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(* Title: HOL/BNF/Tools/bnf_gfp_rec_sugar.ML
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Author: Lorenz Panny, TU Muenchen
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Author: Jasmin Blanchette, TU Muenchen
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Copyright 2013
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Corecursor sugar.
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*)
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signature BNF_GFP_REC_SUGAR =
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sig
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val add_primcorecursive_cmd: bool ->
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(binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
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Proof.context -> Proof.state
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val add_primcorec_cmd: bool ->
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(binding * string option * mixfix) list * ((Attrib.binding * string) * string option) list ->
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local_theory -> local_theory
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end;
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structure BNF_GFP_Rec_Sugar : BNF_GFP_REC_SUGAR =
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struct
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open Ctr_Sugar
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open BNF_Util
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open BNF_Def
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open BNF_FP_Util
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open BNF_FP_Def_Sugar
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open BNF_FP_N2M_Sugar
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open BNF_FP_Rec_Sugar_Util
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open BNF_GFP_Rec_Sugar_Tactics
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val codeN = "code"
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val ctrN = "ctr"
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val discN = "disc"
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val selN = "sel"
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val nitpicksimp_attrs = @{attributes [nitpick_simp]};
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val simp_attrs = @{attributes [simp]};
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val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
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exception Primcorec_Error of string * term list;
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fun primcorec_error str = raise Primcorec_Error (str, []);
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fun primcorec_error_eqn str eqn = raise Primcorec_Error (str, [eqn]);
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fun primcorec_error_eqns str eqns = raise Primcorec_Error (str, eqns);
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datatype corec_call =
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Dummy_No_Corec of int |
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No_Corec of int |
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Mutual_Corec of int * int * int |
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Nested_Corec of int;
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type basic_corec_ctr_spec =
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{ctr: term,
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disc: term,
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sels: term list};
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type corec_ctr_spec =
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{ctr: term,
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disc: term,
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sels: term list,
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pred: int option,
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calls: corec_call list,
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discI: thm,
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sel_thms: thm list,
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collapse: thm,
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corec_thm: thm,
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disc_corec: thm,
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sel_corecs: thm list};
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type corec_spec =
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{corec: term,
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nested_maps: thm list,
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nested_map_idents: thm list,
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nested_map_comps: thm list,
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ctr_specs: corec_ctr_spec list};
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exception AINT_NO_MAP of term;
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fun not_codatatype ctxt T =
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error ("Not a codatatype: " ^ Syntax.string_of_typ ctxt T);
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fun ill_formed_corec_call ctxt t =
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error ("Ill-formed corecursive call: " ^ quote (Syntax.string_of_term ctxt t));
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fun invalid_map ctxt t =
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error ("Invalid map function in " ^ quote (Syntax.string_of_term ctxt t));
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fun unexpected_corec_call ctxt t =
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error ("Unexpected corecursive call: " ^ quote (Syntax.string_of_term ctxt t));
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val mk_conjs = try (foldr1 HOLogic.mk_conj) #> the_default @{const True};
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val mk_disjs = try (foldr1 HOLogic.mk_disj) #> the_default @{const False};
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val conjuncts_s = filter_out (curry (op =) @{const True}) o HOLogic.conjuncts;
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fun s_not @{const True} = @{const False}
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| s_not @{const False} = @{const True}
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| s_not (@{const Not} $ t) = t
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| s_not (@{const conj} $ t $ u) = @{const disj} $ s_not t $ s_not u
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| s_not (@{const disj} $ t $ u) = @{const conj} $ s_not t $ s_not u
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| s_not t = @{const Not} $ t;
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val s_not_conj = conjuncts_s o s_not o mk_conjs;
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fun propagate_unit_pos u cs = if member (op aconv) cs u then [@{const False}] else cs;
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fun propagate_unit_neg not_u cs = remove (op aconv) not_u cs;
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fun propagate_units css =
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(case List.partition (can the_single) css of
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([], _) => css
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| ([u] :: uss, css') =>
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[u] :: propagate_units (map (propagate_unit_neg (s_not u))
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(map (propagate_unit_pos u) (uss @ css'))));
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fun s_conjs cs =
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if member (op aconv) cs @{const False} then @{const False}
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else mk_conjs (remove (op aconv) @{const True} cs);
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fun s_disjs ds =
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if member (op aconv) ds @{const True} then @{const True}
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else mk_disjs (remove (op aconv) @{const False} ds);
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fun s_dnf css0 =
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let val css = propagate_units css0 in
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if null css then
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[@{const False}]
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else if exists null css then
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[]
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else
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map (fn c :: cs => (c, cs)) css
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|> AList.coalesce (op =)
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|> map (fn (c, css) => c :: s_dnf css)
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|> (fn [cs] => cs | css => [s_disjs (map s_conjs css)])
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end;
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fun fold_rev_let_if_case ctxt f bound_Ts t =
