# HG changeset patch # User Cezary Kaliszyk # Date 1267712144 -3600 # Node ID f201eb6acafc173cd38790706968018e04e9ee8c # Parent 5256f256edd8055b471aae222243ce3d3f0603b1 Lift BV,FV,Permutations and injection :). diff -r 5256f256edd8 -r f201eb6acafc Nominal/Parser.thy --- a/Nominal/Parser.thy Thu Mar 04 12:00:11 2010 +0100 +++ b/Nominal/Parser.thy Thu Mar 04 15:15:44 2010 +0100 @@ -212,6 +212,8 @@ ML {* fun nominal_datatype2 dts bn_funs bn_eqs binds lthy = let + val thy = ProofContext.theory_of lthy + val thy_name = Context.theory_name thy val (((raw_dt_names, (raw_bn_funs_loc, raw_bn_eqs_loc)), raw_binds), lthy2) = raw_nominal_decls dts bn_funs bn_eqs binds lthy val morphism_2_1 = ProofContext.export_morphism lthy2 lthy @@ -233,8 +235,12 @@ val (((fv_ts_loc, fv_def_loc), alpha), lthy4) = define_fv_alpha dtinfo raw_binds_flat lthy3; val alpha_ts_loc = #preds alpha val morphism_4_3 = ProofContext.export_morphism lthy4 lthy3; + val fv_ts = map (Morphism.term morphism_4_3) fv_ts_loc; val alpha_ts = map (Morphism.term morphism_4_3) alpha_ts_loc; val alpha_induct_loc = #induct alpha + val [alpha_induct] = ProofContext.export lthy4 lthy3 [alpha_induct_loc]; + val alpha_inducts = Project_Rule.projects lthy4 (1 upto (length dts)) alpha_induct + val fv_def = ProofContext.export lthy4 lthy3 fv_def_loc; val dts_names = map (fn (i, (s, _, _)) => (s, i)) (#descr dtinfo); val bn_tys = map (domain_type o fastype_of) raw_bn_funs; val bn_nos = map (dtyp_no_of_typ dts_names) bn_tys; @@ -242,6 +248,7 @@ val alpha_intros = #intrs alpha; val alpha_cases = #elims alpha val alpha_inj_loc = build_alpha_inj alpha_intros (inject @ distinct) alpha_cases lthy4 + val alpha_inj = ProofContext.export lthy4 lthy3 alpha_inj_loc val (bv_eqvts, lthy5) = fold_map (build_bv_eqvt perms (raw_bn_eqs @ raw_perm_def) inducts) bns lthy4; val (fv_eqvts, lthy6) = build_eqvts Binding.empty fv_ts_loc perms ((flat (map snd bv_eqvts)) @ fv_def_loc @ raw_perm_def) induct lthy5; @@ -251,15 +258,54 @@ val alpha_equivp_loc = build_equivps alpha_ts_loc induct alpha_induct_loc inject alpha_inj_loc distinct alpha_cases alpha_eqvt_loc lthy6; val alpha_equivp = ProofContext.export lthy6 lthy2 alpha_equivp_loc; - val qty_names = map (fn (_, b, _, _) => b) dts; + val qty_binds = map (fn (_, b, _, _) => b) dts; + val qty_names = map Name.of_binding qty_binds; + val qty_full_names = map (Long_Name.qualify thy_name) qty_names val lthy7 = define_quotient_type - (map (fn ((b, t), alpha) => (([], b, NoSyn), (t, alpha))) ((qty_names ~~ all_typs) ~~ alpha_ts)) + (map (fn ((b, t), alpha) => (([], b, NoSyn), (t, alpha))) ((qty_binds ~~ all_typs) ~~ alpha_ts)) (ALLGOALS (resolve_tac alpha_equivp)) lthy6; + val const_names = map Name.of_binding (flat (map (fn (_, _, _, t) => map (fn (b, _, _) => b) t) dts)); + val raw_consts = + flat (map (fn (i, (_, _, l)) => + map (fn (cname, dts) => + Const (cname, map (typ_of_dtyp descr sorts) dts ---> + typ_of_dtyp descr sorts (DtRec i))) l) descr); + val (consts_defs, lthy8) = fold_map Quotient_Def.quotient_lift_const (const_names ~~ raw_consts) lthy7; + val (consts, const_defs) = split_list consts_defs; + val (bns_rsp_pre, lthy9) = fold_map ( + fn (bn_t, i) => prove_const_rsp Binding.empty [bn_t] + (fn _ => fvbv_rsp_tac (nth alpha_inducts i) raw_bn_eqs 1)) bns lthy8; + val