author | huffman |
Wed, 03 Mar 2010 07:55:52 -0800 | |
changeset 35558 | bb088a6fafbc |
parent 35557 | 5da670d57118 |
child 35559 | 119653afcd6e |
permissions | -rw-r--r-- |
32126 | 1 |
(* Title: HOLCF/Tools/Domain/domain_theorems.ML |
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Author: David von Oheimb |
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Author: Brian Huffman |
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Proof generator for domain command. |
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*) |
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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: |
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Domain_Library.eq * Domain_Library.eq list |
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-> typ * (binding * (bool * binding option * typ) list * mixfix) list |
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-> Domain_Take_Proofs.iso_info |
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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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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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(* 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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(* ----- 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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(iso_info : Domain_Take_Proofs.iso_info) |
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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_Take_Proofs.get_map_tab thy; |
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|
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(* ----- getting the axioms and definitions --------------------------------- *) |
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val ax_abs_iso = #abs_inverse iso_info; |
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val ax_rep_iso = #rep_inverse iso_info; |
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|
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val abs_const = #abs_const iso_info; |
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val rep_const = #rep_const iso_info; |
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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_take_0 = ga "take_0" dname; |
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val ax_take_Suc = ga "take_Suc" dname; |
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val ax_take_strict = ga "take_strict" dname; |
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end; (* local *) |
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||
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(* ----- define constructors ------------------------------------------------ *) |
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||
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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) (snd dom_eqn) iso_info 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 mat_rews = #match_rews result; |
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val pat_rews = #pat_rews result; |
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(* ----- theorems concerning the isomorphism -------------------------------- *) |
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val pg = pg' thy; |
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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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(* ----- theorems concerning one induction step ----------------------------- *) |
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||
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local |
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fun dc_take dn = %%:(dn^"_take"); |
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val dnames = map (fst o fst) eqs; |
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val deflation_thms = Domain_Take_Proofs.get_deflation_thms thy; |