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let
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val thy = Proof_Context.theory_of ctxt;
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fun fld conds t =
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(case Term.strip_comb t of
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(Const (@{const_name Let}, _), [_, _]) => fld conds (unfold_let t)
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| (Const (@{const_name If}, _), [cond, then_branch, else_branch]) =>
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fld (conds @ conjuncts_s cond) then_branch o fld (conds @ s_not_conj [cond]) else_branch
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| (Const (c, _), args as _ :: _ :: _) =>
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let val n = num_binder_types (Sign.the_const_type thy c) - 1 in
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if n >= 0 andalso n < length args then
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(case fastype_of1 (bound_Ts, nth args n) of
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Type (s, Ts) =>
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(case dest_case ctxt s Ts t of
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NONE => apsnd (f conds t)
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| SOME (conds', branches) =>
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apfst (cons s) o fold_rev (uncurry fld)
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(map (append conds o conjuncts_s) conds' ~~ branches))
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| _ => apsnd (f conds t))
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else
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apsnd (f conds t)
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end
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| _ => apsnd (f conds t))
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in
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fld [] t o pair []
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end;
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fun case_of ctxt = ctr_sugar_of ctxt #> Option.map (fst o dest_Const o #casex);
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fun massage_let_if_case ctxt has_call massage_leaf =
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let
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val thy = Proof_Context.theory_of ctxt;
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fun check_no_call t = if has_call t then unexpected_corec_call ctxt t else ();
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fun massage_abs bound_Ts 0 t = massage_rec bound_Ts t
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| massage_abs bound_Ts m (Abs (s, T, t)) = Abs (s, T, massage_abs (T :: bound_Ts) (m - 1) t)
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| massage_abs bound_Ts m t =
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let val T = domain_type (fastype_of1 (bound_Ts, t)) in
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Abs (Name.uu, T, massage_abs (T :: bound_Ts) (m - 1) (incr_boundvars 1 t $ Bound 0))
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end
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and massage_rec bound_Ts t =
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let val typof = curry fastype_of1 bound_Ts in
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(case Term.strip_comb t of
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(Const (@{const_name Let}, _), [_, _]) => massage_rec bound_Ts (unfold_let t)
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| (Const (@{const_name If}, _), obj :: (branches as [_, _])) =>
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let val branches' = map (massage_rec bound_Ts) branches in
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Term.list_comb (If_const (typof (hd branches')) $ tap check_no_call obj, branches')
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end
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| (Const (c, _), args as _ :: _ :: _) =>
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(case try strip_fun_type (Sign.the_const_type thy c) of
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SOME (gen_branch_Ts, gen_body_fun_T) =>
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let
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val gen_branch_ms = map num_binder_types gen_branch_Ts;
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val n = length gen_branch_ms;
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in
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if n < length args then
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(case gen_body_fun_T of
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Type (_, [Type (T_name, _), _]) =>
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if case_of ctxt T_name = SOME c then
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let
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val (branches, obj_leftovers) = chop n args;
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val branches' = map2 (massage_abs bound_Ts) gen_branch_ms branches;
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val branch_Ts' = map typof branches';
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val body_T' = snd (strip_typeN (hd gen_branch_ms) (hd branch_Ts'));
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val casex' = Const (c, branch_Ts' ---> map typof obj_leftovers ---> body_T');
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in
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Term.list_comb (casex', branches' @ tap (List.app check_no_call) obj_leftovers)
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end
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else
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massage_leaf bound_Ts t
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| _ => massage_leaf bound_Ts t)
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else
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massage_leaf bound_Ts t
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end
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| NONE => massage_leaf bound_Ts t)
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| _ => massage_leaf bound_Ts t)
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end
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in
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massage_rec
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end;
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val massage_mutual_corec_call = massage_let_if_case;
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fun curried_type (Type (@{type_name fun}, [Type (@{type_name prod}, Ts), T])) = Ts ---> T;
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fun massage_nested_corec_call ctxt has_call raw_massage_call bound_Ts U t =
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let
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fun check_no_call t = if has_call t then unexpected_corec_call ctxt t else ();
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val build_map_Inl = build_map ctxt (uncurry Inl_const o dest_sumT o snd);
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fun massage_mutual_call bound_Ts U T t =
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if has_call t then
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(case try dest_sumT U of
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SOME (U1, U2) => if U1 = T then raw_massage_call bound_Ts T U2 t else invalid_map ctxt t
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| NONE => invalid_map ctxt t)
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else
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build_map_Inl (T, U) $ t;
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fun massage_mutual_fun bound_Ts U T t =
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(case t of
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Const (@{const_name comp}, _) $ t1 $ t2 =>
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mk_comp bound_Ts (massage_mutual_fun bound_Ts U T t1, tap check_no_call t2)
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| _ =>
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let
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val var = Var ((Name.uu, Term.maxidx_of_term t + 1),
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domain_type (fastype_of1 (bound_Ts, t)));
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in
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Term.lambda var (massage_mutual_call bound_Ts U T (t $ var))
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end);
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fun massage_map bound_Ts (Type (_, Us)) (Type (s, Ts)) t =
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(case try (dest_map ctxt s) t of
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SOME (map0, fs) =>
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let
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val Type (_, dom_Ts) = domain_type (fastype_of1 (bound_Ts, t));
