--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/BNF/bnf_gfp_rec_sugar.ML Mon Jan 20 18:24:56 2014 +0100
@@ -0,0 +1,1359 @@
+(* Title: HOL/BNF/Tools/bnf_gfp_rec_sugar.ML
+ Author: Lorenz Panny, TU Muenchen
+ Author: Jasmin Blanchette, TU Muenchen
+ Copyright 2013
+
+Corecursor sugar.
+*)
+
+signature BNF_GFP_REC_SUGAR =
+sig
+ datatype primcorec_option = Sequential_Option | Exhaustive_Option
+
+ val add_primcorecursive_cmd: primcorec_option list ->
+ (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
+ Proof.context -> Proof.state
+ val add_primcorec_cmd: primcorec_option list ->
+ (binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
+ local_theory -> local_theory
+end;
+
+structure BNF_GFP_Rec_Sugar : BNF_GFP_REC_SUGAR =
+struct
+
+open Ctr_Sugar_General_Tactics
+open Ctr_Sugar
+open BNF_Util
+open BNF_Def
+open BNF_FP_Util
+open BNF_FP_Def_Sugar
+open BNF_FP_N2M_Sugar
+open BNF_FP_Rec_Sugar_Util
+open BNF_GFP_Rec_Sugar_Tactics
+
+val codeN = "code"
+val ctrN = "ctr"
+val discN = "disc"
+val disc_iffN = "disc_iff"
+val excludeN = "exclude"
+val selN = "sel"
+
+val nitpicksimp_attrs = @{attributes [nitpick_simp]};
+val simp_attrs = @{attributes [simp]};
+val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
+
+exception Primcorec_Error of string * term list;
+
+fun primcorec_error str = raise Primcorec_Error (str, []);
+fun primcorec_error_eqn str eqn = raise Primcorec_Error (str, [eqn]);
+fun primcorec_error_eqns str eqns = raise Primcorec_Error (str, eqns);
+
+datatype primcorec_option = Sequential_Option | Exhaustive_Option;
+
+datatype corec_call =
+ Dummy_No_Corec of int |
+ No_Corec of int |
+ Mutual_Corec of int * int * int |
+ Nested_Corec of int;
+
+type basic_corec_ctr_spec =
+ {ctr: term,
+ disc: term,
+ sels: term list};
+
+type corec_ctr_spec =
+ {ctr: term,
+ disc: term,
+ sels: term list,
+ pred: int option,
+ calls: corec_call list,
+ discI: thm,
+ sel_thms: thm list,
+ disc_excludess: thm list list,
+ collapse: thm,
+ corec_thm: thm,
+ disc_corec: thm,
+ sel_corecs: thm list};
+
+type corec_spec =
+ {corec: term,
+ disc_exhausts: thm list,
+ nested_maps: thm list,
+ nested_map_idents: thm list,
+ nested_map_comps: thm list,
+ ctr_specs: corec_ctr_spec list};
+
+exception AINT_NO_MAP of term;
+
+fun not_codatatype ctxt T =
+ error ("Not a codatatype: " ^ Syntax.string_of_typ ctxt T);
+fun ill_formed_corec_call ctxt t =
+ error ("Ill-formed corecursive call: " ^ quote (Syntax.string_of_term ctxt t));
+fun invalid_map ctxt t =
+ error ("Invalid map function in " ^ quote (Syntax.string_of_term ctxt t));
+fun unexpected_corec_call ctxt t =
+ error ("Unexpected corecursive call: " ^ quote (Syntax.string_of_term ctxt t));
+
+fun order_list_duplicates xs = map snd (sort (int_ord o pairself fst) xs)
+
+val mk_conjs = try (foldr1 HOLogic.mk_conj) #> the_default @{const True};
+val mk_disjs = try (foldr1 HOLogic.mk_disj) #> the_default @{const False};
+val mk_dnf = mk_disjs o map mk_conjs;
+
+val conjuncts_s = filter_out (curry (op aconv) @{const True}) o HOLogic.conjuncts;
+
+fun s_not @{const True} = @{const False}
+ | s_not @{const False} = @{const True}
+ | s_not (@{const Not} $ t) = t
+ | s_not (@{const conj} $ t $ u) = @{const disj} $ s_not t $ s_not u
+ | s_not (@{const disj} $ t $ u) = @{const conj} $ s_not t $ s_not u
+ | s_not t = @{const Not} $ t;
+
+val s_not_conj = conjuncts_s o s_not o mk_conjs;
+
+fun propagate_unit_pos u cs = if member (op aconv) cs u then [@{const False}] else cs;
+
+fun propagate_unit_neg not_u cs = remove (op aconv) not_u cs;
+
+fun propagate_units css =
+ (case List.partition (can the_single) css of
+ ([], _) => css
+ | ([u] :: uss, css') =>
+ [u] :: propagate_units (map (propagate_unit_neg (s_not u))
+ (map (propagate_unit_pos u) (uss @ css'))));
+
+fun s_conjs cs =
+ if member (op aconv) cs @{const False} then @{const False}
+ else mk_conjs (remove (op aconv) @{const True} cs);
+
+fun s_disjs ds =
+ if member (op aconv) ds @{const True} then @{const True}
+ else mk_disjs (remove (op aconv) @{const False} ds);
+
+fun s_dnf css0 =
+ let val css = propagate_units css0 in
+ if null css then
+ [@{const False}]
+ else if exists null css then
+ []
+ else
+ map (fn c :: cs => (c, cs)) css
+ |> AList.coalesce (op =)
+ |> map (fn (c, css) => c :: s_dnf css)
+ |> (fn [cs] => cs | css => [s_disjs (map s_conjs css)])
+ end;
+
+fun fold_rev_let_if_case ctxt f bound_Ts t =
+ let
+ val thy = Proof_Context.theory_of ctxt;
+
+ fun fld conds t =
+ (case Term.strip_comb t of
+ (Const (@{const_name Let}, _), [_, _]) => fld conds (unfold_let t)
+ | (Const (@{const_name If}, _), [cond, then_branch, else_branch]) =>
+ fld (conds @ conjuncts_s cond) then_branch o fld (conds @ s_not_conj [cond]) else_branch
+ | (Const (c, _), args as _ :: _ :: _) =>
+ let val n = num_binder_types (Sign.the_const_type thy c) - 1 in
+ if n >= 0 andalso n < length args then
+ (case fastype_of1 (bound_Ts, nth args n) of
+ Type (s, Ts) =>
+ (case dest_case ctxt s Ts t of
+ SOME (ctr_sugar as {sel_splits = _ :: _, ...}, conds', branches) =>
+ apfst (cons ctr_sugar) o fold_rev (uncurry fld)
+ (map (append conds o conjuncts_s) conds' ~~ branches)
+ | _ => apsnd (f conds t))
+ | _ => apsnd (f conds t))
+ else
+ apsnd (f conds t)
+ end
+ | _ => apsnd (f conds t))
+ in
+ fld [] t o pair []
+ end;
+
+fun case_of ctxt s =
+ (case ctr_sugar_of ctxt s of
+ SOME {casex = Const (s', _), sel_splits = _ :: _, ...} => SOME s'
+ | _ => NONE);
+
+fun massage_let_if_case ctxt has_call massage_leaf =
+ let
+ val thy = Proof_Context.theory_of ctxt;
+
+ fun check_no_call t = if has_call t then unexpected_corec_call ctxt t else ();
+
+ fun massage_abs bound_Ts 0 t = massage_rec bound_Ts t
+ | massage_abs bound_Ts m (Abs (s, T, t)) = Abs (s, T, massage_abs (T :: bound_Ts) (m - 1) t)
+ | massage_abs bound_Ts m t =
+ let val T = domain_type (fastype_of1 (bound_Ts, t)) in
+ Abs (Name.uu, T, massage_abs (T :: bound_Ts) (m - 1) (incr_boundvars 1 t $ Bound 0))
+ end
+ and massage_rec bound_Ts t =
+ let val typof = curry fastype_of1 bound_Ts in
+ (case Term.strip_comb t of
+ (Const (@{const_name Let}, _), [_, _]) => massage_rec bound_Ts (unfold_let t)
+ | (Const (@{const_name If}, _), obj :: (branches as [_, _])) =>
+ let val branches' = map (massage_rec bound_Ts) branches in