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fun get_deflation_take dn = PureThy.get_thm thy (dn ^ ".deflation_take"); |
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val axs_deflation_take = map get_deflation_take dnames; |
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|
35521 | 163 |
fun one_take_app (con, args) = |
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let |
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fun mk_take n = dc_take (List.nth (dnames, n)) $ %:"n"; |
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fun one_rhs arg = |
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if Datatype_Aux.is_rec_type (dtyp_of arg) |
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then Domain_Axioms.copy_of_dtyp map_tab |
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mk_take (dtyp_of arg) ` (%# arg) |
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else (%# arg); |
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val lhs = (dc_take dname $ (%%:"Suc" $ %:"n"))`(con_app con args); |
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val rhs = con_app2 con one_rhs args; |
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val goal = mk_trp (lhs === rhs); |
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val rules = [ax_take_Suc, ax_abs_iso, @{thm cfcomp2}]; |
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val rules2 = |
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@{thms take_con_rules ID1 deflation_strict} |
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@ deflation_thms @ axs_deflation_take; |
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val tacs = |
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[simp_tac (HOL_basic_ss addsimps rules) 1, |
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asm_simp_tac (HOL_basic_ss addsimps rules2) 1]; |
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in pg con_appls goal (K tacs) end; |
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val take_apps = map one_take_app cons; |
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in |
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val take_rews = ax_take_0 :: ax_take_strict :: take_apps; |
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end; |
186 |
||
187 |
in |
|
188 |
thy |
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|> Sign.add_path (Long_Name.base_name dname) |
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|> snd o PureThy.add_thmss [ |
191 |
((Binding.name "iso_rews" , iso_rews ), [Simplifier.simp_add]), |
|
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((Binding.name "exhaust" , [exhaust] ), []), |
|
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((Binding.name "casedist" , [casedist] ), [Induct.cases_type dname]), |
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((Binding.name "when_rews" , when_rews ), [Simplifier.simp_add]), |
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((Binding.name "compacts" , con_compacts), [Simplifier.simp_add]), |
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((Binding.name "con_rews" , con_rews ), |
197 |
[Simplifier.simp_add, Fixrec.fixrec_simp_add]), |
|
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((Binding.name "sel_rews" , sel_rews ), [Simplifier.simp_add]), |
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((Binding.name "dis_rews" , dis_rews ), [Simplifier.simp_add]), |
|
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((Binding.name "pat_rews" , pat_rews ), [Simplifier.simp_add]), |
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((Binding.name "dist_les" , dist_les ), [Simplifier.simp_add]), |
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((Binding.name "dist_eqs" , dist_eqs ), [Simplifier.simp_add]), |
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((Binding.name "inverts" , inverts ), [Simplifier.simp_add]), |
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((Binding.name "injects" , injects ), [Simplifier.simp_add]), |