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val map' = mk_map (length fs) dom_Ts Us map0;
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val fs' =
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map_flattened_map_args ctxt s (map3 (massage_map_or_map_arg bound_Ts) Us Ts) fs;
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in
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Term.list_comb (map', fs')
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end
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| NONE => raise AINT_NO_MAP t)
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| massage_map _ _ _ t = raise AINT_NO_MAP t
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and massage_map_or_map_arg bound_Ts U T t =
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if T = U then
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tap check_no_call t
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else
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massage_map bound_Ts U T t
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handle AINT_NO_MAP _ => massage_mutual_fun bound_Ts U T t;
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fun massage_call bound_Ts U T =
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blanchet@55698
|
268 |
massage_let_if_case ctxt has_call (fn bound_Ts => fn t =>
|
blanchet@55698
|
269 |
if has_call t then
|
blanchet@55698
|
270 |
(case U of
|
blanchet@55698
|
271 |
Type (s, Us) =>
|
blanchet@55698
|
272 |
(case try (dest_ctr ctxt s) t of
|
blanchet@55698
|
273 |
SOME (f, args) =>
|
blanchet@55698
|
274 |
let
|
blanchet@55698
|
275 |
val typof = curry fastype_of1 bound_Ts;
|
blanchet@55698
|
276 |
val f' = mk_ctr Us f
|
blanchet@55698
|
277 |
val f'_T = typof f';
|
blanchet@55698
|
278 |
val arg_Ts = map typof args;
|
blanchet@55698
|
279 |
in
|
blanchet@55698
|
280 |
Term.list_comb (f', map3 (massage_call bound_Ts) (binder_types f'_T) arg_Ts args)
|
blanchet@55698
|
281 |
end
|
blanchet@55698
|
282 |
| NONE =>
|
blanchet@55698
|
283 |
(case t of
|
blanchet@55698
|
284 |
Const (@{const_name prod_case}, _) $ t' =>
|
blanchet@55698
|
285 |
let
|
blanchet@55698
|
286 |
val U' = curried_type U;
|
blanchet@55698
|
287 |
val T' = curried_type T;
|
blanchet@55698
|
288 |
in
|
blanchet@55698
|
289 |
Const (@{const_name prod_case}, U' --> U) $ massage_call bound_Ts U' T' t'
|
blanchet@55698
|
290 |
end
|
blanchet@55698
|
291 |
| t1 $ t2 =>
|
blanchet@55698
|
292 |
(if has_call t2 then
|
blanchet@55698
|
293 |
massage_mutual_call bound_Ts U T t
|
blanchet@55698
|
294 |
else
|
blanchet@55698
|
295 |
massage_map bound_Ts U T t1 $ t2
|
blanchet@55698
|
296 |
handle AINT_NO_MAP _ => massage_mutual_call bound_Ts U T t)
|
blanchet@55698
|
297 |
| Abs (s, T', t') =>
|
blanchet@55698
|
298 |
Abs (s, T', massage_call (T' :: bound_Ts) (range_type U) (range_type T) t')
|
blanchet@55698
|
299 |
| _ => massage_mutual_call bound_Ts U T t))
|
blanchet@55698
|
300 |
| _ => ill_formed_corec_call ctxt t)
|
blanchet@55698
|
301 |
else
|
blanchet@55698
|
302 |
build_map_Inl (T, U) $ t) bound_Ts;
|
blanchet@55698
|
303 |
|
blanchet@55698
|
304 |
val T = fastype_of1 (bound_Ts, t);
|
blanchet@55698
|
305 |
in
|
blanchet@55698
|
306 |
if has_call t then massage_call bound_Ts U T t else build_map_Inl (T, U) $ t
|
blanchet@55698
|
307 |
end;
|
blanchet@55698
|
308 |
|
blanchet@55698
|
309 |
val fold_rev_corec_call = fold_rev_let_if_case;
|
blanchet@55698
|
310 |
|
blanchet@55698
|
311 |
fun expand_to_ctr_term ctxt s Ts t =
|
blanchet@55698
|
312 |
(case ctr_sugar_of ctxt s of
|
blanchet@55698
|
313 |
SOME {ctrs, casex, ...} =>
|
blanchet@55698
|
314 |
Term.list_comb (mk_case Ts (Type (s, Ts)) casex, map (mk_ctr Ts) ctrs) $ t
|
blanchet@55698
|
315 |
| NONE => raise Fail "expand_to_ctr_term");
|
blanchet@55698
|
316 |
|
blanchet@55698
|
317 |
fun expand_corec_code_rhs ctxt has_call bound_Ts t =
|
blanchet@55698
|
318 |
(case fastype_of1 (bound_Ts, t) of
|
blanchet@55698
|
319 |
Type (s, Ts) =>
|
blanchet@55698
|
320 |
massage_let_if_case ctxt has_call (fn _ => fn t =>
|
blanchet@55698
|
321 |
if can (dest_ctr ctxt s) t then t else expand_to_ctr_term ctxt s Ts t) bound_Ts t
|
blanchet@55698
|
322 |
| _ => raise Fail "expand_corec_code_rhs");
|
blanchet@55698
|
323 |
|
blanchet@55698
|
324 |
fun massage_corec_code_rhs ctxt massage_ctr =
|
blanchet@55698
|
325 |
massage_let_if_case ctxt (K false)
|
blanchet@55698
|
326 |
(fn bound_Ts => uncurry (massage_ctr bound_Ts) o Term.strip_comb);
|
blanchet@55698
|
327 |
|
blanchet@55698
|
328 |
fun fold_rev_corec_code_rhs ctxt f =
|
blanchet@55698
|
329 |
snd ooo fold_rev_let_if_case ctxt (fn conds => uncurry (f conds) o Term.strip_comb);
|
blanchet@55698
|
330 |
|
blanchet@55698
|
331 |
fun case_thms_of_term ctxt bound_Ts t =
|
blanchet@55698
|
332 |
let
|
blanchet@55698
|
333 |
val (caseT_names, _) = fold_rev_let_if_case ctxt (K (K I)) bound_Ts t ();
|
blanchet@55698
|
334 |
val ctr_sugars = map (the o ctr_sugar_of ctxt) caseT_names;
|
blanchet@55698
|
335 |
in
|
blanchet@55698
|
336 |
(maps #distincts ctr_sugars, maps #discIs ctr_sugars, maps #sel_splits ctr_sugars,
|
blanchet@55698
|
337 |
maps #sel_split_asms ctr_sugars)
|
blanchet@55698
|
338 |
end;
|
blanchet@55698
|
339 |
|
blanchet@55698
|
340 |
fun basic_corec_specs_of ctxt res_T =
|
blanchet@55698
|
341 |
(case res_T of
|
blanchet@55698
|
342 |
Type (T_name, _) =>
|
blanchet@55698
|
343 |
(case Ctr_Sugar.ctr_sugar_of ctxt T_name of
|
blanchet@55698
|
344 |
NONE => not_codatatype ctxt res_T
|
blanchet@55698
|
345 |
| SOME {ctrs, discs, selss, ...} =>
|
blanchet@55698
|
346 |
let
|
blanchet@55698
|
347 |
val thy = Proof_Context.theory_of ctxt;
|
blanchet@55698
|
348 |
val gfpT = body_type (fastype_of (hd ctrs));
|
blanchet@55698
|
349 |
val As_rho = tvar_subst thy [gfpT] [res_T];
|
blanchet@55698
|
350 |
val substA = Term.subst_TVars As_rho;
|
blanchet@55698
|
351 |
|
blanchet@55698
|
352 |
fun mk_spec ctr disc sels = {ctr = substA ctr, disc = substA disc, sels = map substA sels};
|
blanchet@55698
|
353 |
in
|
blanchet@55698
|
354 |
map3 mk_spec ctrs discs selss
|
blanchet@55698
|
355 |
end)
|
blanchet@55698
|
356 |
| _ => not_codatatype ctxt res_T);
|
blanchet@55698
|
357 |
|
blanchet@55698
|
358 |
(*FIXME: remove special cases for product and sum once they are registered as datatypes*)
|
blanchet@55698
|
359 |
fun map_thms_of_typ ctxt (Type (s, _)) =
|
blanchet@55698
|
360 |
if s = @{type_name prod} then
|
blanchet@55698
|
361 |
@{thms map_pair_simp}
|
blanchet@55698
|
362 |
else if s = @{type_name sum} then
|
blanchet@55698
|
363 |
@{thms sum_map.simps}
|
blanchet@55698
|
364 |
else
|
blanchet@55698
|
365 |
(case fp_sugar_of ctxt s of
|
blanchet@55698
|
366 |
SOME {index, mapss, ...} => nth mapss index
|
blanchet@55698
|
367 |
| NONE => [])
|
blanchet@55698
|
368 |
| map_thms_of_typ _ _ = [];
|
blanchet@55698
|
369 |
|
blanchet@55698
|
370 |
fun corec_specs_of bs arg_Ts res_Ts get_indices callssss0 lthy =
|
blanchet@55698
|
371 |
let
|
blanchet@55698
|
372 |
val thy = Proof_Context.theory_of lthy;
|
blanchet@55698
|
373 |
|
blanchet@55698
|
374 |
val ((missing_res_Ts, perm0_kks,
|
blanchet@55698
|
375 |
fp_sugars as {nested_bnfs, fp_res = {xtor_co_iterss = dtor_coiters1 :: _, ...},
|
blanchet@55698
|
376 |
co_inducts = coinduct_thms, ...} :: _, (_, gfp_sugar_thms)), lthy') =
|
blanchet@55698
|
377 |
nested_to_mutual_fps Greatest_FP bs res_Ts get_indices callssss0 lthy;
|
blanchet@55698
|
378 |
|
blanchet@55698
|
379 |
val perm_fp_sugars = sort (int_ord o pairself #index) fp_sugars;
|
blanchet@55698
|
380 |
|
blanchet@55698
|
381 |
val indices = map #index fp_sugars;
|
blanchet@55698
|
382 |
val perm_indices = map #index perm_fp_sugars;
|
blanchet@55698
|
383 |
|
blanchet@55698
|
384 |
val perm_ctrss = map (#ctrs o of_fp_sugar #ctr_sugars) perm_fp_sugars;
|
blanchet@55698
|
385 |
val perm_ctr_Tsss = map (map (binder_types o fastype_of)) perm_ctrss;
|
blanchet@55698
|
386 |
val perm_gfpTs = map (body_type o fastype_of o hd) perm_ctrss;
|
blanchet@55698
|
387 |
|
blanchet@55698
|
388 |
val nn0 = length res_Ts;
|
blanchet@55698
|
389 |
val nn = length perm_gfpTs;
|
blanchet@55698
|
390 |
val kks = 0 upto nn - 1;
|
blanchet@55698
|
391 |
val perm_ns = map length perm_ctr_Tsss;
|
blanchet@55698
|
392 |
|
blanchet@55698
|
393 |
val perm_Cs = map (domain_type o body_fun_type o fastype_of o co_rec_of o
|
blanchet@55698
|
394 |
of_fp_sugar (#xtor_co_iterss o #fp_res)) perm_fp_sugars;
|
blanchet@55698
|
395 |
val (perm_p_Tss, (perm_q_Tssss, _, perm_f_Tssss, _)) =
|
blanchet@55698
|
396 |
mk_coiter_fun_arg_types perm_ctr_Tsss perm_Cs perm_ns (co_rec_of dtor_coiters1);
|
blanchet@55698
|
397 |
|
blanchet@55698
|
398 |
val (perm_p_hss, h) = indexedd perm_p_Tss 0;
|
blanchet@55698
|
399 |
val (perm_q_hssss, h') = indexedddd perm_q_Tssss h;
|
blanchet@55698
|
400 |
val (perm_f_hssss, _) = indexedddd perm_f_Tssss h';
|
blanchet@55698
|
401 |
|
blanchet@55698
|
402 |
val fun_arg_hs =
|
blanchet@55698
|
403 |
flat (map3 flat_corec_preds_predsss_gettersss perm_p_hss perm_q_hssss perm_f_hssss);
|
blanchet@55698
|
404 |
|
blanchet@55698
|
405 |
fun unpermute0 perm0_xs = permute_like (op =) perm0_kks kks perm0_xs;
|
blanchet@55698
|
406 |
fun unpermute perm_xs = permute_like (op =) perm_indices indices perm_xs;
|
blanchet@55698
|
407 |
|
blanchet@55698
|
408 |
val coinduct_thmss = map (unpermute0 o conj_dests nn) coinduct_thms;