+ Term.list_comb (If_const (typof (hd branches')) $ tap check_no_call obj, branches')
+ end
+ | (Const (c, _), args as _ :: _ :: _) =>
+ (case try strip_fun_type (Sign.the_const_type thy c) of
+ SOME (gen_branch_Ts, gen_body_fun_T) =>
+ let
+ val gen_branch_ms = map num_binder_types gen_branch_Ts;
+ val n = length gen_branch_ms;
+ in
+ if n < length args then
+ (case gen_body_fun_T of
+ Type (_, [Type (T_name, _), _]) =>
+ if case_of ctxt T_name = SOME c then
+ let
+ val (branches, obj_leftovers) = chop n args;
+ val branches' = map2 (massage_abs bound_Ts) gen_branch_ms branches;
+ val branch_Ts' = map typof branches';
+ val body_T' = snd (strip_typeN (hd gen_branch_ms) (hd branch_Ts'));
+ val casex' = Const (c, branch_Ts' ---> map typof obj_leftovers ---> body_T');
+ in
+ Term.list_comb (casex',
+ branches' @ tap (List.app check_no_call) obj_leftovers)
+ end
+ else
+ massage_leaf bound_Ts t
+ | _ => massage_leaf bound_Ts t)
+ else
+ massage_leaf bound_Ts t
+ end
+ | NONE => massage_leaf bound_Ts t)
+ | _ => massage_leaf bound_Ts t)
+ end
+ in
+ massage_rec
+ end;
+
+val massage_mutual_corec_call = massage_let_if_case;
+
+fun curried_type (Type (@{type_name fun}, [Type (@{type_name prod}, Ts), T])) = Ts ---> T;
+
+fun massage_nested_corec_call ctxt has_call raw_massage_call bound_Ts U t =
+ let
+ fun check_no_call t = if has_call t then unexpected_corec_call ctxt t else ();
+
+ val build_map_Inl = build_map ctxt (uncurry Inl_const o dest_sumT o snd);
+
+ fun massage_mutual_call bound_Ts U T t =
+ if has_call t then
+ (case try dest_sumT U of
+ SOME (U1, U2) => if U1 = T then raw_massage_call bound_Ts T U2 t else invalid_map ctxt t
+ | NONE => invalid_map ctxt t)
+ else
+ build_map_Inl (T, U) $ t;
+
+ fun massage_mutual_fun bound_Ts U T t =
+ (case t of
+ Const (@{const_name comp}, _) $ t1 $ t2 =>
+ mk_comp bound_Ts (massage_mutual_fun bound_Ts U T t1, tap check_no_call t2)
+ | _ =>
+ let
+ val var = Var ((Name.uu, Term.maxidx_of_term t + 1),
+ domain_type (fastype_of1 (bound_Ts, t)));
+ in
+ Term.lambda var (massage_mutual_call bound_Ts U T (t $ var))
+ end);
+
+ fun massage_map bound_Ts (Type (_, Us)) (Type (s, Ts)) t =
+ (case try (dest_map ctxt s) t of
+ SOME (map0, fs) =>
+ let
+ val Type (_, dom_Ts) = domain_type (fastype_of1 (bound_Ts, t));
+ val map' = mk_map (length fs) dom_Ts Us map0;
+ val fs' =
+ map_flattened_map_args ctxt s (map3 (massage_map_or_map_arg bound_Ts) Us Ts) fs;
+ in
+ Term.list_comb (map', fs')
+ end
+ | NONE => raise AINT_NO_MAP t)
+ | massage_map _ _ _ t = raise AINT_NO_MAP t
+ and massage_map_or_map_arg bound_Ts U T t =
+ if T = U then
+ tap check_no_call t
+ else
+ massage_map bound_Ts U T t
+ handle AINT_NO_MAP _ => massage_mutual_fun bound_Ts U T t;
+
+ fun massage_call bound_Ts U T =
+ massage_let_if_case ctxt has_call (fn bound_Ts => fn t =>
+ if has_call t then
+ (case U of
+ Type (s, Us) =>
+ (case try (dest_ctr ctxt s) t of
+ SOME (f, args) =>
+ let
+ val typof = curry fastype_of1 bound_Ts;
+ val f' = mk_ctr Us f
+ val f'_T = typof f';
+ val arg_Ts = map typof args;
+ in
+ Term.list_comb (f', map3 (massage_call bound_Ts) (binder_types f'_T) arg_Ts args)
+ end
+ | NONE =>
+ (case t of
+ Const (@{const_name prod_case}, _) $ t' =>
+ let
+ val U' = curried_type U;
+ val T' = curried_type T;
+ in
+ Const (@{const_name prod_case}, U' --> U) $ massage_call bound_Ts U' T' t'
+ end
+ | t1 $ t2 =>
+ (if has_call t2 then
+ massage_mutual_call bound_Ts U T t
+ else
+ massage_map bound_Ts U T t1 $ t2
+ handle AINT_NO_MAP _ => massage_mutual_call bound_Ts U T t)
+ | Abs (s, T', t') =>
+ Abs (s, T', massage_call (T' :: bound_Ts) (range_type U) (range_type T) t')
+ | _ => massage_mutual_call bound_Ts U T t))
+ | _ => ill_formed_corec_call ctxt t)
+ else
+ build_map_Inl (T, U) $ t) bound_Ts;
+
+ val T = fastype_of1 (bound_Ts, t);
+ in
+ if has_call t then massage_call bound_Ts U T t else build_map_Inl (T, U) $ t
+ end;
+
+fun expand_to_ctr_term ctxt s Ts t =
+ (case ctr_sugar_of ctxt s of
+ SOME {ctrs, casex, ...} =>
+ Term.list_comb (mk_case Ts (Type (s, Ts)) casex, map (mk_ctr Ts) ctrs) $ t
+ | NONE => raise Fail "expand_to_ctr_term");
+
+fun expand_corec_code_rhs ctxt has_call bound_Ts t =
+ (case fastype_of1 (bound_Ts, t) of
+ Type (s, Ts) =>
+ massage_let_if_case ctxt has_call (fn _ => fn t =>
+ if can (dest_ctr ctxt s) t then t else expand_to_ctr_term ctxt s Ts t) bound_Ts t
+ | _ => raise Fail "expand_corec_code_rhs");
+
+fun massage_corec_code_rhs ctxt massage_ctr =
+ massage_let_if_case ctxt (K false)
+ (fn bound_Ts => uncurry (massage_ctr bound_Ts) o Term.strip_comb);
+
+fun fold_rev_corec_code_rhs ctxt f =
+ snd ooo fold_rev_let_if_case ctxt (fn conds => uncurry (f conds) o Term.strip_comb);
+
+fun case_thms_of_term ctxt bound_Ts t =
+ let val (ctr_sugars, _) = fold_rev_let_if_case ctxt (K (K I)) bound_Ts t () in
+ (maps #distincts ctr_sugars, maps #discIs ctr_sugars, maps #disc_exhausts ctr_sugars,
+ maps #sel_splits ctr_sugars, maps #sel_split_asms ctr_sugars)
+ end;
+
+fun basic_corec_specs_of ctxt res_T =
+ (case res_T of
+ Type (T_name, _) =>
+ (case Ctr_Sugar.ctr_sugar_of ctxt T_name of
+ NONE => not_codatatype ctxt res_T
+ | SOME {ctrs, discs, selss, ...} =>
+ let
+ val thy = Proof_Context.theory_of ctxt;
+
+ val gfpT = body_type (fastype_of (hd ctrs));
+ val As_rho = tvar_subst thy [gfpT] [res_T];
+ val substA = Term.subst_TVars As_rho;
+
+ fun mk_spec ctr disc sels = {ctr = substA ctr, disc = substA disc, sels = map substA sels};
+ in
+ map3 mk_spec ctrs discs selss
+ handle ListPair.UnequalLengths => not_codatatype ctxt res_T
+ end)
+ | _ => not_codatatype ctxt res_T);
+
+fun map_thms_of_typ ctxt (Type (s, _)) =
+ (case fp_sugar_of ctxt s of
+ SOME {index, mapss, ...} => nth mapss index
+ | NONE => [])
+ | map_thms_of_typ _ _ = [];
+
+fun corec_specs_of bs arg_Ts res_Ts get_indices callssss0 lthy0 =
+ let
+ val thy = Proof_Context.theory_of lthy0;
+
+ val ((missing_res_Ts, perm0_kks,
+ fp_sugars as {nested_bnfs, fp_res = {xtor_co_iterss = dtor_coiters1 :: _, ...},
+ co_inducts = coinduct_thms, ...} :: _, (_, gfp_sugar_thms)), lthy) =
+ nested_to_mutual_fps Greatest_FP bs res_Ts get_indices callssss0 lthy0;
+
+ val perm_fp_sugars = sort (int_ord o pairself #index) fp_sugars;
+