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((Binding.name "take_rews" , take_rews ), [Simplifier.simp_add]), |
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((Binding.name "match_rews", mat_rews ), |
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[Simplifier.simp_add, Fixrec.fixrec_simp_add])] |
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|> Sign.parent_path |
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|> pair (iso_rews @ when_rews @ con_rews @ sel_rews @ dis_rews @ |
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pat_rews @ dist_les @ dist_eqs) |
23152 | 211 |
end; (* let *) |
212 |
||
213 |
fun comp_theorems (comp_dnam, eqs: eq list) thy = |
|
214 |
let |
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215 |
val map_tab = Domain_Take_Proofs.get_map_tab thy; |
27232 | 216 |
|
23152 | 217 |
val dnames = map (fst o fst) eqs; |
218 |
val conss = map snd eqs; |
|
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val comp_dname = Sign.full_bname thy comp_dnam; |
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|
29402 | 221 |
val _ = message ("Proving induction properties of domain "^comp_dname^" ..."); |
35497 | 222 |
|
223 |
(* ----- define bisimulation predicate -------------------------------------- *) |
|
224 |
||
225 |
local |
|
226 |
open HOLCF_Library |
|
227 |
val dtypes = map (Type o fst) eqs; |
|
228 |
val relprod = mk_tupleT (map (fn tp => tp --> tp --> boolT) dtypes); |
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val bisim_bind = Binding.name (comp_dnam ^ "_bisim"); |
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230 |
val bisim_type = relprod --> boolT; |
|
231 |
in |
|
232 |
val (bisim_const, thy) = |
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233 |
Sign.declare_const ((bisim_bind, bisim_type), NoSyn) thy; |
|
234 |
end; |
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235 |
||
236 |
local |
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237 |
||
238 |
fun legacy_infer_term thy t = |
|
239 |
singleton (Syntax.check_terms (ProofContext.init thy)) (Sign.intern_term thy t); |
|
240 |
fun legacy_infer_prop thy t = legacy_infer_term thy (TypeInfer.constrain propT t); |
|
241 |
fun infer_props thy = map (apsnd (legacy_infer_prop thy)); |
|
242 |
fun add_defs_i x = PureThy.add_defs false (map Thm.no_attributes x); |
|
243 |
fun add_defs_infer defs thy = add_defs_i (infer_props thy defs) thy; |
|
244 |
||
245 |
val comp_dname = Sign.full_bname thy comp_dnam; |
|
246 |
val dnames = map (fst o fst) eqs; |
|
247 |
val x_name = idx_name dnames "x"; |
|
248 |
||
35521 | 249 |
fun one_con (con, args) = |
35497 | 250 |
let |
251 |
val nonrec_args = filter_out is_rec args; |
|
252 |
val rec_args = filter is_rec args; |
|
253 |
val recs_cnt = length rec_args; |
|
254 |
val allargs = nonrec_args @ rec_args |
|
255 |
@ map (upd_vname (fn s=> s^"'")) rec_args; |
|
256 |
val allvns = map vname allargs; |
|
257 |
fun vname_arg s arg = if is_rec arg then vname arg^s else vname arg; |
|
258 |
val vns1 = map (vname_arg "" ) args; |
|
259 |
val vns2 = map (vname_arg "'") args; |
|
260 |
val allargs_cnt = length nonrec_args + 2*recs_cnt; |
|
261 |
val rec_idxs = (recs_cnt-1) downto 0; |
|
262 |
val nonlazy_idxs = map snd (filter_out (fn (arg,_) => is_lazy arg) |
|
263 |
(allargs~~((allargs_cnt-1) downto 0))); |
|
264 |
fun rel_app i ra = proj (Bound(allargs_cnt+2)) eqs (rec_of ra) $ |
|
265 |
Bound (2*recs_cnt-i) $ Bound (recs_cnt-i); |
|
266 |
val capps = |
|
267 |
List.foldr |
|
268 |
mk_conj |
|
269 |
(mk_conj( |
|
270 |
Bound(allargs_cnt+1)===list_ccomb(%%:con,map (bound_arg allvns) vns1), |
|
271 |
Bound(allargs_cnt+0)===list_ccomb(%%:con,map (bound_arg allvns) vns2))) |
|
272 |
(mapn rel_app 1 rec_args); |
|
273 |
in |
|
274 |
List.foldr |
|
275 |
mk_ex |
|
276 |
(Library.foldr mk_conj |
|
277 |
(map (defined o Bound) nonlazy_idxs,capps)) allvns |
|
278 |
end; |
|
279 |
fun one_comp n (_,cons) = |
|
280 |
mk_all (x_name(n+1), |
|
281 |
mk_all (x_name(n+1)^"'", |
|
282 |
mk_imp (proj (Bound 2) eqs n $ Bound 1 $ Bound 0, |
|
283 |
foldr1 mk_disj (mk_conj(Bound 1 === UU,Bound 0 === UU) |