|
blanchet@55698
|
409 |
|
blanchet@55698
|
410 |
val p_iss = map (map (find_index_eq fun_arg_hs)) (unpermute perm_p_hss);
|
blanchet@55698
|
411 |
val q_issss = map (map (map (map (find_index_eq fun_arg_hs)))) (unpermute perm_q_hssss);
|
blanchet@55698
|
412 |
val f_issss = map (map (map (map (find_index_eq fun_arg_hs)))) (unpermute perm_f_hssss);
|
blanchet@55698
|
413 |
|
blanchet@55698
|
414 |
val f_Tssss = unpermute perm_f_Tssss;
|
blanchet@55698
|
415 |
val gfpTs = unpermute perm_gfpTs;
|
blanchet@55698
|
416 |
val Cs = unpermute perm_Cs;
|
blanchet@55698
|
417 |
|
blanchet@55698
|
418 |
val As_rho = tvar_subst thy (take nn0 gfpTs) res_Ts;
|
blanchet@55698
|
419 |
val Cs_rho = map (fst o dest_TVar) Cs ~~ pad_list HOLogic.unitT nn arg_Ts;
|
blanchet@55698
|
420 |
|
blanchet@55698
|
421 |
val substA = Term.subst_TVars As_rho;
|
blanchet@55698
|
422 |
val substAT = Term.typ_subst_TVars As_rho;
|
blanchet@55698
|
423 |
val substCT = Term.typ_subst_TVars Cs_rho;
|
blanchet@55698
|
424 |
|
blanchet@55698
|
425 |
val perm_Cs' = map substCT perm_Cs;
|
blanchet@55698
|
426 |
|
blanchet@55698
|
427 |
fun call_of nullary [] [g_i] [Type (@{type_name fun}, [_, T])] =
|
blanchet@55698
|
428 |
(if exists_subtype_in Cs T then Nested_Corec
|
blanchet@55698
|
429 |
else if nullary then Dummy_No_Corec
|
blanchet@55698
|
430 |
else No_Corec) g_i
|
blanchet@55698
|
431 |
| call_of _ [q_i] [g_i, g_i'] _ = Mutual_Corec (q_i, g_i, g_i');
|
blanchet@55698
|
432 |
|
blanchet@55698
|
433 |
fun mk_ctr_spec ctr disc sels p_ho q_iss f_iss f_Tss discI sel_thms collapse corec_thm
|
blanchet@55698
|
434 |
disc_corec sel_corecs =
|
blanchet@55698
|
435 |
let val nullary = not (can dest_funT (fastype_of ctr)) in
|
blanchet@55698
|
436 |
{ctr = substA ctr, disc = substA disc, sels = map substA sels, pred = p_ho,
|
blanchet@55698
|
437 |
calls = map3 (call_of nullary) q_iss f_iss f_Tss, discI = discI, sel_thms = sel_thms,
|
blanchet@55698
|
438 |
collapse = collapse, corec_thm = corec_thm, disc_corec = disc_corec,
|
blanchet@55698
|
439 |
sel_corecs = sel_corecs}
|
blanchet@55698
|
440 |
end;
|
blanchet@55698
|
441 |
|
blanchet@55698
|
442 |
fun mk_ctr_specs index (ctr_sugars : ctr_sugar list) p_is q_isss f_isss f_Tsss coiter_thmsss
|
blanchet@55698
|
443 |
disc_coitersss sel_coiterssss =
|
blanchet@55698
|
444 |
let
|
blanchet@55698
|
445 |
val ctrs = #ctrs (nth ctr_sugars index);
|
blanchet@55698
|
446 |
val discs = #discs (nth ctr_sugars index);
|
blanchet@55698
|
447 |
val selss = #selss (nth ctr_sugars index);
|
blanchet@55698
|
448 |
val p_ios = map SOME p_is @ [NONE];
|
blanchet@55698
|
449 |
val discIs = #discIs (nth ctr_sugars index);
|
blanchet@55698
|
450 |
val sel_thmss = #sel_thmss (nth ctr_sugars index);
|
blanchet@55698
|
451 |
val collapses = #collapses (nth ctr_sugars index);
|
blanchet@55698
|
452 |
val corec_thms = co_rec_of (nth coiter_thmsss index);
|
blanchet@55698
|
453 |
val disc_corecs = co_rec_of (nth disc_coitersss index);
|
blanchet@55698
|
454 |
val sel_corecss = co_rec_of (nth sel_coiterssss index);
|
blanchet@55698
|
455 |
in
|
blanchet@55698
|
456 |
map13 mk_ctr_spec ctrs discs selss p_ios q_isss f_isss f_Tsss discIs sel_thmss collapses
|
blanchet@55698
|
457 |
corec_thms disc_corecs sel_corecss
|
blanchet@55698
|
458 |
end;
|
blanchet@55698
|
459 |
|
blanchet@55698
|
460 |
fun mk_spec ({T, index, ctr_sugars, co_iterss = coiterss, co_iter_thmsss = coiter_thmsss,
|
blanchet@55698
|
461 |
disc_co_itersss = disc_coitersss, sel_co_iterssss = sel_coiterssss, ...} : fp_sugar)
|
blanchet@55698
|
462 |
p_is q_isss f_isss f_Tsss =
|
blanchet@55698
|
463 |
{corec = mk_co_iter thy Greatest_FP (substAT T) perm_Cs' (co_rec_of (nth coiterss index)),
|
blanchet@55698
|
464 |
nested_maps = maps (map_thms_of_typ lthy o T_of_bnf) nested_bnfs,
|
blanchet@55698
|
465 |
nested_map_idents = map (unfold_thms lthy @{thms id_def} o map_id0_of_bnf) nested_bnfs,
|
blanchet@55698
|
466 |
nested_map_comps = map map_comp_of_bnf nested_bnfs,
|
blanchet@55698
|
467 |
ctr_specs = mk_ctr_specs index ctr_sugars p_is q_isss f_isss f_Tsss coiter_thmsss
|
blanchet@55698
|
468 |
disc_coitersss sel_coiterssss};
|
blanchet@55698
|
469 |
in
|
blanchet@55698
|
470 |
((is_some gfp_sugar_thms, map5 mk_spec fp_sugars p_iss q_issss f_issss f_Tssss, missing_res_Ts,
|
blanchet@55698
|
471 |
co_induct_of coinduct_thms, strong_co_induct_of coinduct_thms, co_induct_of coinduct_thmss,
|
blanchet@55698
|
472 |
strong_co_induct_of coinduct_thmss), lthy')
|
blanchet@55698
|
473 |
end;
|
blanchet@55698
|
474 |
|
panny@54495
|
475 |
val undef_const = Const (@{const_name undefined}, dummyT);
|
panny@54494
|
476 |
|
panny@54538
|
477 |
val abs_tuple = HOLogic.tupled_lambda o HOLogic.mk_tuple;
|
panny@54857
|
478 |
fun abstract vs =
|
panny@54857
|
479 |
let fun a n (t $ u) = a n t $ a n u
|
panny@54857
|
480 |
| a n (Abs (v, T, b)) = Abs (v, T, a (n + 1) b)
|
panny@54857
|
481 |
| a n t = let val idx = find_index (equal t) vs in
|
panny@54857
|
482 |
if idx < 0 then t else Bound (n + idx) end
|
panny@54857
|
483 |
in a 0 end;
|
blanchet@55723
|
484 |
|
blanchet@55723
|
485 |
fun mk_prod1 bound_Ts (t, u) =
|
blanchet@55723
|
486 |
HOLogic.pair_const (fastype_of1 (bound_Ts, t)) (fastype_of1 (bound_Ts, u)) $ t $ u;
|
blanchet@55723
|
487 |
fun mk_tuple1 bound_Ts = the_default HOLogic.unit o try (foldr1 (mk_prod1 bound_Ts));
|
blanchet@54440
|
488 |
|
blanchet@55605
|
489 |
type coeqn_data_disc = {
|
blanchet@54440
|
490 |
fun_name: string,
|
panny@54857
|
491 |
fun_T: typ,
|
panny@54538
|
492 |
fun_args: term list,
|
panny@54857
|
493 |
ctr: term,
|
panny@54478
|
494 |
ctr_no: int, (*###*)
|
panny@54857
|
495 |
disc: term,
|
panny@54791
|
496 |
prems: term list,
|
panny@54959
|
497 |
auto_gen: bool,
|
panny@55549
|
498 |
maybe_ctr_rhs: term option,
|
panny@55549
|
499 |
maybe_code_rhs: term option,
|
blanchet@54440
|
500 |
user_eqn: term
|
blanchet@54440
|
501 |
};
|
blanchet@55138
|
502 |
|
blanchet@55605
|
503 |
type coeqn_data_sel = {
|
blanchet@54440
|
504 |
fun_name: string,
|
panny@54857
|
505 |
fun_T: typ,
|
panny@54538
|
506 |
fun_args: term list,
|
panny@54478
|
507 |
ctr: term,
|
panny@54478
|
508 |
sel: term,
|
blanchet@54440
|
509 |
rhs_term: term,
|
blanchet@54440
|
510 |
user_eqn: term
|
blanchet@54440
|
511 |
};
|
blanchet@55138
|
512 |
|
blanchet@55605
|
513 |
datatype coeqn_data =
|
blanchet@55605
|
514 |
Disc of coeqn_data_disc |
|
blanchet@55605
|
515 |
Sel of coeqn_data_sel;
|
blanchet@54440
|
516 |
|
panny@55612
|
517 |
fun dissect_coeqn_disc seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list)
|
panny@55612
|
518 |
maybe_ctr_rhs maybe_code_rhs prems' concl matchedsss =
|
blanchet@54440
|
519 |
let
|
blanchet@54440
|
520 |
fun find_subterm p = let (* FIXME \<exists>? *)
|
panny@54538
|
521 |
fun f (t as u $ v) = if p t then SOME t else merge_options (f u, f v)
|
blanchet@54440
|
522 |
| f t = if p t then SOME t else NONE
|
blanchet@54440
|
523 |
in f end;
|
blanchet@54440
|
524 |
|
panny@54791
|
525 |
val applied_fun = concl
|
panny@54791
|
526 |
|> find_subterm (member ((op =) o apsnd SOME) fun_names o try (fst o dest_Free o head_of))
|
panny@54791
|
527 |
|> the
|
blanchet@55698
|
528 |
handle Option.Option => primcorec_error_eqn "malformed discriminator formula" concl;
|
panny@54857
|
529 |
val ((fun_name, fun_T), fun_args) = strip_comb applied_fun |>> dest_Free;
|
blanchet@55661
|
530 |
val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
|
blanchet@54440
|
531 |
|
panny@55612
|
532 |
val discs = map #disc basic_ctr_specs;
|
panny@55612
|
533 |
val ctrs = map #ctr basic_ctr_specs;
|
panny@54791
|
534 |
val not_disc = head_of concl = @{term Not};
|
panny@54538
|
535 |
val _ = not_disc andalso length ctrs <> 2 andalso
|
blanchet@55698
|
536 |
primcorec_error_eqn "negated discriminator for a type with \<noteq> 2 constructors" concl;
|
panny@55612
|
537 |
val disc' = find_subterm (member (op =) discs o head_of) concl;
|
blanchet@55661
|
538 |
val eq_ctr0 = concl |> perhaps (try HOLogic.dest_not) |> try (HOLogic.dest_eq #> snd)
|
blanchet@54440
|
539 |
|> (fn SOME t => let val n = find_index (equal t) ctrs in
|
blanchet@54440
|
540 |
if n >= 0 then SOME n else NONE end | _ => NONE);
|
panny@55612
|
541 |
val _ = is_some disc' orelse is_some eq_ctr0 orelse
|
blanchet@55698
|
542 |
primcorec_error_eqn "no discriminator in equation" concl;
|
blanchet@54440
|
543 |
val ctr_no' =
|
panny@55612
|
544 |
if is_none disc' then the eq_ctr0 else find_index (equal (head_of (the disc'))) discs;
|
blanchet@54440
|
545 |
val ctr_no = if not_disc then 1 - ctr_no' else ctr_no';
|
panny@55612
|
546 |
val {ctr, disc, ...} = nth basic_ctr_specs ctr_no;
|
blanchet@54440
|
547 |
|
panny@54791
|
548 |
val catch_all = try (fst o dest_Free o the_single) prems' = SOME Name.uu_;
|
panny@54857
|
549 |
val matchedss = AList.lookup (op =) matchedsss fun_name |> the_default [];
|
panny@54857
|
550 |
val prems = map (abstract (List.rev fun_args)) prems';
|
panny@54857
|
551 |
val real_prems =
|
blanchet@55519
|
552 |
(if catch_all orelse seq then maps s_not_conj matchedss else []) @
|
panny@54791
|
553 |
(if catch_all then [] else prems);
|
blanchet@54440
|
554 |
|
panny@54857
|
555 |
val matchedsss' = AList.delete (op =) fun_name matchedsss
|
panny@55517
|
556 |
|> cons (fun_name, if seq then matchedss @ [prems] else matchedss @ [real_prems]);
|
panny@54791
|
557 |
|