+ val indices = map #index fp_sugars;
+ val perm_indices = map #index perm_fp_sugars;
+
+ val perm_ctrss = map (#ctrs o of_fp_sugar #ctr_sugars) perm_fp_sugars;
+ val perm_ctr_Tsss = map (map (binder_types o fastype_of)) perm_ctrss;
+ val perm_gfpTs = map (body_type o fastype_of o hd) perm_ctrss;
+
+ val nn0 = length res_Ts;
+ val nn = length perm_gfpTs;
+ val kks = 0 upto nn - 1;
+ val perm_ns = map length perm_ctr_Tsss;
+
+ val perm_Cs = map (domain_type o body_fun_type o fastype_of o co_rec_of o
+ of_fp_sugar (#xtor_co_iterss o #fp_res)) perm_fp_sugars;
+ val (perm_p_Tss, (perm_q_Tssss, _, perm_f_Tssss, _)) =
+ mk_coiter_fun_arg_types perm_ctr_Tsss perm_Cs perm_ns (co_rec_of dtor_coiters1);
+
+ val (perm_p_hss, h) = indexedd perm_p_Tss 0;
+ val (perm_q_hssss, h') = indexedddd perm_q_Tssss h;
+ val (perm_f_hssss, _) = indexedddd perm_f_Tssss h';
+
+ val fun_arg_hs =
+ flat (map3 flat_corec_preds_predsss_gettersss perm_p_hss perm_q_hssss perm_f_hssss);
+
+ fun unpermute0 perm0_xs = permute_like (op =) perm0_kks kks perm0_xs;
+ fun unpermute perm_xs = permute_like (op =) perm_indices indices perm_xs;
+
+ val coinduct_thmss = map (unpermute0 o conj_dests nn) coinduct_thms;
+
+ val p_iss = map (map (find_index_eq fun_arg_hs)) (unpermute perm_p_hss);
+ val q_issss = map (map (map (map (find_index_eq fun_arg_hs)))) (unpermute perm_q_hssss);
+ val f_issss = map (map (map (map (find_index_eq fun_arg_hs)))) (unpermute perm_f_hssss);
+
+ val f_Tssss = unpermute perm_f_Tssss;
+ val gfpTs = unpermute perm_gfpTs;
+ val Cs = unpermute perm_Cs;
+
+ val As_rho = tvar_subst thy (take nn0 gfpTs) res_Ts;
+ val Cs_rho = map (fst o dest_TVar) Cs ~~ pad_list HOLogic.unitT nn arg_Ts;
+
+ val substA = Term.subst_TVars As_rho;
+ val substAT = Term.typ_subst_TVars As_rho;
+ val substCT = Term.typ_subst_TVars Cs_rho;
+
+ val perm_Cs' = map substCT perm_Cs;
+
+ fun call_of nullary [] [g_i] [Type (@{type_name fun}, [_, T])] =
+ (if exists_subtype_in Cs T then Nested_Corec
+ else if nullary then Dummy_No_Corec
+ else No_Corec) g_i
+ | call_of _ [q_i] [g_i, g_i'] _ = Mutual_Corec (q_i, g_i, g_i');
+
+ fun mk_ctr_spec ctr disc sels p_io q_iss f_iss f_Tss discI sel_thms disc_excludess collapse
+ corec_thm disc_corec sel_corecs =
+ let val nullary = not (can dest_funT (fastype_of ctr)) in
+ {ctr = substA ctr, disc = substA disc, sels = map substA sels, pred = p_io,
+ calls = map3 (call_of nullary) q_iss f_iss f_Tss, discI = discI, sel_thms = sel_thms,
+ disc_excludess = disc_excludess, collapse = collapse, corec_thm = corec_thm,
+ disc_corec = disc_corec, sel_corecs = sel_corecs}
+ end;
+
+ fun mk_ctr_specs index ctr_sugars p_is q_isss f_isss f_Tsss coiter_thmsss disc_coitersss
+ sel_coiterssss =
+ let
+ val {ctrs, discs, selss, discIs, sel_thmss, disc_excludesss, collapses, ...} : ctr_sugar =
+ nth ctr_sugars index;
+ val p_ios = map SOME p_is @ [NONE];
+ val discIs = #discIs (nth ctr_sugars index);
+ val corec_thms = co_rec_of (nth coiter_thmsss index);
+ val disc_corecs = co_rec_of (nth disc_coitersss index);
+ val sel_corecss = co_rec_of (nth sel_coiterssss index);
+ in
+ map14 mk_ctr_spec ctrs discs selss p_ios q_isss f_isss f_Tsss discIs sel_thmss
+ disc_excludesss collapses corec_thms disc_corecs sel_corecss
+ end;
+
+ fun mk_spec ({T, index, ctr_sugars, co_iterss = coiterss, co_iter_thmsss = coiter_thmsss,
+ disc_co_itersss = disc_coitersss, sel_co_iterssss = sel_coiterssss, ...} : fp_sugar)
+ p_is q_isss f_isss f_Tsss =
+ {corec = mk_co_iter thy Greatest_FP (substAT T) perm_Cs' (co_rec_of (nth coiterss index)),
+ disc_exhausts = #disc_exhausts (nth ctr_sugars index),
+ nested_maps = maps (map_thms_of_typ lthy o T_of_bnf) nested_bnfs,
+ nested_map_idents = map (unfold_thms lthy @{thms id_def} o map_id0_of_bnf) nested_bnfs,
+ nested_map_comps = map map_comp_of_bnf nested_bnfs,
+ ctr_specs = mk_ctr_specs index ctr_sugars p_is q_isss f_isss f_Tsss coiter_thmsss
+ disc_coitersss sel_coiterssss};
+ in
+ ((is_some gfp_sugar_thms, map5 mk_spec fp_sugars p_iss q_issss f_issss f_Tssss, missing_res_Ts,
+ co_induct_of coinduct_thms, strong_co_induct_of coinduct_thms, co_induct_of coinduct_thmss,
+ strong_co_induct_of coinduct_thmss), lthy)
+ end;
+
+val undef_const = Const (@{const_name undefined}, dummyT);
+
+val abs_tuple = HOLogic.tupled_lambda o HOLogic.mk_tuple;
+
+fun abstract vs =
+ let fun a n (t $ u) = a n t $ a n u
+ | a n (Abs (v, T, b)) = Abs (v, T, a (n + 1) b)
+ | a n t = let val idx = find_index (curry (op =) t) vs in
+ if idx < 0 then t else Bound (n + idx) end
+ in a 0 end;
+
+fun mk_prod1 bound_Ts (t, u) =
+ HOLogic.pair_const (fastype_of1 (bound_Ts, t)) (fastype_of1 (bound_Ts, u)) $ t $ u;
+fun mk_tuple1 bound_Ts = the_default HOLogic.unit o try (foldr1 (mk_prod1 bound_Ts));
+
+type coeqn_data_disc = {
+ fun_name: string,
+ fun_T: typ,
+ fun_args: term list,
+ ctr: term,
+ ctr_no: int,
+ disc: term,
+ prems: term list,
+ auto_gen: bool,
+ ctr_rhs_opt: term option,
+ code_rhs_opt: term option,
+ eqn_pos: int,
+ user_eqn: term
+};
+
+type coeqn_data_sel = {
+ fun_name: string,
+ fun_T: typ,
+ fun_args: term list,
+ ctr: term,
+ sel: term,
+ rhs_term: term,
+ ctr_rhs_opt: term option,
+ code_rhs_opt: term option,
+ eqn_pos: int,
+ user_eqn: term
+};
+
+datatype coeqn_data =
+ Disc of coeqn_data_disc |
+ Sel of coeqn_data_sel;
+
+fun dissect_coeqn_disc fun_names sequentials (basic_ctr_specss : basic_corec_ctr_spec list list)
+ eqn_pos ctr_rhs_opt code_rhs_opt prems' concl matchedsss =
+ let
+ fun find_subterm p =
+ let (* FIXME \<exists>? *)
+ fun find (t as u $ v) = if p t then SOME t else merge_options (find u, find v)
+ | find t = if p t then SOME t else NONE;
+ in find end;
+
+ val applied_fun = concl
+ |> find_subterm (member (op = o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
+ |> the
+ handle Option.Option => primcorec_error_eqn "malformed discriminator formula" concl;
+ val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
+ val SOME (sequential, basic_ctr_specs) =
+ AList.lookup (op =) (fun_names ~~ (sequentials ~~ basic_ctr_specss)) fun_name;
+
+ val discs = map #disc basic_ctr_specs;
+ val ctrs = map #ctr basic_ctr_specs;
+ val not_disc = head_of concl = @{term Not};
+ val _ = not_disc andalso length ctrs <> 2 andalso