|
284 |
::map one_con cons)))); |
|
285 |
val bisim_eqn = |
|
286 |
%%:(comp_dname^"_bisim") == |
|
287 |
mk_lam("R", foldr1 mk_conj (mapn one_comp 0 eqs)); |
|
288 |
||
289 |
in |
|
290 |
val ([ax_bisim_def], thy) = |
|
291 |
thy |
|
292 |
|> Sign.add_path comp_dnam |
|
293 |
|> add_defs_infer [(Binding.name "bisim_def", bisim_eqn)] |
|
294 |
||> Sign.parent_path; |
|
295 |
end; (* local *) |
|
296 |
||
23152 | 297 |
val pg = pg' thy; |
298 |
||
299 |
(* ----- getting the composite axiom and definitions ------------------------ *) |
|
300 |
||
301 |
local |
|
26343
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wenzelm
parents:
26342
diff
changeset
|
302 |
fun ga s dn = PureThy.get_thm thy (dn ^ "." ^ s); |
23152 | 303 |
in |
304 |
val axs_take_def = map (ga "take_def" ) dnames; |
|
35494
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domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
305 |
val axs_chain_take = map (ga "chain_take") dnames; |
45c9a8278faf
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parents:
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diff
changeset
|
306 |
val axs_lub_take = map (ga "lub_take" ) dnames; |
23152 | 307 |
val axs_finite_def = map (ga "finite_def") dnames; |
308 |
end; |
|
309 |
||
310 |
local |
|
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26342
diff
changeset
|
311 |
fun gt s dn = PureThy.get_thm thy (dn ^ "." ^ s); |
0dd2eab7b296
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wenzelm
parents:
26342
diff
changeset
|
312 |
fun gts s dn = PureThy.get_thms thy (dn ^ "." ^ s); |
23152 | 313 |
in |
314 |
val cases = map (gt "casedist" ) dnames; |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
315 |
val con_rews = maps (gts "con_rews" ) dnames; |
23152 | 316 |
end; |
317 |
||
318 |
fun dc_take dn = %%:(dn^"_take"); |
|
319 |
val x_name = idx_name dnames "x"; |
|
320 |
val P_name = idx_name dnames "P"; |
|
321 |
val n_eqs = length eqs; |
|
322 |
||
323 |
(* ----- theorems concerning finite approximation and finite induction ------ *) |
|
324 |
||
35494
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domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
325 |
val take_rews = |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
326 |
maps (fn dn => PureThy.get_thms thy (dn ^ ".take_rews")) dnames; |
23152 | 327 |
|
328 |
local |
|
35521 | 329 |
fun one_con p (con, args) = |
23152 | 330 |
let |
35443
2e0f9516947e
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huffman
parents:
35288
diff
changeset
|
331 |
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
|
332 |
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
|
333 |
val nonlazy_vns = map snd (filter_out (is_lazy o fst) (args ~~ vns)); |
23152 | 334 |
fun ind_hyp arg = %:(P_name (1 + rec_of arg)) $ bound_arg args arg; |
335 |
val t1 = mk_trp (%:p $ con_app2 con (bound_arg args) args); |
|
33317 | 336 |
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
|
337 |
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
|
338 |
in Library.foldr mk_All (vns, t3) end; |
23152 | 339 |
|
340 |
fun one_eq ((p, cons), concl) = |
|
341 |
mk_trp (%:p $ UU) ===> Logic.list_implies (map (one_con p) cons, concl); |
|
342 |
||
343 |
fun ind_term concf = Library.foldr one_eq |
|
344 |
(mapn (fn n => fn x => (P_name n, x)) 1 conss, |
|
345 |
mk_trp (foldr1 mk_conj (mapn concf 1 dnames))); |
|
35494
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
346 |
val take_ss = HOL_ss addsimps (@{thm Rep_CFun_strict1} :: take_rews); |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
347 |
fun quant_tac ctxt i = EVERY |
27239 | 348 |
(mapn (fn n => fn _ => res_inst_tac ctxt [(("x", 0), x_name n)] spec i) 1 dnames); |
23152 | 349 |
|
350 |
fun ind_prems_tac prems = EVERY |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
351 |
(maps (fn cons => |
23152 | 352 |
(resolve_tac prems 1 :: |
35521 | 353 |
maps (fn (_,args) => |
23152 | 354 |
resolve_tac prems 1 :: |
355 |
map (K(atac 1)) (nonlazy args) @ |
|
33317 | 356 |
map (K(atac 1)) (filter is_rec args)) |
