monofun_cfun_fun} 1, |
|
384 |
REPEAT (resolve_tac rules 1), |
|
385 |
rtac @{thm iterate_below_fix} 1]; |
|
386 |
in pg axs_take_def goal (K tacs) end; |
|
387 |
val take_stricts = map one_take_strict eqs; |
|
23152 | 388 |
fun take_0 n dn = |
389 |
let |
|
35058
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
390 |
val goal = mk_trp ((dc_take dn $ @{term "0::nat"}) `% x_name n === UU); |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
391 |
in pg axs_take_def goal (K [simp_tac iterate_Cprod_ss 1]) end; |
23152 | 392 |
val take_0s = mapn take_0 1 dnames; |
29402 | 393 |
val _ = trace " Proving take_apps..."; |
35288 | 394 |
fun one_take_app dn (con, _, args) = |
23152 | 395 |
let |
35058
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
396 |
fun mk_take n = dc_take (List.nth (dnames, n)) $ %:"n"; |
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
397 |
fun one_rhs arg = |
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
398 |
if Datatype_Aux.is_rec_type (dtyp_of arg) |
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
399 |
then Domain_Axioms.copy_of_dtyp map_tab |
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
400 |
mk_take (dtyp_of arg) ` (%# arg) |
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
401 |
else (%# arg); |
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
402 |
val lhs = (dc_take dn $ (%%:"Suc" $ %:"n"))`(con_app con args); |
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
403 |
val rhs = con_app2 con one_rhs args; |
35059
acbc346e5310
correct definedness side conditions for copy_apps and take_apps
huffman
parents:
35058
diff
changeset
|
404 |
fun is_rec arg = Datatype_Aux.is_rec_type (dtyp_of arg); |
acbc346e5310
correct definedness side conditions for copy_apps and take_apps
huffman
parents:
35058
diff
changeset
|
405 |
fun is_nonlazy_rec arg = is_rec arg andalso not (is_lazy arg); |
acbc346e5310
correct definedness side conditions for copy_apps and take_apps
huffman
parents:
35058
diff
changeset
|
406 |
fun nonlazy_rec args = map vname (filter is_nonlazy_rec args); |
acbc346e5310
correct definedness side conditions for copy_apps and take_apps
huffman
parents:
35058
diff
changeset
|
407 |
val goal = lift_defined %: (nonlazy_rec args, mk_trp (lhs === rhs)); |
acbc346e5310
correct definedness side conditions for copy_apps and take_apps
huffman
parents:
35058
diff
changeset
|
408 |
val tacs = [asm_simp_tac (HOLCF_ss addsimps copy_con_rews) 1]; |
acbc346e5310
correct definedness side conditions for copy_apps and take_apps
huffman
parents:
35058
diff
changeset
|
409 |
in pg copy_take_defs goal (K tacs) end; |
35058
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
410 |
fun one_take_apps ((dn, _), cons) = map (one_take_app dn) cons; |
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
411 |
val take_apps = maps one_take_apps eqs; |
23152 | 412 |
in |
35021
c839a4c670c6
renamed old-style Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
34974
diff
changeset
|
413 |
val take_rews = map Drule.export_without_context |
35058
d0cc1650b378
handle case where copy_stricts cannot be proven; rewrite proof script for take_apps
huffman
parents:
35057
diff
changeset
|
414 |
(take_stricts @ take_0s @ take_apps); |
23152 | 415 |
end; (* local *) |
416 |
||
417 |
local |
|
35288 | 418 |
fun one_con p (con, _, args) = |
23152 | 419 |
let |
35443
2e0f9516947e
change domain package's treatment of variable names in theorems to be like datatype package