+ primcorec_error_eqn "negated discriminator for a type with \<noteq> 2 constructors" concl;
+ val disc' = find_subterm (member (op =) discs o head_of) concl;
+ val eq_ctr0 = concl |> perhaps (try HOLogic.dest_not) |> try (HOLogic.dest_eq #> snd)
+ |> (fn SOME t => let val n = find_index (curry (op =) t) ctrs in
+ if n >= 0 then SOME n else NONE end | _ => NONE);
+ val _ = is_some disc' orelse is_some eq_ctr0 orelse
+ primcorec_error_eqn "no discriminator in equation" concl;
+ val ctr_no' =
+ if is_none disc' then the eq_ctr0 else find_index (curry (op =) (head_of (the disc'))) discs;
+ val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
+ val {ctr, disc, ...} = nth basic_ctr_specs ctr_no;
+
+ val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
+ val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
+ val prems = map (abstract (List.rev fun_args)) prems';
+ val actual_prems =
+ (if catch_all orelse sequential then maps s_not_conj matchedss else []) @
+ (if catch_all then [] else prems);
+
+ val matchedsss' = AList.delete (op =) fun_name matchedsss
+ |> cons (fun_name, if sequential then matchedss @ [prems] else matchedss @ [actual_prems]);
+
+ val user_eqn =
+ (actual_prems, concl)
+ |>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop o abstract (List.rev fun_args)
+ |> curry Logic.list_all (map dest_Free fun_args) o Logic.list_implies;
+ in
+ (Disc {
+ fun_name = fun_name,
+ fun_T = fun_T,
+ fun_args = fun_args,
+ ctr = ctr,
+ ctr_no = ctr_no,
+ disc = disc,
+ prems = actual_prems,
+ auto_gen = catch_all,
+ ctr_rhs_opt = ctr_rhs_opt,
+ code_rhs_opt = code_rhs_opt,
+ eqn_pos = eqn_pos,
+ user_eqn = user_eqn
+ }, matchedsss')
+ end;
+
+fun dissect_coeqn_sel fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn_pos
+ ctr_rhs_opt code_rhs_opt eqn0 of_spec_opt eqn =
+ let
+ val (lhs, rhs) = HOLogic.dest_eq eqn
+ handle TERM _ =>
+ primcorec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
+ val sel = head_of lhs;
+ val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
+ handle TERM _ =>
+ primcorec_error_eqn "malformed selector argument in left-hand side" eqn;
+ val basic_ctr_specs = the (AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name)
+ handle Option.Option =>
+ primcorec_error_eqn "malformed selector argument in left-hand side" eqn;
+ val {ctr, ...} =
+ (case of_spec_opt of
+ SOME of_spec => the (find_first (curry (op =) of_spec o #ctr) basic_ctr_specs)
+ | NONE => filter (exists (curry (op =) sel) o #sels) basic_ctr_specs |> the_single
+ handle List.Empty => primcorec_error_eqn "ambiguous selector - use \"of\"" eqn);
+ val user_eqn = drop_all eqn0;
+ in
+ Sel {
+ fun_name = fun_name,
+ fun_T = fun_T,
+ fun_args = fun_args,
+ ctr = ctr,
+ sel = sel,
+ rhs_term = rhs,
+ ctr_rhs_opt = ctr_rhs_opt,
+ code_rhs_opt = code_rhs_opt,
+ eqn_pos = eqn_pos,
+ user_eqn = user_eqn
+ }
+ end;
+
+fun dissect_coeqn_ctr fun_names sequentials (basic_ctr_specss : basic_corec_ctr_spec list list)
+ eqn_pos eqn0 code_rhs_opt prems concl matchedsss =
+ let
+ val (lhs, rhs) = HOLogic.dest_eq concl;
+ val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
+ val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
+ val (ctr, ctr_args) = strip_comb (unfold_let rhs);
+ val {disc, sels, ...} = the (find_first (curry (op =) ctr o #ctr) basic_ctr_specs)
+ handle Option.Option => primcorec_error_eqn "not a constructor" ctr;
+
+ val disc_concl = betapply (disc, lhs);
+ val (eqn_data_disc_opt, matchedsss') =
+ if null (tl basic_ctr_specs) then
+ (NONE, matchedsss)
+ else
+ apfst SOME (dissect_coeqn_disc fun_names sequentials basic_ctr_specss eqn_pos
+ (SOME (abstract (List.rev fun_args) rhs)) code_rhs_opt prems disc_concl matchedsss);
+
+ val sel_concls = sels ~~ ctr_args
+ |> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
+
+(*
+val _ = tracing ("reduced\n " ^ Syntax.string_of_term @{context} concl ^ "\nto\n \<cdot> " ^
+ (is_some eqn_data_disc_opt ? K (Syntax.string_of_term @{context} disc_concl ^ "\n \<cdot> ")) "" ^
+ space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) sel_concls) ^
+ "\nfor premise(s)\n \<cdot> " ^
+ space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) prems));
+*)
+
+ val eqns_data_sel =
+ map (dissect_coeqn_sel fun_names basic_ctr_specss eqn_pos
+ (SOME (abstract (List.rev fun_args) rhs)) code_rhs_opt eqn0 (SOME ctr)) sel_concls;
+ in
+ (the_list eqn_data_disc_opt @ eqns_data_sel, matchedsss')
+ end;
+
+fun dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn_pos eqn0 concl matchedsss =
+ let
+ val (lhs, (rhs', rhs)) = HOLogic.dest_eq concl ||> `(expand_corec_code_rhs lthy has_call []);
+ val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
+ val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
+
+ val cond_ctrs = fold_rev_corec_code_rhs lthy (fn cs => fn ctr => fn _ =>
+ if member (op = o apsnd #ctr) basic_ctr_specs ctr then cons (ctr, cs)
+ else primcorec_error_eqn "not a constructor" ctr) [] rhs' []
+ |> AList.group (op =);
+
+ val ctr_premss = (case cond_ctrs of [_] => [[]] | _ => map (s_dnf o snd) cond_ctrs);
+ val ctr_concls = cond_ctrs |> map (fn (ctr, _) =>
+ binder_types (fastype_of ctr)
+ |> map_index (fn (n, T) => massage_corec_code_rhs lthy (fn _ => fn ctr' => fn args =>
+ if ctr' = ctr then nth args n else Const (@{const_name undefined}, T)) [] rhs')
+ |> curry list_comb ctr
+ |> curry HOLogic.mk_eq lhs);
+
+ val sequentials = replicate (length fun_names) false;
+ in
+ fold_map2 (dissect_coeqn_ctr fun_names sequentials basic_ctr_specss eqn_pos eqn0
+ (SOME (abstract (List.rev fun_args) rhs)))
+ ctr_premss ctr_concls matchedsss
+ end;
+
+fun dissect_coeqn lthy has_call fun_names sequentials
+ (basic_ctr_specss : basic_corec_ctr_spec list list) (eqn_pos, eqn0) of_spec_opt matchedsss =
+ let
+ val eqn = drop_all eqn0
+ handle TERM _ => primcorec_error_eqn "malformed function equation" eqn0;
+ val (prems, concl) = Logic.strip_horn eqn
+ |> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
+
+ val head = concl
+ |> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
+ |> head_of;
+
+ val rhs_opt = concl |> perhaps (try HOLogic.dest_not) |> try (snd o HOLogic.dest_eq);
+
+ val discs = maps (map #disc) basic_ctr_specss;
+ val sels = maps (maps #sels) basic_ctr_specss;