panny@54791
|
558 |
val user_eqn =
|
panny@55549
|
559 |
(real_prems, concl)
|
panny@55549
|
560 |
|>> map HOLogic.mk_Trueprop ||> HOLogic.mk_Trueprop o abstract (List.rev fun_args)
|
panny@55549
|
561 |
|> curry Logic.list_all (map dest_Free fun_args) o Logic.list_implies;
|
blanchet@54440
|
562 |
in
|
panny@54478
|
563 |
(Disc {
|
blanchet@54440
|
564 |
fun_name = fun_name,
|
panny@54857
|
565 |
fun_T = fun_T,
|
panny@54538
|
566 |
fun_args = fun_args,
|
panny@54857
|
567 |
ctr = ctr,
|
blanchet@54440
|
568 |
ctr_no = ctr_no,
|
panny@55612
|
569 |
disc = disc,
|
panny@54791
|
570 |
prems = real_prems,
|
panny@54959
|
571 |
auto_gen = catch_all,
|
panny@55549
|
572 |
maybe_ctr_rhs = maybe_ctr_rhs,
|
panny@55549
|
573 |
maybe_code_rhs = maybe_code_rhs,
|
panny@54791
|
574 |
user_eqn = user_eqn
|
panny@54857
|
575 |
}, matchedsss')
|
blanchet@54440
|
576 |
end;
|
blanchet@54440
|
577 |
|
blanchet@55661
|
578 |
fun dissect_coeqn_sel fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn'
|
blanchet@55661
|
579 |
maybe_of_spec eqn =
|
blanchet@54440
|
580 |
let
|
blanchet@54440
|
581 |
val (lhs, rhs) = HOLogic.dest_eq eqn
|
blanchet@54440
|
582 |
handle TERM _ =>
|
blanchet@55698
|
583 |
primcorec_error_eqn "malformed function equation (expected \"lhs = rhs\")" eqn;
|
blanchet@54440
|
584 |
val sel = head_of lhs;
|
panny@54857
|
585 |
val ((fun_name, fun_T), fun_args) = dest_comb lhs |> snd |> strip_comb |> apfst dest_Free
|
blanchet@54440
|
586 |
handle TERM _ =>
|
blanchet@55698
|
587 |
primcorec_error_eqn "malformed selector argument in left-hand side" eqn;
|
panny@55612
|
588 |
val basic_ctr_specs = the (AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name)
|
blanchet@55698
|
589 |
handle Option.Option => primcorec_error_eqn "malformed selector argument in left-hand side" eqn;
|
panny@55612
|
590 |
val {ctr, ...} =
|
blanchet@55661
|
591 |
(case maybe_of_spec of
|
blanchet@55661
|
592 |
SOME of_spec => the (find_first (equal of_spec o #ctr) basic_ctr_specs)
|
blanchet@55661
|
593 |
| NONE => filter (exists (equal sel) o #sels) basic_ctr_specs |> the_single
|
blanchet@55698
|
594 |
handle List.Empty => primcorec_error_eqn "ambiguous selector - use \"of\"" eqn);
|
panny@54791
|
595 |
val user_eqn = drop_All eqn';
|
blanchet@54440
|
596 |
in
|
panny@54478
|
597 |
Sel {
|
blanchet@54440
|
598 |
fun_name = fun_name,
|
panny@54857
|
599 |
fun_T = fun_T,
|
panny@54538
|
600 |
fun_args = fun_args,
|
panny@55612
|
601 |
ctr = ctr,
|
panny@54478
|
602 |
sel = sel,
|
blanchet@54440
|
603 |
rhs_term = rhs,
|
panny@54791
|
604 |
user_eqn = user_eqn
|
blanchet@54440
|
605 |
}
|
blanchet@54440
|
606 |
end;
|
blanchet@54440
|
607 |
|
panny@55612
|
608 |
fun dissect_coeqn_ctr seq fun_names (basic_ctr_specss : basic_corec_ctr_spec list list) eqn'
|
panny@55612
|
609 |
maybe_code_rhs prems concl matchedsss =
|
blanchet@55047
|
610 |
let
|
panny@55517
|
611 |
val (lhs, rhs) = HOLogic.dest_eq concl;
|
panny@55549
|
612 |
val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
|
blanchet@55661
|
613 |
val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
|
blanchet@55526
|
614 |
val (ctr, ctr_args) = strip_comb (unfold_let rhs);
|
panny@55612
|
615 |
val {disc, sels, ...} = the (find_first (equal ctr o #ctr) basic_ctr_specs)
|
blanchet@55698
|
616 |
handle Option.Option => primcorec_error_eqn "not a constructor" ctr;
|
panny@54478
|
617 |
|
panny@55517
|
618 |
val disc_concl = betapply (disc, lhs);
|
panny@55612
|
619 |
val (maybe_eqn_data_disc, matchedsss') = if length basic_ctr_specs = 1
|
panny@54857
|
620 |
then (NONE, matchedsss)
|
panny@55612
|
621 |
else apfst SOME (dissect_coeqn_disc seq fun_names basic_ctr_specss
|
panny@55549
|
622 |
(SOME (abstract (List.rev fun_args) rhs)) maybe_code_rhs prems disc_concl matchedsss);
|
blanchet@54440
|
623 |
|
blanchet@55611
|
624 |
val sel_concls = sels ~~ ctr_args
|
blanchet@54440
|
625 |
|> map (fn (sel, ctr_arg) => HOLogic.mk_eq (betapply (sel, lhs), ctr_arg));
|
blanchet@54440
|
626 |
|
blanchet@54993
|
627 |
(*
|
panny@55517
|
628 |
val _ = tracing ("reduced\n " ^ Syntax.string_of_term @{context} concl ^ "\nto\n \<cdot> " ^
|
panny@55517
|
629 |
(is_some maybe_eqn_data_disc ? K (Syntax.string_of_term @{context} disc_concl ^ "\n \<cdot> ")) "" ^
|
panny@55549
|
630 |
space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) sel_concls) ^
|
panny@55549
|
631 |
"\nfor premise(s)\n \<cdot> " ^
|
panny@55549
|
632 |
space_implode "\n \<cdot> " (map (Syntax.string_of_term @{context}) prems));
|
blanchet@54993
|
633 |
*)
|
blanchet@54440
|
634 |
|
panny@55612
|
635 |
val eqns_data_sel =
|
panny@55612
|
636 |
map (dissect_coeqn_sel fun_names basic_ctr_specss eqn' (SOME ctr)) sel_concls;
|
blanchet@54440
|
637 |
in
|
panny@54857
|
638 |
(the_list maybe_eqn_data_disc @ eqns_data_sel, matchedsss')
|
blanchet@54440
|
639 |
end;
|
blanchet@54440
|
640 |
|
panny@55612
|
641 |
fun dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss =
|
panny@55517
|
642 |
let
|
panny@55517
|
643 |
val (lhs, (rhs', rhs)) = HOLogic.dest_eq concl ||> `(expand_corec_code_rhs lthy has_call []);
|
panny@55549
|
644 |
val (fun_name, fun_args) = strip_comb lhs |>> fst o dest_Free;
|
blanchet@55661
|
645 |
val SOME basic_ctr_specs = AList.lookup (op =) (fun_names ~~ basic_ctr_specss) fun_name;
|
panny@55517
|
646 |
|
panny@55517
|
647 |
val cond_ctrs = fold_rev_corec_code_rhs lthy (fn cs => fn ctr => fn _ =>
|
panny@55612
|
648 |
if member ((op =) o apsnd #ctr) basic_ctr_specs ctr
|
panny@55517
|
649 |
then cons (ctr, cs)
|
blanchet@55698
|
650 |
else primcorec_error_eqn "not a constructor" ctr) [] rhs' []
|
panny@55517
|
651 |
|> AList.group (op =);
|
panny@55517
|
652 |
|
blanchet@55520
|
653 |
val ctr_premss = (case cond_ctrs of [_] => [[]] | _ => map (s_dnf o snd) cond_ctrs);
|
panny@55517
|
654 |
val ctr_concls = cond_ctrs |> map (fn (ctr, _) =>
|
panny@55517
|
655 |
binder_types (fastype_of ctr)
|
panny@55517
|
656 |
|> map_index (fn (n, T) => massage_corec_code_rhs lthy (fn _ => fn ctr' => fn args =>
|
panny@55517
|
657 |
if ctr' = ctr then nth args n else Const (@{const_name undefined}, T)) [] rhs')
|
panny@55517
|
658 |
|> curry list_comb ctr
|
panny@55517
|
659 |
|> curry HOLogic.mk_eq lhs);
|
panny@55517
|
660 |
in
|
panny@55612
|
661 |
fold_map2 (dissect_coeqn_ctr false fun_names basic_ctr_specss eqn'
|
panny@55549
|
662 |
(SOME (abstract (List.rev fun_args) rhs)))
|
panny@55549
|
663 |
ctr_premss ctr_concls matchedsss
|
panny@55517
|
664 |
end;
|
panny@55517
|
665 |
|
panny@55612
|
666 |
fun dissect_coeqn lthy seq has_call fun_names (basic_ctr_specss : basic_corec_ctr_spec list list)
|
blanchet@55661
|
667 |
eqn' maybe_of_spec matchedsss =
|
blanchet@54440
|
668 |
let
|
panny@54791
|
669 |
val eqn = drop_All eqn'
|
blanchet@55698
|
670 |
handle TERM _ => primcorec_error_eqn "malformed function equation" eqn';
|
panny@55517
|
671 |
val (prems, concl) = Logic.strip_horn eqn
|
panny@54478
|
672 |
|> apfst (map HOLogic.dest_Trueprop) o apsnd HOLogic.dest_Trueprop;
|
blanchet@54440
|
673 |
|
panny@55517
|
674 |
val head = concl
|
blanchet@54440
|
675 |
|> perhaps (try HOLogic.dest_not) |> perhaps (try (fst o HOLogic.dest_eq))
|
blanchet@54440
|
676 |
|> head_of;
|
blanchet@54440
|
677 |
|
blanchet@55661
|
678 |
val maybe_rhs = concl |> perhaps (try HOLogic.dest_not) |> try (snd o HOLogic.dest_eq);
|
blanchet@54440
|
679 |
|
panny@55612
|
680 |
val discs = maps (map #disc) basic_ctr_specss;
|
panny@55612
|
681 |
val sels = maps (maps #sels) basic_ctr_specss;
|
panny@55612
|
682 |
val ctrs = maps (map #ctr) basic_ctr_specss;
|
blanchet@54440
|
683 |
in
|
blanchet@54440
|
684 |
if member (op =) discs head orelse
|
blanchet@54440
|
685 |
is_some maybe_rhs andalso
|
blanchet@54440
|
686 |
member (op =) (filter (null o binder_types o fastype_of) ctrs) (the maybe_rhs) then
|
panny@55612
|
687 |
dissect_coeqn_disc seq fun_names basic_ctr_specss NONE NONE prems concl matchedsss
|
blanchet@54440
|
688 |
|>> single
|
blanchet@54440
|
689 |
else if member (op =) sels head then
|
blanchet@55661
|
690 |
([dissect_coeqn_sel fun_names basic_ctr_specss eqn' maybe_of_spec concl], matchedsss)
|
panny@55517
|
691 |
else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
|
blanchet@55526
|
692 |
member (op =) ctrs (head_of (unfold_let (the maybe_rhs))) then
|
panny@55612
|
693 |
dissect_coeqn_ctr seq fun_names basic_ctr_specss eqn' NONE prems concl matchedsss
|
panny@55517
|
694 |
else if is_Free head andalso member (op =) fun_names (fst (dest_Free head)) andalso
|
panny@55517
|
695 |
null prems then
|
panny@55612
|
696 |
dissect_coeqn_code lthy has_call fun_names basic_ctr_specss eqn' concl matchedsss
|
panny@55517
|
697 |
|>> flat
|
blanchet@54440
|
698 |
else
|
blanchet@55698
|
699 |
primcorec_error_eqn "malformed function equation" eqn
|
blanchet@54440
|
700 |
end;
|
blanchet@54440
|
701 |
|
blanchet@55139
|
702 |
fun build_corec_arg_disc (ctr_specs : corec_ctr_spec list)
|
blanchet@55605
|
703 |
({fun_args, ctr_no, prems, ...} : coeqn_data_disc) =
|
panny@54791
|
704 |
if is_none (#pred (nth ctr_specs ctr_no)) then I else
|
blanchet@55520
|
705 |
s_conjs prems
|
panny@54791
|
706 |
|> curry subst_bounds (List.rev fun_args)
|
panny@54791
|
707 |
|> HOLogic.tupled_lambda (HOLogic.mk_tuple fun_args)
|
panny@54791
|
708 |
|> K |> nth_map (the (#pred (nth ctr_specs ctr_no)));
|
blanchet@54440
|
709 |
|
blanchet@55605
|
710 |