huffman
parents:
35288
diff
changeset
|
420 |
val P_names = map P_name (1 upto (length dnames)); |
2e0f9516947e
change domain package's treatment of variable names in theorems to be like datatype package
huffman
parents:
35288
diff
changeset
|
421 |
val vns = Name.variant_list P_names (map vname args); |
2e0f9516947e
change domain package's treatment of variable names in theorems to be like datatype package
huffman
parents:
35288
diff
changeset
|
422 |
val nonlazy_vns = map snd (filter_out (is_lazy o fst) (args ~~ vns)); |
23152 | 423 |
fun ind_hyp arg = %:(P_name (1 + rec_of arg)) $ bound_arg args arg; |
424 |
val t1 = mk_trp (%:p $ con_app2 con (bound_arg args) args); |
|
33317 | 425 |
val t2 = lift ind_hyp (filter is_rec args, t1); |
35443
2e0f9516947e
change domain package's treatment of variable names in theorems to be like datatype package
huffman
parents:
35288
diff
changeset
|
426 |
val t3 = lift_defined (bound_arg vns) (nonlazy_vns, t2); |
2e0f9516947e
change domain package's treatment of variable names in theorems to be like datatype package
huffman
parents:
35288
diff
changeset
|
427 |
in Library.foldr mk_All (vns, t3) end; |
23152 | 428 |
|
429 |
fun one_eq ((p, cons), concl) = |
|
430 |
mk_trp (%:p $ UU) ===> Logic.list_implies (map (one_con p) cons, concl); |
|
431 |
||
432 |
fun ind_term concf = Library.foldr one_eq |
|
433 |
(mapn (fn n => fn x => (P_name n, x)) 1 conss, |
|
434 |
mk_trp (foldr1 mk_conj (mapn concf 1 dnames))); |
|
435 |
val take_ss = HOL_ss addsimps take_rews; |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
436 |
fun quant_tac ctxt i = EVERY |
27239 | 437 |
(mapn (fn n => fn _ => res_inst_tac ctxt [(("x", 0), x_name n)] spec i) 1 dnames); |
23152 | 438 |
|
439 |
fun ind_prems_tac prems = EVERY |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
440 |
(maps (fn cons => |
23152 | 441 |
(resolve_tac prems 1 :: |
35288 | 442 |
maps (fn (_,_,args) => |
23152 | 443 |
resolve_tac prems 1 :: |
444 |
map (K(atac 1)) (nonlazy args) @ |
|
33317 | 445 |
map (K(atac 1)) (filter is_rec args)) |
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
446 |
cons)) |
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
447 |
conss); |
23152 | 448 |
local |
449 |
(* check whether every/exists constructor of the n-th part of the equation: |
|
450 |
it has a possibly indirectly recursive argument that isn't/is possibly |
|
451 |
indirectly lazy *) |
|
452 |
fun rec_to quant nfn rfn ns lazy_rec (n,cons) = quant (exists (fn arg => |
|
453 |
is_rec arg andalso not(rec_of arg mem ns) andalso |
|
454 |
((rec_of arg = n andalso nfn(lazy_rec orelse is_lazy arg)) orelse |
|
455 |
rec_of arg <> n andalso rec_to quant nfn rfn (rec_of arg::ns) |
|
456 |
(lazy_rec orelse is_lazy arg) (n, (List.nth(conss,rec_of arg)))) |
|
35288 | 457 |
) o third) cons; |
23152 | 458 |
fun all_rec_to ns = rec_to forall not all_rec_to ns; |
459 |
fun warn (n,cons) = |
|
460 |
if all_rec_to [] false (n,cons) |
|
461 |
then (warning ("domain "^List.nth(dnames,n)^" is empty!"); true) |
|
462 |
else false; |
|
463 |
fun lazy_rec_to ns = rec_to exists I lazy_rec_to ns; |
|
464 |
||
465 |
in |
|
466 |
val n__eqs = mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs; |
|
467 |
val is_emptys = map warn n__eqs; |
|
468 |
val is_finite = forall (not o lazy_rec_to [] false) n__eqs; |
|
469 |
end; |
|
470 |
in (* local *) |
|
29402 | 471 |
val _ = trace " Proving finite_ind..."; |
23152 | 472 |