+ val ctrs = maps (map #ctr) basic_ctr_specss;
+ in
+ if member (op =) discs head orelse
+ is_some rhs_opt andalso
+ member (op =) (filter (null o binder_types o fastype_of) ctrs) (the rhs_opt) then
+ dissect_coeqn_disc fun_names sequentials basic_ctr_specss eqn_pos NONE NONE prems concl
+ matchedsss
+ |>> single
+ else if member (op =) sels head then
+ ([dissect_coeqn_sel fun_names basic_ctr_specss eqn_pos NONE NONE eqn0 of_spec_opt concl],
+ matchedsss)
+ else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) then
+ if member (op =) ctrs (head_of (unfold_let (the rhs_opt))) then
+ dissect_coeqn_ctr fun_names sequentials basic_ctr_specss eqn_pos eqn0
+ (if null prems then
+ SOME (snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (Logic.strip_assums_concl eqn0))))
+ else
+ NONE)
+ prems concl matchedsss
+ else if null prems then
+ dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn_pos eqn0 concl matchedsss
+ |>> flat
+ else
+ primcorec_error_eqn "cannot mix constructor and code views (see manual for details)" eqn
+ else
+ primcorec_error_eqn "malformed function equation" eqn
+ end;
+
+fun build_corec_arg_disc (ctr_specs : corec_ctr_spec list)
+ ({fun_args, ctr_no, prems, ...} : coeqn_data_disc) =
+ if is_none (#pred (nth ctr_specs ctr_no)) then I else
+ s_conjs prems
+ |> curry subst_bounds (List.rev fun_args)
+ |> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
+ |> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
+
+fun build_corec_arg_no_call (sel_eqns : coeqn_data_sel list) sel =
+ find_first (curry (op =) sel o #sel) sel_eqns
+ |> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
+ |> the_default undef_const
+ |> K;
+
+fun build_corec_args_mutual_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
+ (case find_first (curry (op =) sel o #sel) sel_eqns of
+ NONE => (I, I, I)
+ | SOME {fun_args, rhs_term, ... } =>
+ let
+ val bound_Ts = List.rev (map fastype_of fun_args);
+ fun rewrite_stop _ t = if has_call t then @{term False} else @{term True};
+ fun rewrite_end _ t = if has_call t then undef_const else t;
+ fun rewrite_cont bound_Ts t =
+ if has_call t then mk_tuple1 bound_Ts (snd (strip_comb t)) else undef_const;
+ fun massage f _ = massage_mutual_corec_call lthy has_call f bound_Ts rhs_term
+ |> abs_tuple fun_args;
+ in
+ (massage rewrite_stop, massage rewrite_end, massage rewrite_cont)
+ end);
+
+fun build_corec_arg_nested_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
+ (case find_first (curry (op =) sel o #sel) sel_eqns of
+ NONE => I
+ | SOME {fun_args, rhs_term, ...} =>
+ let
+ val bound_Ts = List.rev (map fastype_of fun_args);
+ fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b)
+ | rewrite bound_Ts U T (t as _ $ _) =
+ let val (u, vs) = strip_comb t in
+ if is_Free u andalso has_call u then
+ Inr_const U T $ mk_tuple1 bound_Ts vs
+ else if try (fst o dest_Const) u = SOME @{const_name prod_case} then
+ map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb
+ else
+ list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs)
+ end
+ | rewrite _ U T t =
+ if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t;
+ fun massage t =
+ rhs_term
+ |> massage_nested_corec_call lthy has_call rewrite bound_Ts (range_type (fastype_of t))
+ |> abs_tuple fun_args;
+ in
+ massage
+ end);
+
+fun build_corec_args_sel lthy has_call (all_sel_eqns : coeqn_data_sel list)
+ (ctr_spec : corec_ctr_spec) =
+ (case filter (curry (op =) (#ctr ctr_spec) o #ctr) all_sel_eqns of
+ [] => I
+ | sel_eqns =>
+ let
+ val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
+ val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
+ val mutual_calls' = map_filter (try (apsnd (fn Mutual_Corec n => n))) sel_call_list;
+ val nested_calls' = map_filter (try (apsnd (fn Nested_Corec n => n))) sel_call_list;
+ in
+ I
+ #> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls'
+ #> fold (fn (sel, (q, g, h)) =>
+ let val (fq, fg, fh) = build_corec_args_mutual_call lthy has_call sel_eqns sel in
+ nth_map q fq o nth_map g fg o nth_map h fh end) mutual_calls'
+ #> fold (fn (sel, n) => nth_map n
+ (build_corec_arg_nested_call lthy has_call sel_eqns sel)) nested_calls'
+ end);
+
+fun build_codefs lthy bs mxs has_call arg_Tss (corec_specs : corec_spec list)
+ (disc_eqnss : coeqn_data_disc list list) (sel_eqnss : coeqn_data_sel list list) =
+ let
+ val corecs = map #corec corec_specs;
+ val ctr_specss = map #ctr_specs corec_specs;
+ val corec_args = hd corecs
+ |> fst o split_last o binder_types o fastype_of
+ |> map (fn T => if range_type T = @{typ bool}
+ then Abs (Name.uu_, domain_type T, @{term False})
+ else Const (@{const_name undefined}, T))
+ |> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
+ |> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
+ fun currys [] t = t
+ | currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0))
+ |> fold_rev (Term.abs o pair Name.uu) Ts;
+
+(*
+val _ = tracing ("corecursor arguments:\n \<cdot> " ^
+ space_implode "\n \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
+*)
+
+ val excludess' =
+ disc_eqnss
+ |> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x))
+ #> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
+ #> maps (uncurry (map o pair)
+ #> map (fn ((fun_args, c, x, a), (_, c', y, a')) =>
+ ((c, c', a orelse a'), (x, s_not (s_conjs y)))
+ ||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
+ ||> Logic.list_implies
+ ||> curry Logic.list_all (map dest_Free fun_args))))
+ in
+ map (list_comb o rpair corec_args) corecs
+ |> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
+ |> map2 currys arg_Tss
+ |> Syntax.check_terms lthy
+ |> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t)))
+ bs mxs
+ |> rpair excludess'
+ end;
+
+fun mk_actual_disc_eqns fun_binding arg_Ts exhaustive ({ctr_specs, ...} : corec_spec)
+ (sel_eqns : coeqn_data_sel list) (disc_eqns : coeqn_data_disc list) =
+ let val num_disc_eqns = length disc_eqns in
+ if (exhaustive andalso num_disc_eqns <> 0) orelse num_disc_eqns <> length ctr_specs - 1 then
+ disc_eqns
+ else
+ let
+ val n = 0 upto length ctr_specs
+ |> the o find_first (fn idx => not (exists (curry (op =) idx o #ctr_no) disc_eqns));
+ val {ctr, disc, ...} = nth ctr_specs n;
+ val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