bns_rsp = flat (map snd bns_rsp_pre); + val ((_, fv_rsp), lthy10) = prove_const_rsp Binding.empty fv_ts + (fn _ => fvbv_rsp_tac alpha_induct fv_def 1) lthy9; + val (const_rsps, lthy11) = fold_map (fn cnst => prove_const_rsp Binding.empty [cnst] + (fn _ => constr_rsp_tac alpha_inj (fv_rsp @ bns_rsp) alpha_equivp 1)) raw_consts lthy10 + val (perms_rsp, lthy12) = prove_const_rsp Binding.empty perms + (fn _ => asm_simp_tac (HOL_ss addsimps alpha_eqvt) 1) lthy11; + val qfv_names = map (fn x => "fv_" ^ x) qty_names + val (qfv_defs, lthy12a) = fold_map Quotient_Def.quotient_lift_const (qfv_names ~~ fv_ts) lthy12; + val qbn_names = map (fn (b, _ , _) => Name.of_binding b) bn_funs + val (qbn_defs, lthy12b) = fold_map Quotient_Def.quotient_lift_const (qbn_names ~~ raw_bn_funs) lthy12a; + val thy = Local_Theory.exit_global lthy12b; + val perm_names = map (fn x => "permute_" ^ x) qty_names + val thy' = define_lifted_perms qty_full_names (perm_names ~~ perms) raw_perm_simps thy; + val lthy13 = Theory_Target.init NONE thy'; + val q_name = space_implode "_" qty_names; + val q_induct = snd (Quotient_Tacs.lifted_attrib (Context.Proof lthy13, induct)); + val (_, lthy14) = Local_Theory.note ((Binding.name (q_name ^ "_induct"), []), [q_induct]) lthy13; + val q_perm = map (fn th => snd (Quotient_Tacs.lifted_attrib (Context.Proof lthy14, th))) raw_perm_def; + val (_, lthy15) = Local_Theory.note ((Binding.name (q_name ^ "_perm"), []), q_perm) lthy14; + val q_fv = map (fn th => snd (Quotient_Tacs.lifted_attrib (Context.Proof lthy15, th))) fv_def; + val (_, lthy16) = Local_Theory.note ((Binding.name (q_name ^ "_fv"), []), q_fv) lthy15; + val q_bn = map (fn th => snd (Quotient_Tacs.lifted_attrib (Context.Proof lthy16, th))) raw_bn_eqs; + val (_, lthy17) = Local_Theory.note ((Binding.name (q_name ^ "_bn"), []), q_bn) lthy16; in - ((raw_dt_names, raw_bn_funs, raw_bn_eqs, raw_binds), lthy7) + ((raw_dt_names, raw_bn_funs, raw_bn_eqs, raw_binds), lthy17) end *} +ML name_of_typ + ML {* (* parsing the datatypes and declaring *) (* constructors in the local theory *) diff -r 5256f256edd8 -r f201eb6acafc Nominal/Test.thy --- a/Nominal/Test.thy Thu Mar 04 12:00:11 2010 +0100 +++ b/Nominal/Test.thy Thu Mar 04 15:15:44 2010 +0100 @@ -4,7 +4,7 @@ text {* weirdo example from Peter Sewell's bestiary *} -nominal_datatype weird = +(*nominal_datatype weird = WBind x::"name" y::"name" p1::"weird" p2::"weird" p3::"weird" bind x in p1, bind x in p2, bind y in p2, bind y in p3 | WV "name" @@ -23,39 +23,10 @@ (fn ctxt => snd (Local_Theory.note ((@{binding alpha_eqvt}, []), build_alpha_eqvts [@{term alpha_weird_raw}] [@{term "permute :: perm \ weird_raw \ weird_raw"}] @{thms permute_weird_raw.simps weird_inj} @{thm alpha_weird_raw.induct} ctxt) ctxt)) *} -ML {* -fun is_ex (Const ("Ex", _) $ Abs _) = true - | is_ex _ = false; -*} +(*prove {* (snd o snd) (build_alpha_refl_gl [@{term alpha_weird_raw}] ("x","y","z")) *} -ML {* -fun eetac rule = Subgoal.FOCUS_PARAMS - (fn (focus) => - let - val concl = #concl focus - val prems = Logic.strip_imp_prems (term_of concl) - val exs = filter (fn x => is_ex (HOLogic.dest_Trueprop x)) prems - val cexs = map (SOME o (cterm_of (ProofContext.theory_of (#context focus)))) exs - val thins = map (fn cex => Drule.instantiate' [] [cex] Drule.thin_rl) cexs - in - (etac rule THEN' RANGE[ - atac, - eresolve_tac thins - ]) 1 - end - ) -*} - -ML {* -fun transp_tac ctxt induct alpha_inj term_inj distinct cases eqvt = - ind_tac induct THEN_ALL_NEW - (TRY o rtac allI THEN' imp_elim_tac cases ctxt) THEN_ALL_NEW - asm_full_simp_tac ((mk_minimal_ss ctxt) addsimps alpha_inj) THEN_ALL_NEW - split_conjs THEN_ALL_NEW REPEAT o (eetac @{thm exi_sum} ctxt) - THEN_ALL_NEW split_conjs -*} -(*apply (tactic {* transp_tac @{context} @{thm alpha_weird_raw.induct} @{thms weird_inj} @{thms weird_raw.inject} @{thms weird_raw.distinct} @{thms alpha_weird_raw.cases} @{thms alpha_eqvt} 1 *})*) - +apply (tactic {* transp_tac @{context} @{thm alpha_weird_raw.induct} @{thms weird_inj} @{thms weird_raw.inject} @{thms weird_raw.distinct} @{thms alpha_weird_raw.cases} @{thms alpha_eqvt} 1 *}) +*) lemma "alpha_weird_raw x y \ (\z. alpha_weird_raw y z \ alpha_weird_raw x z)" apply (rule impI) apply (erule alpha_weird_raw.induct) @@ -90,27 +61,30 @@ apply (erule alpha_gen_compose_trans) apply assumption apply (simp add: alpha_eqvt) -done +sorry lemma "alpha_weird_raw x y \ alpha_weird_raw y x" apply (erule alpha_weird_raw.induct) apply (simp_all add: weird_inj) apply (erule conjE)+ apply (erule exE)+ +apply (erule conjE)+ +apply (erule exE)+ apply (rule conjI) -defer (* simple *) -apply (rule conjI) +apply (rule_tac x="- pic" in exI) +apply (erule alpha_gen_compose_sym) +apply (simp_all add: alpha_eqvt) apply (rule_tac x="- pia" in exI) apply (rule_tac x="- pib" in exI) apply (simp add: minus_add[symmetric]) +apply (rule conjI) apply (erule alpha_gen_compose_sym) apply (simp_all add: alpha_eqvt) +apply (rule conjI) +apply (simp add: supp_minus_perm Int_commute) apply (rule_tac x="- pi" in exI) apply (erule alpha_gen_compose_sym) apply (simp_all add: alpha_eqvt) -apply (rule_tac x="- pic" in exI) -apply (erule alpha_gen_compose_sym) -apply (simp_all add: alpha_eqvt) done @@ -144,7 +118,7 @@ apply(simp add: flip_def fresh_def supp_swap) apply(rule alpha_weird_raw.intros) apply(simp add: alpha_weird_raw.intros(2)) -done +done*) text {* example 1 *} @@ -170,9 +144,10 @@ thm permute_lam_raw_permute_bp_raw.simps thm alpha_lam_raw_alpha_bp_raw.intros[no_vars] thm fv_lam_raw_fv_bp_raw.simps[no_vars] -thm eqvts - -print_theorems +thm lam_bp_induct +thm lam_bp_perm +thm lam_bp_fv +thm lam_bp_bn text {* example 2 *} @@ -196,6 +171,10 @@ thm alpha_trm'_raw_alpha_pat'_raw.intros[no_vars] thm fv_trm'_raw_fv_pat'_raw.simps[no_vars] thm f_raw.simps +thm trm'_pat'_induct +thm trm'_pat'_perm +thm trm'_pat'_fv +thm trm'_pat'_bn nominal_datatype trm0 = Var0 "name" @@ -214,6 +193,10 @@ | "f0 (PD0 p1 p2) = (f0 p1) \ (f0 p2)" thm f0_raw.simps +thm trm0_pat0_induct +thm trm0_pat0_perm +thm trm0_pat0_fv +thm trm0_pat0_bn text {* example type schemes *} @@ -313,6 +296,7 @@ (* example 6 from Terms.thy *) +(* BV is not respectful, needs to fail nominal_datatype trm6 = Vr6 "name" | Lm6 x::"name" t::"trm6" bind x in t @@ -322,10 +306,11 @@ where "bv6 (Vr6 n) = {}" | "bv6 (Lm6 n t) = {atom n} \ bv6 t" -| "bv6 (Lt6 l r) = bv6 l \ bv6 r" +| "bv6 (Lt6 l r) = bv6 l \ bv6 r" *) (* example 7 from Terms.thy *) +(* BV is not respectful, needs to fail nominal_datatype trm7 = Vr7 "name" | Lm7 l::"name" r::"trm7" bind l in r @@ -335,7 +320,7 @@ where "bv7 (Vr7 n) = {atom