val finite_ind = |
473 |
let |
|
474 |
fun concf n dn = %:(P_name n) $ (dc_take dn $ %:"n" `%(x_name n)); |
|
475 |
val goal = ind_term concf; |
|
476 |
||
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
477 |
fun tacf {prems, context} = |
23152 | 478 |
let |
479 |
val tacs1 = [ |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
480 |
quant_tac context 1, |
23152 | 481 |
simp_tac HOL_ss 1, |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
482 |
InductTacs.induct_tac context [[SOME "n"]] 1, |
23152 | 483 |
simp_tac (take_ss addsimps prems) 1, |
484 |
TRY (safe_tac HOL_cs)]; |
|
485 |
fun arg_tac arg = |
|
35443
2e0f9516947e
change domain package's treatment of variable names in theorems to be like datatype package
huffman
parents:
35288
diff
changeset
|
486 |
(* FIXME! case_UU_tac *) |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
487 |
case_UU_tac context (prems @ con_rews) 1 |
23152 | 488 |
(List.nth (dnames, rec_of arg) ^ "_take n$" ^ vname arg); |
35288 | 489 |
fun con_tacs (con, _, args) = |
23152 | 490 |
asm_simp_tac take_ss 1 :: |
33317 | 491 |
map arg_tac (filter is_nonlazy_rec args) @ |
23152 | 492 |
[resolve_tac prems 1] @ |
33317 | 493 |
map (K (atac 1)) (nonlazy args) @ |
494 |
map (K (etac spec 1)) (filter is_rec args); |
|
23152 | 495 |
fun cases_tacs (cons, cases) = |
27239 | 496 |
res_inst_tac context [(("x", 0), "x")] cases 1 :: |
23152 | 497 |
asm_simp_tac (take_ss addsimps prems) 1 :: |
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
498 |
maps con_tacs cons; |
23152 | 499 |
in |
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
500 |
tacs1 @ maps cases_tacs (conss ~~ cases) |
23152 | 501 |
end; |
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
502 |
in pg'' thy [] goal tacf |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
503 |
handle ERROR _ => (warning "Proof of finite_ind failed."; TrueI) |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
504 |
end; |
23152 | 505 |
|
29402 | 506 |
val _ = trace " Proving take_lemmas..."; |
23152 | 507 |
val take_lemmas = |
508 |
let |
|
509 |
fun take_lemma n (dn, ax_reach) = |
|
510 |
let |
|
511 |
val lhs = dc_take dn $ Bound 0 `%(x_name n); |
|
512 |
val rhs = dc_take dn $ Bound 0 `%(x_name n^"'"); |
|
513 |
val concl = mk_trp (%:(x_name n) === %:(x_name n^"'")); |
|
514 |
val goal = mk_All ("n", mk_trp (lhs === rhs)) ===> concl; |
|
33396 | 515 |
val rules = [contlub_fst RS contlubE RS ssubst, |
516 |
contlub_snd RS contlubE RS ssubst]; |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
517 |
fun tacf {prems, context} = [ |
27239 | 518 |
res_inst_tac context [(("t", 0), x_name n )] (ax_reach RS subst) 1, |
519 |
res_inst_tac context [(("t", 0), x_name n^"'")] (ax_reach RS subst) 1, |
|
23152 | 520 |
stac fix_def2 1, |
521 |
REPEAT (CHANGED |
|
33396 | 522 |
(resolve_tac rules 1 THEN chain_tac 1)), |
23152 | 523 |
stac contlub_cfun_fun 1, |
524 |
stac contlub_cfun_fun 2, |
|
525 |
rtac lub_equal 3, |
|
526 |
chain_tac 1, |
|
527 |
rtac allI 1, |
|
528 |
resolve_tac prems 1]; |
|
529 |
in pg'' thy axs_take_def goal tacf end; |
|
530 |
in mapn take_lemma 1 (dnames ~~ axs_reach) end; |
|
531 |
||
532 |
(* ----- theorems concerning finiteness and induction ----------------------- *) |
|
533 |
||
29402 | 534 |
val _ = trace " Proving finites, ind..."; |
23152 | 535 |
val (finites, ind) = |
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
536 |
( |
23152 | 537 |
if is_finite |