+ |> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
+ val sel_eqn_opt = find_first (equal ctr o #ctr) sel_eqns;
+ val extra_disc_eqn = {
+ fun_name = Binding.name_of fun_binding,
+ fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
+ fun_args = fun_args,
+ ctr = ctr,
+ ctr_no = n,
+ disc = disc,
+ prems = maps (s_not_conj o #prems) disc_eqns,
+ auto_gen = true,
+ ctr_rhs_opt = Option.map #ctr_rhs_opt sel_eqn_opt |> the_default NONE,
+ code_rhs_opt = Option.map #ctr_rhs_opt sel_eqn_opt |> the_default NONE,
+ eqn_pos = Option.map (curry (op +) 1 o #eqn_pos) sel_eqn_opt |> the_default 100000 (* FIXME *),
+ user_eqn = undef_const};
+ in
+ chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
+ end
+ end;
+
+fun find_corec_calls ctxt has_call basic_ctr_specs ({ctr, sel, rhs_term, ...} : coeqn_data_sel) =
+ let
+ val sel_no = find_first (curry (op =) ctr o #ctr) basic_ctr_specs
+ |> find_index (curry (op =) sel) o #sels o the;
+ fun find t = if has_call t then snd (fold_rev_let_if_case ctxt (K cons) [] t []) else [];
+ in
+ find rhs_term
+ |> K |> nth_map sel_no |> AList.map_entry (op =) ctr
+ end;
+
+fun applied_fun_of fun_name fun_T fun_args =
+ list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0));
+
+fun is_trivial_implies thm =
+ uncurry (member (op aconv)) (Logic.strip_horn (Thm.prop_of thm));
+
+fun add_primcorec_ursive auto opts fixes specs of_specs_opt lthy =
+ let
+ val thy = Proof_Context.theory_of lthy;
+
+ val (bs, mxs) = map_split (apfst fst) fixes;
+ val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
+
+ val _ = (case filter_out (fn (_, T) => Sign.of_sort thy (T, HOLogic.typeS)) (bs ~~ arg_Ts) of
+ [] => ()
+ | (b, _) :: _ => primcorec_error ("type of " ^ Binding.print b ^ " contains top sort"));
+
+ val actual_nn = length bs;
+
+ val sequentials = replicate actual_nn (member (op =) opts Sequential_Option);
+ val exhaustives = replicate actual_nn (member (op =) opts Exhaustive_Option);
+
+ val fun_names = map Binding.name_of bs;
+ val basic_ctr_specss = map (basic_corec_specs_of lthy) res_Ts;
+ val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
+ val eqns_data =
+ fold_map2 (dissect_coeqn lthy has_call fun_names sequentials basic_ctr_specss) (tag_list 0 (map snd specs))
+ of_specs_opt []
+ |> flat o fst;
+
+ val callssss =
+ map_filter (try (fn Sel x => x)) eqns_data
+ |> partition_eq (op = o pairself #fun_name)
+ |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
+ |> map (flat o snd)
+ |> map2 (fold o find_corec_calls lthy has_call) basic_ctr_specss
+ |> map2 (curry (op |>)) (map (map (fn {ctr, sels, ...} =>
+ (ctr, map (K []) sels))) basic_ctr_specss);
+
+(*
+val _ = tracing ("callssss = " ^ @{make_string} callssss);
+*)
+
+ val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms,
+ strong_coinduct_thms), lthy') =
+ corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
+ val corec_specs = take actual_nn corec_specs';
+ val ctr_specss = map #ctr_specs corec_specs;
+
+ val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data
+ |> partition_eq (op = o pairself #fun_name)
+ |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
+ |> map (sort (op < o pairself #ctr_no |> make_ord) o flat o snd);
+ val _ = disc_eqnss' |> map (fn x =>
+ let val d = duplicates (op = o pairself #ctr_no) x in null d orelse
+ primcorec_error_eqns "excess discriminator formula in definition"
+ (maps (fn t => filter (curry (op =) (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
+
+ val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
+ |> partition_eq (op = o pairself #fun_name)
+ |> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
+ |> map (flat o snd);
+
+ val arg_Tss = map (binder_types o snd o fst) fixes;
+ val disc_eqnss = map6 mk_actual_disc_eqns bs arg_Tss exhaustives corec_specs sel_eqnss
+ disc_eqnss';
+ val (defs, excludess') =
+ build_codefs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
+
+ val tac_opts =
+ map (fn {code_rhs_opt, ...} :: _ =>
+ if auto orelse is_some code_rhs_opt then SOME (auto_tac o #context) else NONE) disc_eqnss;
+
+ fun exclude_tac tac_opt sequential (c, c', a) =
+ if a orelse c = c' orelse sequential then
+ SOME (K (HEADGOAL (mk_primcorec_assumption_tac lthy [])))
+ else
+ tac_opt;
+
+(*
+val _ = tracing ("exclusiveness properties:\n \<cdot> " ^
+ space_implode "\n \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) excludess'));
+*)
+
+ val excludess'' = map3 (fn tac_opt => fn sequential => map (fn (idx, goal) =>
+ (idx, (Option.map (Goal.prove_sorry lthy [] [] goal #> Thm.close_derivation)
+ (exclude_tac tac_opt sequential idx), goal))))
+ tac_opts sequentials excludess';
+ val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) excludess'';
+ val (goal_idxss, exclude_goalss) = excludess''
+ |> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
+ |> split_list o map split_list;
+
+ fun list_all_fun_args extras =
+ map2 (fn [] => I
+ | {fun_args, ...} :: _ => map (curry Logic.list_all (extras @ map dest_Free fun_args)))
+ disc_eqnss;
+
+ val syntactic_exhaustives =
+ map (fn disc_eqns => forall (null o #prems orf is_some o #code_rhs_opt) disc_eqns
+ orelse exists #auto_gen disc_eqns)
+ disc_eqnss;
+ val de_facto_exhaustives =
+ map2 (fn b => fn b' => b orelse b') exhaustives syntactic_exhaustives;
+
+ val nchotomy_goalss =
+ map2 (fn false => K [] | true => single o HOLogic.mk_Trueprop o mk_dnf o map #prems)
+ de_facto_exhaustives disc_eqnss
+ |> list_all_fun_args []
+ val nchotomy_taut_thmss =
+ map6 (fn tac_opt => fn {disc_exhausts = res_disc_exhausts, ...} => fn arg_Ts =>
+ fn {code_rhs_opt, ...} :: _ => fn [] => K []
+ | [goal] => fn true =>
+ let
+ val (_, _, arg_disc_exhausts, _, _) =
+ case_thms_of_term lthy arg_Ts (the_default Term.dummy code_rhs_opt);
+ in
+ [Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
+ mk_primcorec_nchotomy_tac ctxt (res_disc_exhausts @ arg_disc_exhausts))
+ |> Thm.close_derivation]
+ end
+ | false =>
+ (case tac_opt of
+ SOME tac => [Goal.prove_sorry lthy [] [] goal tac |> Thm.close_derivation]
+ | NONE => []))
+ tac_opts corec_specs arg_Tss disc_eqnss nchotomy_goalss syntactic_exhaustives;
+
+ val syntactic_exhaustives =
+ map (fn disc_eqns => forall (null o #prems orf is_some o #code_rhs_opt) disc_eqns
+ orelse exists #auto_gen disc_eqns)