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
357 |
cons)) |
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
358 |
conss); |
23152 | 359 |
local |
360 |
(* check whether every/exists constructor of the n-th part of the equation: |
|
361 |
it has a possibly indirectly recursive argument that isn't/is possibly |
|
362 |
indirectly lazy *) |
|
363 |
fun rec_to quant nfn rfn ns lazy_rec (n,cons) = quant (exists (fn arg => |
|
364 |
is_rec arg andalso not(rec_of arg mem ns) andalso |
|
365 |
((rec_of arg = n andalso nfn(lazy_rec orelse is_lazy arg)) orelse |
|
366 |
rec_of arg <> n andalso rec_to quant nfn rfn (rec_of arg::ns) |
|
367 |
(lazy_rec orelse is_lazy arg) (n, (List.nth(conss,rec_of arg)))) |
|
35521 | 368 |
) o snd) cons; |
23152 | 369 |
fun all_rec_to ns = rec_to forall not all_rec_to ns; |
370 |
fun warn (n,cons) = |
|
371 |
if all_rec_to [] false (n,cons) |
|
372 |
then (warning ("domain "^List.nth(dnames,n)^" is empty!"); true) |
|
373 |
else false; |
|
374 |
fun lazy_rec_to ns = rec_to exists I lazy_rec_to ns; |
|
375 |
||
376 |
in |
|
377 |
val n__eqs = mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs; |
|
378 |
val is_emptys = map warn n__eqs; |
|
379 |
val is_finite = forall (not o lazy_rec_to [] false) n__eqs; |
|
380 |
end; |
|
381 |
in (* local *) |
|
29402 | 382 |
val _ = trace " Proving finite_ind..."; |
23152 | 383 |
val finite_ind = |
384 |
let |
|
385 |
fun concf n dn = %:(P_name n) $ (dc_take dn $ %:"n" `%(x_name n)); |
|
386 |
val goal = ind_term concf; |
|
387 |
||
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
388 |
fun tacf {prems, context} = |
23152 | 389 |
let |
390 |
val tacs1 = [ |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
391 |
quant_tac context 1, |
23152 | 392 |
simp_tac HOL_ss 1, |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
393 |
InductTacs.induct_tac context [[SOME "n"]] 1, |
23152 | 394 |
simp_tac (take_ss addsimps prems) 1, |
395 |
TRY (safe_tac HOL_cs)]; |
|
396 |
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
|
397 |
(* FIXME! case_UU_tac *) |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
398 |
case_UU_tac context (prems @ con_rews) 1 |
23152 | 399 |
(List.nth (dnames, rec_of arg) ^ "_take n$" ^ vname arg); |
35521 | 400 |
fun con_tacs (con, args) = |
23152 | 401 |
asm_simp_tac take_ss 1 :: |
33317 | 402 |
map arg_tac (filter is_nonlazy_rec args) @ |
23152 | 403 |
[resolve_tac prems 1] @ |
33317 | 404 |
map (K (atac 1)) (nonlazy args) @ |
405 |
map (K (etac spec 1)) (filter is_rec args); |
|
23152 | 406 |
fun cases_tacs (cons, cases) = |
35528 | 407 |
res_inst_tac context [(("y", 0), "x")] cases 1 :: |
23152 | 408 |
asm_simp_tac (take_ss addsimps prems) 1 :: |
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
409 |
maps con_tacs cons; |
23152 | 410 |
in |
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
411 |
tacs1 @ maps cases_tacs (conss ~~ cases) |
23152 | 412 |
end; |
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
413 |
in pg'' thy [] goal tacf |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
414 |
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
|
415 |
end; |
23152 | 416 |
|
29402 | 417 |
val _ = trace " Proving take_lemmas..."; |
23152 | 418 |
val take_lemmas = |
419 |
let |
|
35494
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
420 |
fun take_lemma (ax_chain_take, ax_lub_take) = |
35557
5da670d57118
uniformly use variable names m and n in take-related lemmas; use export_without_context where appropriate
huffman
parents:
35528
diff
changeset
|
421 |
Drule.export_without_context |
5da670d57118
uniformly use variable names m and n in take-related lemmas; use export_without_context where appropriate
huffman
parents:
35528
diff
changeset
|
422 |
(@{thm lub_ID_take_lemma} OF [ax_chain_take, ax_lub_take]); |
35494
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
423 |
in map take_lemma (axs_chain_take ~~ axs_lub_take) end; |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
424 |
|
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
425 |
val axs_reach = |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