538 |
then (* finite case *) |
|
539 |
let |
|
540 |
fun take_enough dn = mk_ex ("n",dc_take dn $ Bound 0 ` %:"x" === %:"x"); |
|
541 |
fun dname_lemma dn = |
|
542 |
let |
|
543 |
val prem1 = mk_trp (defined (%:"x")); |
|
544 |
val disj1 = mk_all ("n", dc_take dn $ Bound 0 ` %:"x" === UU); |
|
545 |
val prem2 = mk_trp (mk_disj (disj1, take_enough dn)); |
|
546 |
val concl = mk_trp (take_enough dn); |
|
547 |
val goal = prem1 ===> prem2 ===> concl; |
|
548 |
val tacs = [ |
|
549 |
etac disjE 1, |
|
550 |
etac notE 1, |
|
551 |
resolve_tac take_lemmas 1, |
|
552 |
asm_simp_tac take_ss 1, |
|
553 |
atac 1]; |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
554 |
in pg [] goal (K tacs) end; |
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
555 |
val _ = trace " Proving finite_lemmas1a"; |
23152 | 556 |
val finite_lemmas1a = map dname_lemma dnames; |
557 |
||
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
558 |
val _ = trace " Proving finite_lemma1b"; |
23152 | 559 |
val finite_lemma1b = |
560 |
let |
|
561 |
fun mk_eqn n ((dn, args), _) = |
|
562 |
let |
|
563 |
val disj1 = dc_take dn $ Bound 1 ` Bound 0 === UU; |
|
564 |
val disj2 = dc_take dn $ Bound 1 ` Bound 0 === Bound 0; |
|
565 |
in |
|
566 |
mk_constrainall |
|
567 |
(x_name n, Type (dn,args), mk_disj (disj1, disj2)) |
|
568 |
end; |
|
569 |
val goal = |
|
570 |
mk_trp (mk_all ("n", foldr1 mk_conj (mapn mk_eqn 1 eqs))); |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
571 |
fun arg_tacs ctxt vn = [ |
27239 | 572 |
eres_inst_tac ctxt [(("x", 0), vn)] all_dupE 1, |
23152 | 573 |
etac disjE 1, |
574 |
asm_simp_tac (HOL_ss addsimps con_rews) 1, |
|
575 |
asm_simp_tac take_ss 1]; |
|
35288 | 576 |
fun con_tacs ctxt (con, _, args) = |
23152 | 577 |
asm_simp_tac take_ss 1 :: |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
578 |
maps (arg_tacs ctxt) (nonlazy_rec args); |
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
579 |
fun foo_tacs ctxt n (cons, cases) = |
23152 | 580 |
simp_tac take_ss 1 :: |
581 |
rtac allI 1 :: |
|
27239 | 582 |
res_inst_tac ctxt [(("x", 0), x_name n)] cases 1 :: |
23152 | 583 |
asm_simp_tac take_ss 1 :: |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
584 |
maps (con_tacs ctxt) cons; |
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
585 |
fun tacs ctxt = |
23152 | 586 |
rtac allI 1 :: |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
587 |
InductTacs.induct_tac ctxt [[SOME "n"]] 1 :: |
23152 | 588 |
simp_tac take_ss 1 :: |
589 |
TRY (safe_tac (empty_cs addSEs [conjE] addSIs [conjI])) :: |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
590 |
flat (mapn (foo_tacs ctxt) 1 (conss ~~ cases)); |
23152 | 591 |
in pg [] goal tacs end; |
592 |
||
593 |
fun one_finite (dn, l1b) = |
|
594 |
let |
|
595 |
val goal = mk_trp (%%:(dn^"_finite") $ %:"x"); |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
596 |
fun tacs ctxt = [ |
35443
2e0f9516947e
change domain package's treatment of variable names in theorems to be like datatype package
huffman
parents:
35288
diff
changeset
|
597 |
(* FIXME! case_UU_tac *) |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
598 |
case_UU_tac ctxt take_rews 1 "x", |
23152 | 599 |
eresolve_tac finite_lemmas1a 1, |
600 |
step_tac HOL_cs 1, |
|
601 |
step_tac HOL_cs 1, |
|
602 |
cut_facts_tac [l1b] 1, |
|
603 |
fast_tac HOL_cs 1]; |
|
604 |
in pg axs_finite_def goal tacs end; |
|
605 |
||
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