+ disc_eqnss;
+
+ val nchotomy_goalss =
+ map2 (fn (NONE, false) => map (rpair []) | _ => K []) (tac_opts ~~ syntactic_exhaustives)
+ nchotomy_goalss;
+
+ val goalss = nchotomy_goalss @ exclude_goalss;
+
+ fun prove thmss'' def_thms' lthy =
+ let
+ val def_thms = map (snd o snd) def_thms';
+
+ val (nchotomy_thmss, exclude_thmss) =
+ (map2 append (take actual_nn thmss'') nchotomy_taut_thmss, drop actual_nn thmss'');
+
+ val ps =
+ Variable.variant_frees lthy (maps (maps #fun_args) disc_eqnss) [("P", HOLogic.boolT)];
+
+ val exhaust_thmss =
+ map2 (fn false => K []
+ | true => fn disc_eqns as {fun_args, ...} :: _ =>
+ let
+ val p = Bound (length fun_args);
+ fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
+ in
+ [mk_imp_p (map (mk_imp_p o map HOLogic.mk_Trueprop o #prems) disc_eqns)]
+ end)
+ de_facto_exhaustives disc_eqnss
+ |> list_all_fun_args ps
+ |> map3 (fn disc_eqns as {fun_args, ...} :: _ => fn [] => K []
+ | [nchotomy_thm] => fn [goal] =>
+ [mk_primcorec_exhaust_tac lthy ("" (* for "P" *) :: map (fst o dest_Free) fun_args)
+ (length disc_eqns) nchotomy_thm
+ |> K |> Goal.prove_sorry lthy [] [] goal
+ |> Thm.close_derivation])
+ disc_eqnss nchotomy_thmss;
+ val nontriv_exhaust_thmss = map (filter_out is_trivial_implies) exhaust_thmss;
+
+ val excludess' = map (op ~~) (goal_idxss ~~ exclude_thmss);
+ fun mk_excludesss excludes n =
+ fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm])))
+ excludes (map (fn k => replicate k [asm_rl] @ replicate (n - k) []) (0 upto n - 1));
+ val excludessss =
+ map2 (fn excludes => mk_excludesss excludes o length o #ctr_specs)
+ (map2 append excludess' taut_thmss) corec_specs;
+
+ fun prove_disc ({ctr_specs, ...} : corec_spec) excludesss
+ ({fun_name, fun_T, fun_args, ctr_no, prems, eqn_pos, ...} : coeqn_data_disc) =
+ if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then
+ []
+ else
+ let
+ val {disc, disc_corec, ...} = nth ctr_specs ctr_no;
+ val k = 1 + ctr_no;
+ val m = length prems;
+ val goal =
+ applied_fun_of fun_name fun_T fun_args
+ |> curry betapply disc
+ |> HOLogic.mk_Trueprop
+ |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
+ |> curry Logic.list_all (map dest_Free fun_args);
+ in
+ if prems = [@{term False}] then
+ []
+ else
+ mk_primcorec_disc_tac lthy def_thms disc_corec k m excludesss
+ |> K |> Goal.prove_sorry lthy [] [] goal
+ |> Thm.close_derivation
+ |> pair (#disc (nth ctr_specs ctr_no))
+ |> pair eqn_pos
+ |> single
+ end;
+
+ fun prove_sel ({nested_maps, nested_map_idents, nested_map_comps, ctr_specs, ...}
+ : corec_spec) (disc_eqns : coeqn_data_disc list) excludesss
+ ({fun_name, fun_T, fun_args, ctr, sel, rhs_term, eqn_pos, ...} : coeqn_data_sel) =
+ let
+ val SOME ctr_spec = find_first (curry (op =) ctr o #ctr) ctr_specs;
+ val ctr_no = find_index (curry (op =) ctr o #ctr) ctr_specs;
+ val prems = the_default (maps (s_not_conj o #prems) disc_eqns)
+ (find_first (curry (op =) ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
+ val sel_corec = find_index (curry (op =) sel) (#sels ctr_spec)
+ |> nth (#sel_corecs ctr_spec);
+ val k = 1 + ctr_no;
+ val m = length prems;
+ val goal =
+ applied_fun_of fun_name fun_T fun_args
+ |> curry betapply sel
+ |> rpair (abstract (List.rev fun_args) rhs_term)
+ |> HOLogic.mk_Trueprop o HOLogic.mk_eq
+ |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
+ |> curry Logic.list_all (map dest_Free fun_args);
+ val (distincts, _, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term;
+ in
+ mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps
+ nested_map_idents nested_map_comps sel_corec k m excludesss
+ |> K |> Goal.prove_sorry lthy [] [] goal
+ |> Thm.close_derivation
+ |> pair sel
+ |> pair eqn_pos
+ end;
+
+ fun prove_ctr disc_alist sel_alist (disc_eqns : coeqn_data_disc list)
+ (sel_eqns : coeqn_data_sel list) ({ctr, disc, sels, collapse, ...} : corec_ctr_spec) =
+ (* don't try to prove theorems when some sel_eqns are missing *)
+ if not (exists (curry (op =) ctr o #ctr) disc_eqns)
+ andalso not (exists (curry (op =) ctr o #ctr) sel_eqns)
+ orelse
+ filter (curry (op =) ctr o #ctr) sel_eqns
+ |> fst o finds (op = o apsnd #sel) sels
+ |> exists (null o snd) then
+ []
+ else
+ let
+ val (fun_name, fun_T, fun_args, prems, rhs_opt, eqn_pos) =
+ (find_first (curry (op =) ctr o #ctr) disc_eqns,
+ find_first (curry (op =) ctr o #ctr) sel_eqns)
+ |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x,
+ #ctr_rhs_opt x, #eqn_pos x))
+ ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, [], #ctr_rhs_opt x,
+ #eqn_pos x))
+ |> the o merge_options;
+ val m = length prems;
+ val goal =
+ (case rhs_opt of
+ SOME rhs => rhs
+ | NONE =>
+ filter (curry (op =) ctr o #ctr) sel_eqns
+ |> fst o finds (op = o apsnd #sel) sels
+ |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
+ |> curry list_comb ctr)
+ |> curry mk_Trueprop_eq (applied_fun_of fun_name fun_T fun_args)
+ |> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
+ |> curry Logic.list_all (map dest_Free fun_args);
+ val disc_thm_opt = AList.lookup (op =) disc_alist disc;
+ val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist);
+ in
+ if prems = [@{term False}] then [] else
+ mk_primcorec_ctr_tac lthy m collapse disc_thm_opt sel_thms
+ |> K |> Goal.prove_sorry lthy [] [] goal
+ |> Thm.close_derivation
+ |> pair ctr
+ |> pair eqn_pos
+ |> single
+ end;
+
+ fun prove_code exhaustive disc_eqns sel_eqns nchotomys ctr_alist ctr_specs =
+ let
+ val fun_data_opt =
+ (find_first (member (op =) (map #ctr ctr_specs) o #ctr) disc_eqns,
+ find_first (member (op =) (map #ctr ctr_specs) o #ctr) sel_eqns)
+ |>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #code_rhs_opt x))
+ ||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #code_rhs_opt x))
+ |> merge_options;
+ in
+ (case fun_data_opt of
+ NONE => []
+ | SOME (fun_name, fun_T, fun_args, rhs_opt) =>
+ let
+ val bound_Ts = List.rev (map fastype_of fun_args);
+
+ val lhs = applied_fun_of fun_name fun_T fun_args;
+ val rhs_info_opt =
+ (case rhs_opt of
+ SOME rhs =>
+ let
+ val raw_rhs = expand_corec_code_rhs lthy has_call bound_Ts rhs;
+ val cond_ctrs =
+ fold_rev_corec_code_rhs lthy (K oo (cons oo pair)) bound_Ts raw_rhs [];
+ val ctr_thms =
+ map (the_default FalseE o AList.lookup (op =) ctr_alist o snd) cond_ctrs;