fun build_corec_arg_no_call (sel_eqns : coeqn_data_sel list) sel =
|
panny@54857
|
711 |
find_first (equal sel o #sel) sel_eqns
|
panny@54857
|
712 |
|> try (fn SOME {fun_args, rhs_term, ...} => abs_tuple fun_args rhs_term)
|
panny@54857
|
713 |
|> the_default undef_const
|
panny@54548
|
714 |
|> K;
|
panny@54497
|
715 |
|
blanchet@55605
|
716 |
fun build_corec_args_mutual_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
|
blanchet@55660
|
717 |
(case find_first (equal sel o #sel) sel_eqns of
|
blanchet@55660
|
718 |
NONE => (I, I, I)
|
blanchet@55660
|
719 |
| SOME {fun_args, rhs_term, ... } =>
|
panny@55013
|
720 |
let
|
panny@55549
|
721 |
val bound_Ts = List.rev (map fastype_of fun_args);
|
blanchet@55659
|
722 |
fun rewrite_stop _ t = if has_call t then @{term False} else @{term True};
|
blanchet@55659
|
723 |
fun rewrite_end _ t = if has_call t then undef_const else t;
|
blanchet@55659
|
724 |
fun rewrite_cont bound_Ts t =
|
panny@55036
|
725 |
if has_call t then mk_tuple1 bound_Ts (snd (strip_comb t)) else undef_const;
|
blanchet@55554
|
726 |
fun massage f _ = massage_mutual_corec_call lthy has_call f bound_Ts rhs_term
|
panny@55549
|
727 |
|> abs_tuple fun_args;
|
panny@55013
|
728 |
in
|
blanchet@55659
|
729 |
(massage rewrite_stop, massage rewrite_end, massage rewrite_cont)
|
blanchet@55660
|
730 |
end);
|
panny@54497
|
731 |
|
blanchet@55605
|
732 |
fun build_corec_arg_nested_call lthy has_call (sel_eqns : coeqn_data_sel list) sel =
|
blanchet@55660
|
733 |
(case find_first (equal sel o #sel) sel_eqns of
|
blanchet@55660
|
734 |
NONE => I
|
blanchet@55660
|
735 |
| SOME {fun_args, rhs_term, ...} =>
|
panny@55036
|
736 |
let
|
panny@55549
|
737 |
val bound_Ts = List.rev (map fastype_of fun_args);
|
panny@55036
|
738 |
fun rewrite bound_Ts U T (Abs (v, V, b)) = Abs (v, V, rewrite (V :: bound_Ts) U T b)
|
panny@55036
|
739 |
| rewrite bound_Ts U T (t as _ $ _) =
|
panny@55036
|
740 |
let val (u, vs) = strip_comb t in
|
panny@55036
|
741 |
if is_Free u andalso has_call u then
|
panny@55036
|
742 |
Inr_const U T $ mk_tuple1 bound_Ts vs
|
blanchet@55723
|
743 |
else if try (fst o dest_Const) u = SOME @{const_name prod_case} then
|
panny@55036
|
744 |
map (rewrite bound_Ts U T) vs |> chop 1 |>> HOLogic.mk_split o the_single |> list_comb
|
panny@55036
|
745 |
else
|
panny@55036
|
746 |
list_comb (rewrite bound_Ts U T u, map (rewrite bound_Ts U T) vs)
|
panny@55036
|
747 |
end
|
panny@55036
|
748 |
| rewrite _ U T t =
|
panny@55036
|
749 |
if is_Free t andalso has_call t then Inr_const U T $ HOLogic.unit else t;
|
panny@55036
|
750 |
fun massage t =
|
panny@55549
|
751 |
rhs_term
|
blanchet@55554
|
752 |
|> massage_nested_corec_call lthy has_call rewrite bound_Ts (range_type (fastype_of t))
|
panny@54872
|
753 |
|> abs_tuple fun_args;
|
panny@55036
|
754 |
in
|
panny@55036
|
755 |
massage
|
blanchet@55660
|
756 |
end);
|
panny@54497
|
757 |
|
blanchet@55605
|
758 |
fun build_corec_args_sel lthy has_call (all_sel_eqns : coeqn_data_sel list)
|
blanchet@55139
|
759 |
(ctr_spec : corec_ctr_spec) =
|
blanchet@55660
|
760 |
(case filter (equal (#ctr ctr_spec) o #ctr) all_sel_eqns of
|
blanchet@55660
|
761 |
[] => I
|
blanchet@55660
|
762 |
| sel_eqns =>
|
blanchet@55660
|
763 |
let
|
blanchet@55660
|
764 |
val sel_call_list = #sels ctr_spec ~~ #calls ctr_spec;
|
blanchet@55660
|
765 |
val no_calls' = map_filter (try (apsnd (fn No_Corec n => n))) sel_call_list;
|
blanchet@55660
|
766 |
val mutual_calls' = map_filter (try (apsnd (fn Mutual_Corec n => n))) sel_call_list;
|
blanchet@55660
|
767 |
val nested_calls' = map_filter (try (apsnd (fn Nested_Corec n => n))) sel_call_list;
|
blanchet@55660
|
768 |
in
|
blanchet@55660
|
769 |
I
|
blanchet@55660
|
770 |
#> fold (fn (sel, n) => nth_map n (build_corec_arg_no_call sel_eqns sel)) no_calls'
|
blanchet@55660
|
771 |
#> fold (fn (sel, (q, g, h)) =>
|
blanchet@55660
|
772 |
let val (fq, fg, fh) = build_corec_args_mutual_call lthy has_call sel_eqns sel in
|
blanchet@55660
|
773 |
nth_map q fq o nth_map g fg o nth_map h fh end) mutual_calls'
|
blanchet@55660
|
774 |
#> fold (fn (sel, n) => nth_map n
|
blanchet@55660
|
775 |
(build_corec_arg_nested_call lthy has_call sel_eqns sel)) nested_calls'
|
blanchet@55660
|
776 |
end);
|
blanchet@54440
|
777 |
|
blanchet@55605
|
778 |
fun build_codefs lthy bs mxs has_call arg_Tss (corec_specs : corec_spec list)
|
blanchet@55605
|
779 |
(disc_eqnss : coeqn_data_disc list list) (sel_eqnss : coeqn_data_sel list list) =
|
panny@54791
|
780 |
let
|
panny@55612
|
781 |
val corecs = map #corec corec_specs;
|
panny@55612
|
782 |
val ctr_specss = map #ctr_specs corec_specs;
|
panny@54497
|
783 |
val corec_args = hd corecs
|
panny@54497
|
784 |
|> fst o split_last o binder_types o fastype_of
|
panny@54497
|
785 |
|> map (Const o pair @{const_name undefined})
|
panny@54857
|
786 |
|> fold2 (fold o build_corec_arg_disc) ctr_specss disc_eqnss
|
panny@54497
|
787 |
|> fold2 (fold o build_corec_args_sel lthy has_call) sel_eqnss ctr_specss;
|
panny@54872
|
788 |
fun currys [] t = t
|
panny@54872
|
789 |
| currys Ts t = t $ mk_tuple1 (List.rev Ts) (map Bound (length Ts - 1 downto 0))
|
panny@54872
|
790 |
|> fold_rev (Term.abs o pair Name.uu) Ts;
|
panny@54538
|
791 |
|
blanchet@54993
|
792 |
(*
|
panny@54497
|
793 |
val _ = tracing ("corecursor arguments:\n \<cdot> " ^
|
panny@54548
|
794 |
space_implode "\n \<cdot> " (map (Syntax.string_of_term lthy) corec_args));
|
blanchet@54993
|
795 |
*)
|
blanchet@54440
|
796 |
|
panny@54791
|
797 |
val exclss' =
|
panny@54857
|
798 |
disc_eqnss
|
panny@54959
|
799 |
|> map (map (fn x => (#fun_args x, #ctr_no x, #prems x, #auto_gen x))
|
panny@54791
|
800 |
#> fst o (fn xs => fold_map (fn x => fn ys => ((x, ys), ys @ [x])) xs [])
|
panny@54791
|
801 |
#> maps (uncurry (map o pair)
|
panny@54959
|
802 |
#> map (fn ((fun_args, c, x, a), (_, c', y, a')) =>
|
blanchet@55520
|
803 |
((c, c', a orelse a'), (x, s_not (s_conjs y)))
|
panny@54791
|
804 |
||> apfst (map HOLogic.mk_Trueprop) o apsnd HOLogic.mk_Trueprop
|
panny@54791
|
805 |
||> Logic.list_implies
|
panny@54791
|
806 |
||> curry Logic.list_all (map dest_Free fun_args))))
|
blanchet@54440
|
807 |
in
|
blanchet@54440
|
808 |
map (list_comb o rpair corec_args) corecs
|
blanchet@54440
|
809 |
|> map2 (fn Ts => fn t => if length Ts = 0 then t $ HOLogic.unit else t) arg_Tss
|
blanchet@54440
|
810 |
|> map2 currys arg_Tss
|
blanchet@54440
|
811 |
|> Syntax.check_terms lthy
|
blanchet@55607
|
812 |
|> map3 (fn b => fn mx => fn t => ((b, mx), ((Binding.conceal (Thm.def_binding b), []), t)))
|
blanchet@55607
|
813 |
bs mxs
|
panny@54791
|
814 |
|> rpair exclss'
|
blanchet@54440
|
815 |
end;
|
blanchet@54440
|
816 |
|
blanchet@55139
|
817 |
fun mk_real_disc_eqns fun_binding arg_Ts ({ctr_specs, ...} : corec_spec)
|
blanchet@55605
|
818 |
(sel_eqns : coeqn_data_sel list) (disc_eqns : coeqn_data_disc list) =
|
panny@54857
|
819 |
if length disc_eqns <> length ctr_specs - 1 then disc_eqns else
|
panny@54857
|
820 |
let
|
panny@54857
|
821 |
val n = 0 upto length ctr_specs
|
panny@54857
|
822 |
|> the o find_first (fn idx => not (exists (equal idx o #ctr_no) disc_eqns));
|
panny@54859
|
823 |
val fun_args = (try (#fun_args o hd) disc_eqns, try (#fun_args o hd) sel_eqns)
|
panny@54859
|
824 |
|> the_default (map (curry Free Name.uu) arg_Ts) o merge_options;
|
panny@54857
|
825 |
val extra_disc_eqn = {
|
panny@54857
|
826 |
fun_name = Binding.name_of fun_binding,
|
panny@54857
|
827 |
fun_T = arg_Ts ---> body_type (fastype_of (#ctr (hd ctr_specs))),
|
panny@54859
|
828 |
fun_args = fun_args,
|
panny@54857
|
829 |
ctr = #ctr (nth ctr_specs n),
|
panny@54857
|
830 |
ctr_no = n,
|
panny@54857
|
831 |
disc = #disc (nth ctr_specs n),
|
blanchet@55519
|
832 |
prems = maps (s_not_conj o #prems) disc_eqns,
|
panny@54959
|
833 |
auto_gen = true,
|
panny@55549
|
834 |
maybe_ctr_rhs = NONE,
|
panny@55549
|
835 |
maybe_code_rhs = NONE,
|
panny@54857
|
836 |
user_eqn = undef_const};
|
panny@54857
|
837 |
in
|
panny@54857
|
838 |
chop n disc_eqns ||> cons extra_disc_eqn |> (op @)
|
panny@54857
|
839 |
end;
|
panny@54857
|
840 |
|
blanchet@55695
|
841 |
fun find_corec_calls ctxt has_call basic_ctr_specs ({ctr, sel, rhs_term, ...} : coeqn_data_sel) =
|
panny@55612
|
842 |
let
|
panny@55612
|
843 |
val sel_no = find_first (equal ctr o #ctr) basic_ctr_specs
|
panny@55612
|
844 |
|> find_index (equal sel) o #sels o the;
|
blanchet@55695
|
845 |
fun find t = if has_call t then snd (fold_rev_corec_call ctxt (K cons) [] t []) else [];
|
panny@55612
|
846 |
in
|
panny@55612
|
847 |
find rhs_term
|
panny@55612
|
848 |
|> K |> nth_map sel_no |> AList.map_entry (op =) ctr
|
panny@55612
|
849 |
end;
|
panny@55612
|
850 |
|
blanchet@55661
|
851 |
fun add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy =
|
blanchet@54440
|
852 |
let
|
traytel@54489
|
853 |
val (bs, mxs) = map_split (apfst fst) fixes;
|
blanchet@54440
|
854 |
val (arg_Ts, res_Ts) = map (strip_type o snd o fst #>> HOLogic.mk_tupleT) fixes |> split_list;
|
blanchet@54440
|
855 |
|
panny@55612
|
856 |
val fun_names = map Binding.name_of bs;
|
panny@55612
|
857 |
val basic_ctr_specss = map (basic_corec_specs_of lthy) res_Ts;
|
panny@55612
|
858 |
val has_call = exists_subterm (map (fst #>> Binding.name_of #> Free) fixes |> member (op =));
|
panny@55612
|
859 |
val eqns_data =
|
panny@55612
|
860 |
fold_map2 (dissect_coeqn lthy seq has_call fun_names basic_ctr_specss) (map snd specs)