606 |
val _ = trace " Proving finites"; |
27232 | 607 |
val finites = map one_finite (dnames ~~ atomize global_ctxt finite_lemma1b); |
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
608 |
val _ = trace " Proving ind"; |
23152 | 609 |
val ind = |
610 |
let |
|
611 |
fun concf n dn = %:(P_name n) $ %:(x_name n); |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
612 |
fun tacf {prems, context} = |
23152 | 613 |
let |
614 |
fun finite_tacs (finite, fin_ind) = [ |
|
615 |
rtac(rewrite_rule axs_finite_def finite RS exE)1, |
|
616 |
etac subst 1, |
|
617 |
rtac fin_ind 1, |
|
618 |
ind_prems_tac prems]; |
|
619 |
in |
|
620 |
TRY (safe_tac HOL_cs) :: |
|
27232 | 621 |
maps finite_tacs (finites ~~ atomize global_ctxt finite_ind) |
23152 | 622 |
end; |
623 |
in pg'' thy [] (ind_term concf) tacf end; |
|
624 |
in (finites, ind) end (* let *) |
|
625 |
||
626 |
else (* infinite case *) |
|
627 |
let |
|
628 |
fun one_finite n dn = |
|
27239 | 629 |
read_instantiate global_ctxt [(("P", 0), dn ^ "_finite " ^ x_name n)] excluded_middle; |
23152 | 630 |
val finites = mapn one_finite 1 dnames; |
631 |
||
632 |
val goal = |
|
633 |
let |
|
26012 | 634 |
fun one_adm n _ = mk_trp (mk_adm (%:(P_name n))); |
23152 | 635 |
fun concf n dn = %:(P_name n) $ %:(x_name n); |
636 |
in Logic.list_implies (mapn one_adm 1 dnames, ind_term concf) end; |
|
33396 | 637 |
val cont_rules = |
638 |
[cont_id, cont_const, cont2cont_Rep_CFun, |
|
639 |
cont2cont_fst, cont2cont_snd]; |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
640 |
fun tacf {prems, context} = |
23152 | 641 |
map (fn ax_reach => rtac (ax_reach RS subst) 1) axs_reach @ [ |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
642 |
quant_tac context 1, |
23152 | 643 |
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
|
644 |
REPEAT_DETERM (rtac adm_all 1), |
23152 | 645 |
REPEAT_DETERM ( |
646 |
TRY (rtac adm_conj 1) THEN |
|
647 |
rtac adm_subst 1 THEN |
|
33396 | 648 |
REPEAT (resolve_tac cont_rules 1) THEN |
649 |
resolve_tac prems 1), |
|
23152 | 650 |
strip_tac 1, |
651 |
rtac (rewrite_rule axs_take_def finite_ind) 1, |
|
652 |
ind_prems_tac prems]; |
|
653 |
val ind = (pg'' thy [] goal tacf |
|
654 |
handle ERROR _ => |
|
33396 | 655 |
(warning "Cannot prove infinite induction rule"; TrueI)); |
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
656 |
in (finites, ind) end |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
657 |
) |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
658 |
handle THM _ => |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
659 |
(warning "Induction proofs failed (THM raised)."; ([], TrueI)) |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
660 |
| ERROR _ => |
33810
38375b16ffd9
nicer warning message for indirect-recursive domain definitions
huffman
parents:
33801
diff
changeset
|
661 |
(warning "Cannot prove induction rule"; ([], TrueI)); |
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
662 |
|
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
663 |
|
23152 | 664 |
end; (* local *) |
665 |
||
666 |
(* ----- theorem concerning coinduction ------------------------------------- *) |
|
667 |
||
35444 | 668 |
(* COINDUCTION TEMPORARILY DISABLED |
23152 | 669 |
local |
670 |
val xs = mapn (fn n => K (x_name n)) 1 dnames; |
|
671 |
fun bnd_arg n i = Bound(2*(n_eqs - n)-i-1); |
|
672 |
val take_ss = HOL_ss addsimps take_rews; |
|
673 |
val sproj = prj (fn s => K("fst("^s^")")) (fn s => K("snd("^s^")")); |