+ in SOME (false, rhs, raw_rhs, ctr_thms) end
+ | NONE =>
+ let
+ fun prove_code_ctr {ctr, sels, ...} =
+ if not (exists (curry (op =) ctr o fst) ctr_alist) then NONE else
+ let
+ val prems = find_first (curry (op =) ctr o #ctr) disc_eqns
+ |> Option.map #prems |> the_default [];
+ val t =
+ filter (curry (op =) ctr o #ctr) sel_eqns
+ |> fst o finds (op = o apsnd #sel) sels
+ |> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x))
+ #-> abstract)
+ |> curry list_comb ctr;
+ in
+ SOME (prems, t)
+ end;
+ val ctr_conds_argss_opt = map prove_code_ctr ctr_specs;
+ val exhaustive_code =
+ exhaustive
+ orelse exists (is_some andf (null o fst o the)) ctr_conds_argss_opt
+ orelse forall is_some ctr_conds_argss_opt
+ andalso exists #auto_gen disc_eqns;
+ val rhs =
+ (if exhaustive_code then
+ split_last (map_filter I ctr_conds_argss_opt) ||> snd
+ else
+ Const (@{const_name Code.abort}, @{typ String.literal} -->
+ (@{typ unit} --> body_type fun_T) --> body_type fun_T) $
+ HOLogic.mk_literal fun_name $
+ absdummy @{typ unit} (incr_boundvars 1 lhs)
+ |> pair (map_filter I ctr_conds_argss_opt))
+ |-> fold_rev (fn (prems, u) => mk_If (s_conjs prems) u)
+ in
+ SOME (exhaustive_code, rhs, rhs, map snd ctr_alist)
+ end);
+ in
+ (case rhs_info_opt of
+ NONE => []
+ | SOME (exhaustive_code, rhs, raw_rhs, ctr_thms) =>
+ let
+ val ms = map (Logic.count_prems o prop_of) ctr_thms;
+ val (raw_goal, goal) = (raw_rhs, rhs)
+ |> pairself (curry mk_Trueprop_eq (applied_fun_of fun_name fun_T fun_args)
+ #> curry Logic.list_all (map dest_Free fun_args));
+ val (distincts, discIs, _, sel_splits, sel_split_asms) =
+ case_thms_of_term lthy bound_Ts raw_rhs;
+
+ val raw_code_thm = mk_primcorec_raw_code_tac lthy distincts discIs sel_splits
+ sel_split_asms ms ctr_thms
+ (if exhaustive_code then try the_single nchotomys else NONE)
+ |> K |> Goal.prove_sorry lthy [] [] raw_goal
+ |> Thm.close_derivation;
+ in
+ mk_primcorec_code_tac lthy distincts sel_splits raw_code_thm
+ |> K |> Goal.prove_sorry lthy [] [] goal
+ |> Thm.close_derivation
+ |> single
+ end)
+ end)
+ end;
+
+ val disc_alistss = map3 (map oo prove_disc) corec_specs excludessss disc_eqnss;
+ val disc_alists = map (map snd o flat) disc_alistss;
+ val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss excludessss sel_eqnss;
+ val disc_thmss = map (map snd o order_list_duplicates o flat) disc_alistss;
+ val disc_thmsss' = map (map (map (snd o snd))) disc_alistss;
+ val sel_thmss = map (map snd o order_list_duplicates) sel_alists;
+
+ fun prove_disc_iff ({ctr_specs, ...} : corec_spec) exhaust_thms disc_thmss'
+ (({fun_args = exhaust_fun_args, ...} : coeqn_data_disc) :: _) disc_thms
+ ({fun_name, fun_T, fun_args, ctr_no, prems, eqn_pos, ...} : coeqn_data_disc) =
+ if null exhaust_thms orelse null (tl ctr_specs) then
+ []
+ else
+ let
+ val {disc, disc_excludess, ...} = nth ctr_specs ctr_no;
+ val goal =
+ mk_Trueprop_eq (applied_fun_of fun_name fun_T fun_args |> curry betapply disc,
+ mk_conjs prems)
+ |> curry Logic.list_all (map dest_Free fun_args);
+ in
+ mk_primcorec_disc_iff_tac lthy (map (fst o dest_Free) exhaust_fun_args)
+ (the_single exhaust_thms) disc_thms disc_thmss' (flat disc_excludess)
+ |> K |> Goal.prove_sorry lthy [] [] goal
+ |> Thm.close_derivation
+ |> fold (fn rule => perhaps (try (fn thm => thm RS rule)))
+ @{thms eqTrueE eq_False[THEN iffD1] notnotD}
+ |> pair eqn_pos
+ |> single
+ end;
+
+ val disc_iff_thmss = map6 (flat ooo map2 oooo prove_disc_iff) corec_specs exhaust_thmss
+ disc_thmsss' disc_eqnss disc_thmsss' disc_eqnss
+ |> map order_list_duplicates;
+
+ val ctr_alists = map5 (maps oooo prove_ctr) disc_alists (map (map snd) sel_alists) disc_eqnss
+ sel_eqnss ctr_specss;
+ val ctr_thmss' = map (map snd) ctr_alists;
+ val ctr_thmss = map (map snd o order_list) ctr_alists;
+
+ val code_thmss = map6 prove_code exhaustives disc_eqnss sel_eqnss nchotomy_thmss ctr_thmss'
+ ctr_specss;
+
+ val disc_iff_or_disc_thmss =
+ map2 (fn [] => I | disc_iffs => K disc_iffs) disc_iff_thmss disc_thmss;
+ val simp_thmss = map2 append disc_iff_or_disc_thmss sel_thmss;
+
+ val common_name = mk_common_name fun_names;
+
+ val notes =
+ [(coinductN, map (if n2m then single else K []) coinduct_thms, []),
+ (codeN, code_thmss, code_nitpicksimp_attrs),
+ (ctrN, ctr_thmss, []),
+ (discN, disc_thmss, simp_attrs),
+ (disc_iffN, disc_iff_thmss, []),
+ (excludeN, exclude_thmss, []),
+ (exhaustN, nontriv_exhaust_thmss, []),
+ (selN, sel_thmss, simp_attrs),
+ (simpsN, simp_thmss, []),
+ (strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])]
+ |> maps (fn (thmN, thmss, attrs) =>
+ map2 (fn fun_name => fn thms =>
+ ((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]))
+ fun_names (take actual_nn thmss))
+ |> filter_out (null o fst o hd o snd);
+
+ val common_notes =
+ [(coinductN, if n2m then [coinduct_thm] else [], []),
+ (strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])]
+ |> filter_out (null o #2)
+ |> map (fn (thmN, thms, attrs) =>
+ ((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
+ in
+ lthy |> Local_Theory.notes (notes @ common_notes) |> snd
+ end;
+
+ fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss';
+ in
+ (goalss, after_qed, lthy')
+ end;
+
+fun add_primcorec_ursive_cmd auto opts (raw_fixes, raw_specs') lthy =
+ let
+ val (raw_specs, of_specs_opt) =
+ split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy));
+ val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy;
+ in
+ add_primcorec_ursive auto opts fixes specs of_specs_opt lthy
+ handle ERROR str => primcorec_error str
+ end
+ handle Primcorec_Error (str, eqns) =>
+ if null eqns
+ then error ("primcorec error:\n " ^ str)
+ else error ("primcorec error:\n " ^ str ^ "\nin\n " ^
+ space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns));
+
+val add_primcorecursive_cmd = (fn (goalss, after_qed, lthy) =>
+ lthy
+ |> Proof.theorem NONE after_qed goalss
+ |> Proof.refine (Method.primitive_text (K I))
+ |> Seq.hd) ooo add_primcorec_ursive_cmd false;
+
+val add_primcorec_cmd = (fn (goalss, after_qed, lthy) =>
+ lthy
+ |> after_qed (map (fn [] => []
+ | _ => error "\"auto\" failed -- use \"primcorecursive\" instead of \"primcorec\"")
+ goalss)) ooo add_primcorec_ursive_cmd true;
+
+end;