|
blanchet@55661
|
861 |
maybe_of_specs []
|
panny@55612
|
862 |
|> flat o fst;
|
panny@55612
|
863 |
|
panny@55612
|
864 |
val callssss =
|
panny@55612
|
865 |
map_filter (try (fn Sel x => x)) eqns_data
|
panny@55612
|
866 |
|> partition_eq ((op =) o pairself #fun_name)
|
panny@55612
|
867 |
|> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
|
panny@55613
|
868 |
|> map (flat o snd)
|
blanchet@55695
|
869 |
|> map2 (fold o find_corec_calls lthy has_call) basic_ctr_specss
|
panny@55612
|
870 |
|> map2 (curry (op |>)) (map (map (fn {ctr, sels, ...} =>
|
panny@55612
|
871 |
(ctr, map (K []) sels))) basic_ctr_specss);
|
panny@55612
|
872 |
|
panny@55612
|
873 |
(*
|
panny@55612
|
874 |
val _ = tracing ("callssss = " ^ @{make_string} callssss);
|
panny@55612
|
875 |
*)
|
blanchet@54440
|
876 |
|
blanchet@54967
|
877 |
val ((n2m, corec_specs', _, coinduct_thm, strong_coinduct_thm, coinduct_thms,
|
blanchet@54934
|
878 |
strong_coinduct_thms), lthy') =
|
blanchet@54931
|
879 |
corec_specs_of bs arg_Ts res_Ts (get_indices fixes) callssss lthy;
|
blanchet@54967
|
880 |
val actual_nn = length bs;
|
blanchet@54967
|
881 |
val corec_specs = take actual_nn corec_specs'; (*###*)
|
blanchet@55630
|
882 |
val ctr_specss = map #ctr_specs corec_specs;
|
blanchet@54440
|
883 |
|
panny@54857
|
884 |
val disc_eqnss' = map_filter (try (fn Disc x => x)) eqns_data
|
panny@54791
|
885 |
|> partition_eq ((op =) o pairself #fun_name)
|
panny@54857
|
886 |
|> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
|
panny@54791
|
887 |
|> map (sort ((op <) o pairself #ctr_no |> make_ord) o flat o snd);
|
panny@54857
|
888 |
val _ = disc_eqnss' |> map (fn x =>
|
panny@54857
|
889 |
let val d = duplicates ((op =) o pairself #ctr_no) x in null d orelse
|
blanchet@55698
|
890 |
primcorec_error_eqns "excess discriminator formula in definition"
|
panny@54857
|
891 |
(maps (fn t => filter (equal (#ctr_no t) o #ctr_no) x) d |> map #user_eqn) end);
|
panny@54791
|
892 |
|
panny@54791
|
893 |
val sel_eqnss = map_filter (try (fn Sel x => x)) eqns_data
|
panny@54791
|
894 |
|> partition_eq ((op =) o pairself #fun_name)
|
panny@54857
|
895 |
|> fst o finds (fn (x, ({fun_name, ...} :: _)) => x = fun_name) fun_names
|
panny@54791
|
896 |
|> map (flat o snd);
|
panny@54791
|
897 |
|
panny@54497
|
898 |
val arg_Tss = map (binder_types o snd o fst) fixes;
|
panny@54859
|
899 |
val disc_eqnss = map5 mk_real_disc_eqns bs arg_Tss corec_specs sel_eqnss disc_eqnss';
|
panny@54791
|
900 |
val (defs, exclss') =
|
blanchet@55605
|
901 |
build_codefs lthy' bs mxs has_call arg_Tss corec_specs disc_eqnss sel_eqnss;
|
panny@54791
|
902 |
|
blanchet@55060
|
903 |
fun excl_tac (c, c', a) =
|
blanchet@55629
|
904 |
if a orelse c = c' orelse seq then SOME (K (HEADGOAL (mk_primcorec_assumption_tac lthy [])))
|
blanchet@55629
|
905 |
else maybe_tac;
|
panny@54959
|
906 |
|
blanchet@54993
|
907 |
(*
|
panny@54959
|
908 |
val _ = tracing ("exclusiveness properties:\n \<cdot> " ^
|
panny@54959
|
909 |
space_implode "\n \<cdot> " (maps (map (Syntax.string_of_term lthy o snd)) exclss'));
|
blanchet@54993
|
910 |
*)
|
panny@54959
|
911 |
|
panny@54959
|
912 |
val exclss'' = exclss' |> map (map (fn (idx, t) =>
|
blanchet@55629
|
913 |
(idx, (Option.map (Goal.prove lthy [] [] t #> Thm.close_derivation) (excl_tac idx), t))));
|
panny@54791
|
914 |
val taut_thmss = map (map (apsnd (the o fst)) o filter (is_some o fst o snd)) exclss'';
|
blanchet@55632
|
915 |
val (goal_idxss, goalss) = exclss''
|
panny@54791
|
916 |
|> map (map (apsnd (rpair [] o snd)) o filter (is_none o fst o snd))
|
panny@54791
|
917 |
|> split_list o map split_list;
|
panny@54791
|
918 |
|
panny@54791
|
919 |
fun prove thmss' def_thms' lthy =
|
panny@54791
|
920 |
let
|
panny@54791
|
921 |
val def_thms = map (snd o snd) def_thms';
|
panny@54791
|
922 |
|
blanchet@55632
|
923 |
val exclss' = map (op ~~) (goal_idxss ~~ thmss');
|
panny@54791
|
924 |
fun mk_exclsss excls n =
|
panny@54791
|
925 |
(excls, map (fn k => replicate k [TrueI] @ replicate (n - k) []) (0 upto n - 1))
|
panny@54959
|
926 |
|-> fold (fn ((c, c', _), thm) => nth_map c (nth_map c' (K [thm])));
|
panny@54791
|
927 |
val exclssss = (exclss' ~~ taut_thmss |> map (op @), fun_names ~~ corec_specs)
|
panny@54791
|
928 |
|-> map2 (fn excls => fn (_, {ctr_specs, ...}) => mk_exclsss excls (length ctr_specs));
|
panny@54791
|
929 |
|
blanchet@55139
|
930 |
fun prove_disc ({ctr_specs, ...} : corec_spec) exclsss
|
blanchet@55605
|
931 |
({fun_name, fun_T, fun_args, ctr_no, prems, ...} : coeqn_data_disc) =
|
panny@54859
|
932 |
if Term.aconv_untyped (#disc (nth ctr_specs ctr_no), @{term "\<lambda>x. x = x"}) then [] else
|
panny@54857
|
933 |
let
|
panny@54859
|
934 |
val {disc_corec, ...} = nth ctr_specs ctr_no;
|
panny@54857
|
935 |
val k = 1 + ctr_no;
|
panny@54857
|
936 |
val m = length prems;
|
panny@54857
|
937 |
val t =
|
panny@54857
|
938 |
list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
|
panny@54857
|
939 |
|> curry betapply (#disc (nth ctr_specs ctr_no)) (*###*)
|
panny@54857
|
940 |
|> HOLogic.mk_Trueprop
|
panny@54857
|
941 |
|> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
|
panny@54857
|
942 |
|> curry Logic.list_all (map dest_Free fun_args);
|
panny@54857
|
943 |
in
|
panny@55549
|
944 |
if prems = [@{term False}] then [] else
|
panny@54857
|
945 |
mk_primcorec_disc_tac lthy def_thms disc_corec k m exclsss
|
panny@54857
|
946 |
|> K |> Goal.prove lthy [] [] t
|
blanchet@55628
|
947 |
|> Thm.close_derivation
|
panny@54857
|
948 |
|> pair (#disc (nth ctr_specs ctr_no))
|
panny@54857
|
949 |
|> single
|
panny@54857
|
950 |
end;
|
panny@54857
|
951 |
|
blanchet@55139
|
952 |
fun prove_sel ({nested_maps, nested_map_idents, nested_map_comps, ctr_specs, ...}
|
blanchet@55605
|
953 |
: corec_spec) (disc_eqns : coeqn_data_disc list) exclsss
|
blanchet@55605
|
954 |
({fun_name, fun_T, fun_args, ctr, sel, rhs_term, ...} : coeqn_data_sel) =
|
panny@54791
|
955 |
let
|
blanchet@55046
|
956 |
val SOME ctr_spec = find_first (equal ctr o #ctr) ctr_specs;
|
panny@54857
|
957 |
val ctr_no = find_index (equal ctr o #ctr) ctr_specs;
|
blanchet@55519
|
958 |
val prems = the_default (maps (s_not_conj o #prems) disc_eqns)
|
panny@54857
|
959 |
(find_first (equal ctr_no o #ctr_no) disc_eqns |> Option.map #prems);
|
panny@54857
|
960 |
val sel_corec = find_index (equal sel) (#sels ctr_spec)
|
panny@54857
|
961 |
|> nth (#sel_corecs ctr_spec);
|
panny@54791
|
962 |
val k = 1 + ctr_no;
|
panny@54791
|
963 |
val m = length prems;
|
panny@54791
|
964 |
val t =
|
panny@54857
|
965 |
list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0))
|
panny@54857
|
966 |
|> curry betapply sel
|
panny@54857
|
967 |
|> rpair (abstract (List.rev fun_args) rhs_term)
|
panny@54857
|
968 |
|> HOLogic.mk_Trueprop o HOLogic.mk_eq
|
panny@54791
|
969 |
|> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
|
panny@54857
|
970 |
|> curry Logic.list_all (map dest_Free fun_args);
|
blanchet@55062
|
971 |
val (distincts, _, sel_splits, sel_split_asms) = case_thms_of_term lthy [] rhs_term;
|
panny@54791
|
972 |
in
|
blanchet@55055
|
973 |
mk_primcorec_sel_tac lthy def_thms distincts sel_splits sel_split_asms nested_maps
|
blanchet@55047
|
974 |
nested_map_idents nested_map_comps sel_corec k m exclsss
|
panny@54791
|
975 |
|> K |> Goal.prove lthy [] [] t
|
blanchet@55628
|
976 |
|> Thm.close_derivation
|
panny@54857
|
977 |
|> pair sel
|
panny@54791
|
978 |
end;
|
panny@54791
|
979 |
|
blanchet@55605
|
980 |
fun prove_ctr disc_alist sel_alist (disc_eqns : coeqn_data_disc list)
|
blanchet@55605
|
981 |
(sel_eqns : coeqn_data_sel list) ({ctr, disc, sels, collapse, ...} : corec_ctr_spec) =
|
panny@55549
|
982 |
(* don't try to prove theorems when some sel_eqns are missing *)
|
panny@54857
|
983 |
if not (exists (equal ctr o #ctr) disc_eqns)
|
panny@54859
|
984 |
andalso not (exists (equal ctr o #ctr) sel_eqns)
|
panny@55549
|
985 |
orelse
|
panny@54857
|
986 |
filter (equal ctr o #ctr) sel_eqns
|
panny@54857
|
987 |
|> fst o finds ((op =) o apsnd #sel) sels
|
panny@54857
|
988 |
|> exists (null o snd)
|
panny@54857
|
989 |
then [] else
|
panny@54857
|
990 |
let
|
panny@55549
|
991 |
val (fun_name, fun_T, fun_args, prems, maybe_rhs) =
|
panny@54859
|
992 |
(find_first (equal ctr o #ctr) disc_eqns, find_first (equal ctr o #ctr) sel_eqns)
|
panny@55549
|
993 |
|>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #prems x,
|
panny@55549
|
994 |
#maybe_ctr_rhs x))
|
panny@55549
|
995 |
||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, [], NONE))
|
panny@54859
|
996 |
|> the o merge_options;
|
panny@54857
|
997 |
val m = length prems;
|
panny@55549
|
998 |
val t = (if is_some maybe_rhs then the maybe_rhs else
|
panny@55549
|
999 |
filter (equal ctr o #ctr) sel_eqns
|
panny@55549
|
1000 |
|> fst o finds ((op =) o apsnd #sel) sels
|
panny@55549
|
1001 |
|> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x)) #-> abstract)
|
panny@55549
|
1002 |
|> curry list_comb ctr)
|
panny@54857
|
1003 |
|> curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
|
panny@54857
|
1004 |
map Bound (length fun_args - 1 downto 0)))
|
panny@54857
|
1005 |
|> HOLogic.mk_Trueprop
|
panny@54857
|
1006 |
|> curry Logic.list_implies (map HOLogic.mk_Trueprop prems)
|
panny@54857
|
1007 |
|> curry Logic.list_all (map dest_Free fun_args);
|
blanchet@54928
|
1008 |
val maybe_disc_thm = AList.lookup (op =) disc_alist disc;