426 |
let |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
427 |
fun reach (ax_chain_take, ax_lub_take) = |
35557
5da670d57118
uniformly use variable names m and n in take-related lemmas; use export_without_context where appropriate
huffman
parents:
35528
diff
changeset
|
428 |
Drule.export_without_context |
5da670d57118
uniformly use variable names m and n in take-related lemmas; use export_without_context where appropriate
huffman
parents:
35528
diff
changeset
|
429 |
(@{thm lub_ID_reach} OF [ax_chain_take, ax_lub_take]); |
35494
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
430 |
in map reach (axs_chain_take ~~ axs_lub_take) end; |
23152 | 431 |
|
432 |
(* ----- theorems concerning finiteness and induction ----------------------- *) |
|
433 |
||
35497 | 434 |
val global_ctxt = ProofContext.init thy; |
435 |
||
29402 | 436 |
val _ = trace " Proving finites, ind..."; |
23152 | 437 |
val (finites, ind) = |
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
438 |
( |
23152 | 439 |
if is_finite |
440 |
then (* finite case *) |
|
441 |
let |
|
442 |
fun take_enough dn = mk_ex ("n",dc_take dn $ Bound 0 ` %:"x" === %:"x"); |
|
443 |
fun dname_lemma dn = |
|
444 |
let |
|
445 |
val prem1 = mk_trp (defined (%:"x")); |
|
446 |
val disj1 = mk_all ("n", dc_take dn $ Bound 0 ` %:"x" === UU); |
|
447 |
val prem2 = mk_trp (mk_disj (disj1, take_enough dn)); |
|
448 |
val concl = mk_trp (take_enough dn); |
|
449 |
val goal = prem1 ===> prem2 ===> concl; |
|
450 |
val tacs = [ |
|
451 |
etac disjE 1, |
|
452 |
etac notE 1, |
|
453 |
resolve_tac take_lemmas 1, |
|
454 |
asm_simp_tac take_ss 1, |
|
455 |
atac 1]; |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
456 |
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
|
457 |
val _ = trace " Proving finite_lemmas1a"; |
23152 | 458 |
val finite_lemmas1a = map dname_lemma dnames; |
459 |
||
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
460 |
val _ = trace " Proving finite_lemma1b"; |
23152 | 461 |
val finite_lemma1b = |
462 |
let |
|
463 |
fun mk_eqn n ((dn, args), _) = |
|
464 |
let |
|
465 |
val disj1 = dc_take dn $ Bound 1 ` Bound 0 === UU; |
|
466 |
val disj2 = dc_take dn $ Bound 1 ` Bound 0 === Bound 0; |
|
467 |
in |
|
468 |
mk_constrainall |
|
469 |
(x_name n, Type (dn,args), mk_disj (disj1, disj2)) |
|
470 |
end; |
|
471 |
val goal = |
|
472 |
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
|
473 |
fun arg_tacs ctxt vn = [ |
27239 | 474 |
eres_inst_tac ctxt [(("x", 0), vn)] all_dupE 1, |
23152 | 475 |
etac disjE 1, |
476 |
asm_simp_tac (HOL_ss addsimps con_rews) 1, |
|
477 |
asm_simp_tac take_ss 1]; |
|
35521 | 478 |
fun con_tacs ctxt (con, args) = |
23152 | 479 |
asm_simp_tac take_ss 1 :: |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
480 |
maps (arg_tacs ctxt) (nonlazy_rec args); |
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
481 |
fun foo_tacs ctxt n (cons, cases) = |
23152 | 482 |
simp_tac take_ss 1 :: |
483 |
rtac allI 1 :: |
|
35528 | 484 |
res_inst_tac ctxt [(("y", 0), x_name n)] cases 1 :: |
23152 | 485 |
asm_simp_tac take_ss 1 :: |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
486 |
maps (con_tacs ctxt) cons; |
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
487 |
fun tacs ctxt = |
23152 | 488 |
rtac allI 1 :: |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
489 |
InductTacs.induct_tac ctxt [[SOME "n"]] 1 :: |
23152 | 490 |
simp_tac take_ss 1 :: |
491 |
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
|
492 |
flat (mapn (foo_tacs ctxt) 1 (conss ~~ cases)); |
23152 | 493 |
in pg [] goal tacs end; |
494 |
||
495 |
fun one_finite (dn, l1b) = |
|
496 |
let |
|
497 |
val goal = mk_trp (%%:(dn^"_finite") $ %:"x"); |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
498 |
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
|
499 |
(* FIXME! case_UU_tac *) |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
500 |
case_UU_tac ctxt take_rews 1 "x", |
23152 | 501 |
eresolve_tac finite_lemmas1a 1, |
502 |
step_tac HOL_cs 1, |
|
503 |
step_tac HOL_cs 1, |