|
29402 | 674 |
val _ = trace " Proving coind_lemma..."; |
23152 | 675 |
val coind_lemma = |
676 |
let |
|
677 |
fun mk_prj n _ = proj (%:"R") eqs n $ bnd_arg n 0 $ bnd_arg n 1; |
|
678 |
fun mk_eqn n dn = |
|
679 |
(dc_take dn $ %:"n" ` bnd_arg n 0) === |
|
680 |
(dc_take dn $ %:"n" ` bnd_arg n 1); |
|
681 |
fun mk_all2 (x,t) = mk_all (x, mk_all (x^"'", t)); |
|
682 |
val goal = |
|
683 |
mk_trp (mk_imp (%%:(comp_dname^"_bisim") $ %:"R", |
|
684 |
Library.foldr mk_all2 (xs, |
|
685 |
Library.foldr mk_imp (mapn mk_prj 0 dnames, |
|
686 |
foldr1 mk_conj (mapn mk_eqn 0 dnames))))); |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
687 |
fun x_tacs ctxt n x = [ |
23152 | 688 |
rotate_tac (n+1) 1, |
689 |
etac all2E 1, |
|
27239 | 690 |
eres_inst_tac ctxt [(("P", 1), sproj "R" eqs n^" "^x^" "^x^"'")] (mp RS disjE) 1, |
23152 | 691 |
TRY (safe_tac HOL_cs), |
692 |
REPEAT (CHANGED (asm_simp_tac take_ss 1))]; |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
693 |
fun tacs ctxt = [ |
23152 | 694 |
rtac impI 1, |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
695 |
InductTacs.induct_tac ctxt [[SOME "n"]] 1, |
23152 | 696 |
simp_tac take_ss 1, |
697 |
safe_tac HOL_cs] @ |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
698 |
flat (mapn (x_tacs ctxt) 0 xs); |
23152 | 699 |
in pg [ax_bisim_def] goal tacs end; |
700 |
in |
|
29402 | 701 |
val _ = trace " Proving coind..."; |
23152 | 702 |
val coind = |
703 |
let |
|
704 |
fun mk_prj n x = mk_trp (proj (%:"R") eqs n $ %:x $ %:(x^"'")); |
|
705 |
fun mk_eqn x = %:x === %:(x^"'"); |
|
706 |
val goal = |
|
707 |
mk_trp (%%:(comp_dname^"_bisim") $ %:"R") ===> |
|
708 |
Logic.list_implies (mapn mk_prj 0 xs, |
|
709 |
mk_trp (foldr1 mk_conj (map mk_eqn xs))); |
|
710 |
val tacs = |
|
711 |
TRY (safe_tac HOL_cs) :: |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
712 |
maps (fn take_lemma => [ |
23152 | 713 |
rtac take_lemma 1, |
714 |
cut_facts_tac [coind_lemma] 1, |
|
715 |
fast_tac HOL_cs 1]) |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
716 |
take_lemmas; |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
717 |
in pg [] goal (K tacs) end; |
23152 | 718 |
end; (* local *) |
35444 | 719 |
COINDUCTION TEMPORARILY DISABLED *) |
23152 | 720 |
|
32172 | 721 |
val inducts = Project_Rule.projections (ProofContext.init thy) ind; |
30829 | 722 |
fun ind_rule (dname, rule) = ((Binding.empty, [rule]), [Induct.induct_type dname]); |
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
723 |
val induct_failed = (Thm.prop_of ind = Thm.prop_of TrueI); |
30829 | 724 |
|
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24503
diff
changeset
|
725 |
in thy |> Sign.add_path comp_dnam |
31004 | 726 |
|> snd o PureThy.add_thmss [ |
727 |
((Binding.name "take_rews" , take_rews ), [Simplifier.simp_add]), |
|
728 |
((Binding.name "take_lemmas", take_lemmas ), []), |
|
729 |
((Binding.name "finites" , finites ), []), |
|
730 |
((Binding.name "finite_ind" , [finite_ind]), []), |
|
35444 | 731 |
((Binding.name "ind" , [ind] ), [])(*, |
732 |
((Binding.name "coind" , [coind] ), [])*)] |
|
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
733 |
|> (if induct_failed then I |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
734 |
else snd o PureThy.add_thmss (map ind_rule (dnames ~~ inducts))) |
28536 | 735 |
|> Sign.parent_path |> pair take_rews |
23152 | 736 |
end; (* let *) |
737 |
end; (* struct *) |