|
blanchet@54928
|
1009 |
val sel_thms = map snd (filter (member (op =) sels o fst) sel_alist);
|
panny@54857
|
1010 |
in
|
panny@55549
|
1011 |
if prems = [@{term False}] then [] else
|
panny@55549
|
1012 |
mk_primcorec_ctr_of_dtr_tac lthy m collapse maybe_disc_thm sel_thms
|
panny@55549
|
1013 |
|> K |> Goal.prove lthy [] [] t
|
blanchet@55628
|
1014 |
|> Thm.close_derivation
|
panny@55549
|
1015 |
|> pair ctr
|
panny@55549
|
1016 |
|> single
|
panny@55013
|
1017 |
end;
|
panny@54857
|
1018 |
|
blanchet@55630
|
1019 |
fun prove_code disc_eqns sel_eqns ctr_alist ctr_specs =
|
panny@55550
|
1020 |
let
|
panny@55549
|
1021 |
val (fun_name, fun_T, fun_args, maybe_rhs) =
|
panny@55549
|
1022 |
(find_first (member (op =) (map #ctr ctr_specs) o #ctr) disc_eqns,
|
panny@55549
|
1023 |
find_first (member (op =) (map #ctr ctr_specs) o #ctr) sel_eqns)
|
panny@55549
|
1024 |
|>> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, #maybe_code_rhs x))
|
panny@55549
|
1025 |
||> Option.map (fn x => (#fun_name x, #fun_T x, #fun_args x, NONE))
|
panny@55549
|
1026 |
|> the o merge_options;
|
panny@55549
|
1027 |
|
blanchet@55625
|
1028 |
val bound_Ts = List.rev (map fastype_of fun_args);
|
blanchet@55625
|
1029 |
|
panny@55572
|
1030 |
val lhs = list_comb (Free (fun_name, fun_T), map Bound (length fun_args - 1 downto 0));
|
blanchet@55625
|
1031 |
val maybe_rhs_info =
|
blanchet@55625
|
1032 |
(case maybe_rhs of
|
blanchet@55625
|
1033 |
SOME rhs =>
|
blanchet@55625
|
1034 |
let
|
blanchet@55625
|
1035 |
val raw_rhs = expand_corec_code_rhs lthy has_call bound_Ts rhs;
|
blanchet@55625
|
1036 |
val cond_ctrs =
|
blanchet@55625
|
1037 |
fold_rev_corec_code_rhs lthy (K oo (cons oo pair)) bound_Ts raw_rhs [];
|
blanchet@55625
|
1038 |
val ctr_thms = map (the o AList.lookup (op =) ctr_alist o snd) cond_ctrs;
|
blanchet@55625
|
1039 |
in SOME (rhs, raw_rhs, ctr_thms) end
|
blanchet@55625
|
1040 |
| NONE =>
|
blanchet@55625
|
1041 |
let
|
blanchet@55625
|
1042 |
fun prove_code_ctr {ctr, sels, ...} =
|
blanchet@55625
|
1043 |
if not (exists (equal ctr o fst) ctr_alist) then NONE else
|
blanchet@55625
|
1044 |
let
|
blanchet@55625
|
1045 |
val prems = find_first (equal ctr o #ctr) disc_eqns
|
blanchet@55625
|
1046 |
|> Option.map #prems |> the_default [];
|
blanchet@55625
|
1047 |
val t =
|
blanchet@55625
|
1048 |
filter (equal ctr o #ctr) sel_eqns
|
blanchet@55625
|
1049 |
|> fst o finds ((op =) o apsnd #sel) sels
|
blanchet@55625
|
1050 |
|> map (snd #> (fn [x] => (List.rev (#fun_args x), #rhs_term x))
|
blanchet@55625
|
1051 |
#-> abstract)
|
blanchet@55625
|
1052 |
|> curry list_comb ctr;
|
blanchet@55625
|
1053 |
in
|
blanchet@55625
|
1054 |
SOME (prems, t)
|
blanchet@55625
|
1055 |
end;
|
blanchet@55625
|
1056 |
val maybe_ctr_conds_argss = map prove_code_ctr ctr_specs;
|
blanchet@55625
|
1057 |
in
|
blanchet@55625
|
1058 |
if exists is_none maybe_ctr_conds_argss then NONE else
|
blanchet@55625
|
1059 |
let
|
blanchet@55625
|
1060 |
val rhs = fold_rev (fn SOME (prems, u) => fn t => mk_If (s_conjs prems) u t)
|
blanchet@55625
|
1061 |
maybe_ctr_conds_argss
|
blanchet@55625
|
1062 |
(Const (@{const_name Code.abort}, @{typ String.literal} -->
|
blanchet@55625
|
1063 |
(@{typ unit} --> body_type fun_T) --> body_type fun_T) $
|
blanchet@55630
|
1064 |
HOLogic.mk_literal fun_name $
|
blanchet@55625
|
1065 |
absdummy @{typ unit} (incr_boundvars 1 lhs));
|
blanchet@55625
|
1066 |
in SOME (rhs, rhs, map snd ctr_alist) end
|
blanchet@55625
|
1067 |
end);
|
blanchet@55625
|
1068 |
in
|
blanchet@55625
|
1069 |
(case maybe_rhs_info of
|
blanchet@55625
|
1070 |
NONE => []
|
blanchet@55625
|
1071 |
| SOME (rhs, raw_rhs, ctr_thms) =>
|
panny@55549
|
1072 |
let
|
panny@55549
|
1073 |
val ms = map (Logic.count_prems o prop_of) ctr_thms;
|
blanchet@55624
|
1074 |
val (raw_t, t) = (raw_rhs, rhs)
|
blanchet@55624
|
1075 |
|> pairself
|
blanchet@55624
|
1076 |
(curry HOLogic.mk_eq (list_comb (Free (fun_name, fun_T),
|
blanchet@55624
|
1077 |
map Bound (length fun_args - 1 downto 0)))
|
blanchet@55624
|
1078 |
#> HOLogic.mk_Trueprop
|
blanchet@55624
|
1079 |
#> curry Logic.list_all (map dest_Free fun_args));
|
panny@55550
|
1080 |
val (distincts, discIs, sel_splits, sel_split_asms) =
|
blanchet@55624
|
1081 |
case_thms_of_term lthy bound_Ts raw_rhs;
|
panny@55550
|
1082 |
|
blanchet@55624
|
1083 |
val raw_code_thm = mk_primcorec_raw_code_of_ctr_tac lthy distincts discIs sel_splits
|
panny@55549
|
1084 |
sel_split_asms ms ctr_thms
|
blanchet@55628
|
1085 |
|> K |> Goal.prove lthy [] [] raw_t
|
blanchet@55628
|
1086 |
|> Thm.close_derivation;
|
blanchet@55624
|
1087 |
in
|
blanchet@55626
|
1088 |
mk_primcorec_code_of_raw_code_tac lthy distincts sel_splits raw_code_thm
|
blanchet@55624
|
1089 |
|> K |> Goal.prove lthy [] [] t
|
blanchet@55628
|
1090 |
|> Thm.close_derivation
|
blanchet@55624
|
1091 |
|> single
|
blanchet@55625
|
1092 |
end)
|
blanchet@55625
|
1093 |
end;
|
panny@55549
|
1094 |
|
blanchet@54928
|
1095 |
val disc_alists = map3 (maps oo prove_disc) corec_specs exclssss disc_eqnss;
|
blanchet@54928
|
1096 |
val sel_alists = map4 (map ooo prove_sel) corec_specs disc_eqnss exclssss sel_eqnss;
|
blanchet@54928
|
1097 |
val disc_thmss = map (map snd) disc_alists;
|
blanchet@54928
|
1098 |
val sel_thmss = map (map snd) sel_alists;
|
panny@55549
|
1099 |
|
panny@55549
|
1100 |
val ctr_alists = map5 (maps oooo prove_ctr) disc_alists sel_alists disc_eqnss sel_eqnss
|
blanchet@55630
|
1101 |
ctr_specss;
|
panny@55549
|
1102 |
val ctr_thmss = map (map snd) ctr_alists;
|
panny@55549
|
1103 |
|
blanchet@55630
|
1104 |
val code_thmss = map4 prove_code disc_eqnss sel_eqnss ctr_alists ctr_specss;
|
blanchet@54928
|
1105 |
|
blanchet@55167
|
1106 |
val simp_thmss = map2 append disc_thmss sel_thmss
|
blanchet@54932
|
1107 |
|
blanchet@54934
|
1108 |
val common_name = mk_common_name fun_names;
|
blanchet@54934
|
1109 |
|
blanchet@54928
|
1110 |
val notes =
|
blanchet@54967
|
1111 |
[(coinductN, map (if n2m then single else K []) coinduct_thms, []),
|
blanchet@55597
|
1112 |
(codeN, code_thmss, code_nitpicksimp_attrs),
|
blanchet@54934
|
1113 |
(ctrN, ctr_thmss, []),
|
blanchet@54928
|
1114 |
(discN, disc_thmss, simp_attrs),
|
blanchet@54932
|
1115 |
(selN, sel_thmss, simp_attrs),
|
blanchet@54934
|
1116 |
(simpsN, simp_thmss, []),
|
blanchet@54967
|
1117 |
(strong_coinductN, map (if n2m then single else K []) strong_coinduct_thms, [])]
|
blanchet@54928
|
1118 |
|> maps (fn (thmN, thmss, attrs) =>
|
blanchet@54928
|
1119 |
map2 (fn fun_name => fn thms =>
|
blanchet@54928
|
1120 |
((Binding.qualify true fun_name (Binding.name thmN), attrs), [(thms, [])]))
|
blanchet@54967
|
1121 |
fun_names (take actual_nn thmss))
|
blanchet@54928
|
1122 |
|> filter_out (null o fst o hd o snd);
|
blanchet@54934
|
1123 |
|
blanchet@54934
|
1124 |
val common_notes =
|
blanchet@54967
|
1125 |
[(coinductN, if n2m then [coinduct_thm] else [], []),
|
blanchet@54967
|
1126 |
(strong_coinductN, if n2m then [strong_coinduct_thm] else [], [])]
|
blanchet@54934
|
1127 |
|> filter_out (null o #2)
|
blanchet@54934
|
1128 |
|> map (fn (thmN, thms, attrs) =>
|
blanchet@54934
|
1129 |
((Binding.qualify true common_name (Binding.name thmN), attrs), [(thms, [])]));
|
panny@54791
|
1130 |
in
|
blanchet@55167
|
1131 |
lthy |> Local_Theory.notes (notes @ common_notes) |> snd
|
panny@54791
|
1132 |
end;
|
panny@54959
|
1133 |
|
panny@54959
|
1134 |
fun after_qed thmss' = fold_map Local_Theory.define defs #-> prove thmss';
|
blanchet@54440
|
1135 |
in
|
blanchet@55629
|
1136 |
(goalss, after_qed, lthy')
|
panny@54959
|
1137 |
end;
|
blanchet@54440
|
1138 |
|
blanchet@55629
|
1139 |
fun add_primcorec_ursive_cmd maybe_tac seq (raw_fixes, raw_specs') lthy =
|
blanchet@54440
|
1140 |
let
|
blanchet@55661
|
1141 |
val (raw_specs, maybe_of_specs) =
|
blanchet@55661
|
1142 |
split_list raw_specs' ||> map (Option.map (Syntax.read_term lthy));
|
panny@54968
|
1143 |
val ((fixes, specs), _) = Specification.read_spec raw_fixes raw_specs lthy;
|
blanchet@54440
|
1144 |
in
|
blanchet@55661
|
1145 |
add_primcorec_ursive maybe_tac seq fixes specs maybe_of_specs lthy
|
blanchet@55698
|
1146 |
handle ERROR str => primcorec_error str
|
blanchet@54440
|
1147 |
end
|
blanchet@55698
|
1148 |
handle Primcorec_Error (str, eqns) =>
|
blanchet@54440
|
1149 |
if null eqns
|
blanchet@54440
|
1150 |
then error ("primcorec error:\n " ^ str)
|
blanchet@54440
|
1151 |
else error ("primcorec error:\n " ^ str ^ "\nin\n " ^
|
panny@54959
|
1152 |
space_implode "\n " (map (quote o Syntax.string_of_term lthy) eqns));
|
panny@54959
|
1153 |
|
blanchet@55629
|
1154 |
val add_primcorecursive_cmd = (fn (goalss, after_qed, lthy) =>
|
blanchet@55629
|
1155 |
lthy
|
blanchet@55629
|
1156 |
|> Proof.theorem NONE after_qed goalss
|
blanchet@55629
|
1157 |
|> Proof.refine (Method.primitive_text I)
|
blanchet@55629
|
1158 |
|> Seq.hd) ooo add_primcorec_ursive_cmd NONE;
|
blanchet@55629
|
1159 |
|
blanchet@55629
|
1160 |
val add_primcorec_cmd = (fn (goalss, after_qed, lthy) =>
|
blanchet@55629
|
1161 |
lthy
|
blanchet@55629
|
1162 |
|> after_qed (map (fn [] => []
|
blanchet@55698
|
1163 |
| _ => primcorec_error "need exclusiveness proofs - use primcorecursive instead of primcorec")
|
blanchet@55629
|
1164 |
goalss)) ooo add_primcorec_ursive_cmd (SOME (fn {context = ctxt, ...} => auto_tac ctxt));
|
blanchet@54440
|
1165 |
|
blanchet@54440
|
1166 |
end;
|