|
504 |
cut_facts_tac [l1b] 1, |
|
505 |
fast_tac HOL_cs 1]; |
|
506 |
in pg axs_finite_def goal tacs end; |
|
507 |
||
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
508 |
val _ = trace " Proving finites"; |
27232 | 509 |
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
|
510 |
val _ = trace " Proving ind"; |
23152 | 511 |
val ind = |
512 |
let |
|
513 |
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
|
514 |
fun tacf {prems, context} = |
23152 | 515 |
let |
516 |
fun finite_tacs (finite, fin_ind) = [ |
|
517 |
rtac(rewrite_rule axs_finite_def finite RS exE)1, |
|
518 |
etac subst 1, |
|
519 |
rtac fin_ind 1, |
|
520 |
ind_prems_tac prems]; |
|
521 |
in |
|
522 |
TRY (safe_tac HOL_cs) :: |
|
27232 | 523 |
maps finite_tacs (finites ~~ atomize global_ctxt finite_ind) |
23152 | 524 |
end; |
525 |
in pg'' thy [] (ind_term concf) tacf end; |
|
526 |
in (finites, ind) end (* let *) |
|
527 |
||
528 |
else (* infinite case *) |
|
529 |
let |
|
530 |
fun one_finite n dn = |
|
27239 | 531 |
read_instantiate global_ctxt [(("P", 0), dn ^ "_finite " ^ x_name n)] excluded_middle; |
23152 | 532 |
val finites = mapn one_finite 1 dnames; |
533 |
||
534 |
val goal = |
|
535 |
let |
|
26012 | 536 |
fun one_adm n _ = mk_trp (mk_adm (%:(P_name n))); |
23152 | 537 |
fun concf n dn = %:(P_name n) $ %:(x_name n); |
538 |
in Logic.list_implies (mapn one_adm 1 dnames, ind_term concf) end; |
|
33396 | 539 |
val cont_rules = |
540 |
[cont_id, cont_const, cont2cont_Rep_CFun, |
|
541 |
cont2cont_fst, cont2cont_snd]; |
|
35494
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
542 |
val subgoal = |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
543 |
let fun p n dn = %:(P_name n) $ (dc_take dn $ Bound 0 `%(x_name n)); |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
544 |
in mk_trp (mk_all ("n", foldr1 mk_conj (mapn p 1 dnames))) end; |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
545 |
val subgoal' = legacy_infer_term thy subgoal; |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
546 |
fun tacf {prems, context} = |
35494
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
547 |
let |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
548 |
val subtac = |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
549 |
EVERY [rtac allI 1, rtac finite_ind 1, ind_prems_tac prems]; |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
550 |
val subthm = Goal.prove context [] [] subgoal' (K subtac); |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
551 |
in |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
552 |
map (fn ax_reach => rtac (ax_reach RS subst) 1) axs_reach @ [ |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
553 |
cut_facts_tac (subthm :: take (length dnames) prems) 1, |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
554 |
REPEAT (rtac @{thm conjI} 1 ORELSE |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
555 |
EVERY [etac @{thm admD [OF _ ch2ch_Rep_CFunL]} 1, |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
556 |
resolve_tac axs_chain_take 1, |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
557 |
asm_simp_tac HOL_basic_ss 1]) |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
558 |
] |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
559 |
end; |
23152 | 560 |
val ind = (pg'' thy [] goal tacf |
561 |
handle ERROR _ => |
|
35494
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
562 |
(warning "Cannot prove infinite induction rule"; TrueI) |
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
563 |
); |
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
564 |
in (finites, ind) end |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
565 |
) |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
566 |
handle THM _ => |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
567 |
(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
|
568 |
| ERROR _ => |
33810
38375b16ffd9
nicer warning message for indirect-recursive domain definitions
huffman
parents:
33801
diff
changeset
|
569 |
(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