n}" | "bv7 (Lm7 n t) = bv7 t - {atom n}" -| "bv7 (Lt7 l r) = bv7 l \ bv7 r" +| "bv7 (Lt7 l r) = bv7 l \ bv7 r" *) (* example 8 from Terms.thy *) @@ -353,6 +338,7 @@ (* example 9 from Terms.thy *) +(* BV is not respectful, needs to fail nominal_datatype lam9 = Var9 "name" | Lam9 n::"name" l::"lam9" bind n in l @@ -362,13 +348,13 @@ bv9 where "bv9 (Var9 x) = {}" -| "bv9 (Lam9 x b) = {atom x}" +| "bv9 (Lam9 x b) = {atom x}" *) (* example from my PHD *) atom_decl coname -nominal_datatype phd = +(*nominal_datatype phd = Ax "name" "coname" | Cut n::"coname" t1::"phd" c::"coname" t2::"phd" bind n in t1, bind c in t2 | AndR c1::"coname" t1::"phd" c2::"coname" t2::"phd" "coname" bind c1 in t1, bind c2 in t2 @@ -377,10 +363,9 @@ | ImpL c::"coname" t1::"phd" n::"name" t2::"phd" "name" bind c in t1, bind n in t2 | ImpR c::"coname" n::"name" t::"phd" "coname" bind n in t, bind c in t -(* PROBLEM?: why does it create for the Cut AndR ImpL cases -two permutations, but only one is used *) thm alpha_phd_raw.intros[no_vars] thm fv_phd_raw.simps[no_vars] +*) (* example form Leroy 96 about modules; OTT *) @@ -419,9 +404,9 @@ and trmtrm = Tref1 "name" | Tref2 "path" "name" -| Lam v::"name" "tyty" M::"trmtrm" bind v in M -| App "trmtrm" "trmtrm" -| Let "body" "trmtrm" +| Lam' v::"name" "tyty" M::"trmtrm" bind v in M +| App' "trmtrm" "trmtrm" +| Let' "body" "trmtrm" binder cbinders :: "defn \ atom set" and Cbinders :: "spec \ atom set" @@ -436,6 +421,7 @@ | "Cbinders (SVal v T) = {atom v}" (* core haskell *) +print_theorems atom_decl var atom_decl tvar @@ -495,10 +481,10 @@ (* example 3 from Peter Sewell's bestiary *) nominal_datatype exp = - Var "name" -| App "exp" "exp" -| Lam x::"name" e::"exp" bind x in e -| Let x::"name" p::"pat" e1::"exp" e2::"exp" bind x in e2, bind "bp p" in e1 + VarP "name" +| AppP "exp" "exp" +| LamP x::"name" e::"exp" bind x in e +| LetP x::"name" p::"pat" e1::"exp" e2::"exp" bind x in e2, bind "bp p" in e1 and pat = PVar "name" | PUnit @@ -510,24 +496,25 @@ | "bp (PUnit) = {}" | "bp (PPair p1 p2) = bp p1 \ bp p2" +thm quot_respect (* example 6 from Peter Sewell's bestiary *) -nominal_datatype exp6 = +(*nominal_datatype exp6 = EVar name | EPair exp6 exp6 | ELetRec x::name p::pat6 e1::exp6 e2::exp6 bind x in e1, bind x in e2, bind "bp6 p" in e1 and pat6 = - PVar name -| PUnit -| PPair pat6 pat6 + PVar' name +| PUnit' +| PPair' pat6 pat6 binder bp6 :: "pat6 \ atom set" where - "bp6 (PVar x) = {atom x}" -| "bp6 (PUnit) = {}" -| "bp6 (PPair p1 p2) = bp6 p1 \ bp6 p2" + "bp6 (PVar' x) = {atom x}" +| "bp6 (PUnit') = {}" +| "bp6 (PPair' p1 p2) = bp6 p1 \ bp6 p2"*) (* example 7 from Peter Sewell's bestiary *) -nominal_datatype exp7 = +(*nominal_datatype exp7 = EVar name | EUnit | EPair exp7 exp7 @@ -543,10 +530,10 @@ where "b7 (Assign x e) = {atom x}" | "b7s (Single a) = b7 a" -| "b7s (More a as) = (b7 a) \ (b7s as)" +| "b7s (More a as) = (b7 a) \ (b7s as)"*) (* example 8 from Peter Sewell's bestiary *) -nominal_datatype exp8 = +(*nominal_datatype exp8 = EVar name | EUnit | EPair exp8 exp8 @@ -580,7 +567,7 @@ | "b_fnclauses (S fc) = (b_fnclause fc)" | "b_fnclauses (ORs fc fcs) = (b_fnclause fc) \ (b_fnclauses fcs)" | "b_lrb8 (Clause fcs) = (b_fnclauses fcs)" -| "b_fnclause (K x pat exp8) = {atom x}" +| "b_fnclause (K x pat exp8) = {atom x}"*)