|
570 |
|
23152 | 571 |
end; (* local *) |
572 |
||
573 |
(* ----- theorem concerning coinduction ------------------------------------- *) |
|
574 |
||
575 |
local |
|
576 |
val xs = mapn (fn n => K (x_name n)) 1 dnames; |
|
577 |
fun bnd_arg n i = Bound(2*(n_eqs - n)-i-1); |
|
35497 | 578 |
val take_ss = HOL_ss addsimps (@{thm Rep_CFun_strict1} :: take_rews); |
23152 | 579 |
val sproj = prj (fn s => K("fst("^s^")")) (fn s => K("snd("^s^")")); |
29402 | 580 |
val _ = trace " Proving coind_lemma..."; |
23152 | 581 |
val coind_lemma = |
582 |
let |
|
583 |
fun mk_prj n _ = proj (%:"R") eqs n $ bnd_arg n 0 $ bnd_arg n 1; |
|
584 |
fun mk_eqn n dn = |
|
585 |
(dc_take dn $ %:"n" ` bnd_arg n 0) === |
|
586 |
(dc_take dn $ %:"n" ` bnd_arg n 1); |
|
587 |
fun mk_all2 (x,t) = mk_all (x, mk_all (x^"'", t)); |
|
588 |
val goal = |
|
589 |
mk_trp (mk_imp (%%:(comp_dname^"_bisim") $ %:"R", |
|
590 |
Library.foldr mk_all2 (xs, |
|
591 |
Library.foldr mk_imp (mapn mk_prj 0 dnames, |
|
592 |
foldr1 mk_conj (mapn mk_eqn 0 dnames))))); |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
593 |
fun x_tacs ctxt n x = [ |
23152 | 594 |
rotate_tac (n+1) 1, |
595 |
etac all2E 1, |
|
27239 | 596 |
eres_inst_tac ctxt [(("P", 1), sproj "R" eqs n^" "^x^" "^x^"'")] (mp RS disjE) 1, |
23152 | 597 |
TRY (safe_tac HOL_cs), |
598 |
REPEAT (CHANGED (asm_simp_tac take_ss 1))]; |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
599 |
fun tacs ctxt = [ |
23152 | 600 |
rtac impI 1, |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
601 |
InductTacs.induct_tac ctxt [[SOME "n"]] 1, |
23152 | 602 |
simp_tac take_ss 1, |
603 |
safe_tac HOL_cs] @ |
|
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
604 |
flat (mapn (x_tacs ctxt) 0 xs); |
23152 | 605 |
in pg [ax_bisim_def] goal tacs end; |
606 |
in |
|
29402 | 607 |
val _ = trace " Proving coind..."; |
23152 | 608 |
val coind = |
609 |
let |
|
610 |
fun mk_prj n x = mk_trp (proj (%:"R") eqs n $ %:x $ %:(x^"'")); |
|
611 |
fun mk_eqn x = %:x === %:(x^"'"); |
|
612 |
val goal = |
|
613 |
mk_trp (%%:(comp_dname^"_bisim") $ %:"R") ===> |
|
614 |
Logic.list_implies (mapn mk_prj 0 xs, |
|
615 |
mk_trp (foldr1 mk_conj (map mk_eqn xs))); |
|
616 |
val tacs = |
|
617 |
TRY (safe_tac HOL_cs) :: |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
618 |
maps (fn take_lemma => [ |
23152 | 619 |
rtac take_lemma 1, |
620 |
cut_facts_tac [coind_lemma] 1, |
|
621 |
fast_tac HOL_cs 1]) |
|
26336
a0e2b706ce73
renamed datatype thmref to Facts.ref, tuned interfaces;
wenzelm
parents:
26012
diff
changeset
|
622 |
take_lemmas; |
27208
5fe899199f85
proper context for tactics derived from res_inst_tac;
wenzelm
parents:
27153
diff
changeset
|
623 |
in pg [] goal (K tacs) end; |
23152 | 624 |
end; (* local *) |
625 |
||
32172 | 626 |
val inducts = Project_Rule.projections (ProofContext.init thy) ind; |
30829 | 627 |
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
|
628 |
val induct_failed = (Thm.prop_of ind = Thm.prop_of TrueI); |
30829 | 629 |
|
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24503
diff
changeset
|
630 |
in thy |> Sign.add_path comp_dnam |
31004 | 631 |
|> snd o PureThy.add_thmss [ |
632 |
((Binding.name "take_lemmas", take_lemmas ), []), |
|
35494
45c9a8278faf
domain package no longer generates copy functions; all proofs use take functions instead
huffman
parents:
35486
diff
changeset
|
633 |
((Binding.name "reach" , axs_reach ), []), |
31004 | 634 |
((Binding.name "finites" , finites ), []), |
635 |
((Binding.name "finite_ind" , [finite_ind]), []), |
|
35497 | 636 |
((Binding.name "ind" , [ind] ), []), |
637 |
((Binding.name "coind" , [coind] ), [])] |
|
31232
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
638 |
|> (if induct_failed then I |
689aa7da48cc
define copy functions using combinators; add checking for failed proofs of induction rules
huffman
parents:
31160
diff
changeset
|
639 |
else snd o PureThy.add_thmss (map ind_rule (dnames ~~ inducts))) |
28536 | 640 |
|> Sign.parent_path |> pair take_rews |
23152 | 641 |
end; (* let *) |
642 |
end; (* struct *) |