isabelle: comparison src/HOL/ex/predicate

equal deleted inserted replaced

-:fd96d5f49d59
+:09546e654222
-(* Author: Lukas Bulwahn, TU Muenchen
-(Prototype of) A compiler from predicates specified by intro/elim rules
-to equations.
-*)
-signature PREDICATE_COMPILE =
-sig
-type smode = (int * int list option) list
-type mode = smode option list * smode
-datatype tmode = Mode of mode * smode * tmode option list;
-(*val add_equations_of: bool -> string list -> theory -> theory *)
-val register_predicate : (thm list * thm * int) -> theory -> theory
-val is_registered : theory -> string -> bool
-(* val fetch_pred_data : theory -> string -> (thm list * thm * int)  *)
-val predfun_intro_of: theory -> string -> mode -> thm
-val predfun_elim_of: theory -> string -> mode -> thm
-val strip_intro_concl: int -> term -> term * (term list * term list)
-val predfun_name_of: theory -> string -> mode -> string
-val all_preds_of : theory -> string list
-val modes_of: theory -> string -> mode list
-val string_of_mode : mode -> string
-val intros_of: theory -> string -> thm list
-val nparams_of: theory -> string -> int
-val add_intro: thm -> theory -> theory
-val set_elim: thm -> theory -> theory
-val setup: theory -> theory
-val code_pred: string -> Proof.context -> Proof.state
-val code_pred_cmd: string -> Proof.context -> Proof.state
-val print_stored_rules: theory -> unit
-val print_all_modes: theory -> unit
-val do_proofs: bool ref
-val mk_casesrule : Proof.context -> int -> thm list -> term
-val analyze_compr: theory -> term -> term
-val eval_ref: (unit -> term Predicate.pred) option ref
-val add_equations : string list -> theory -> theory
-val code_pred_intros_attrib : attribute
-(* used by Quickcheck_Generator *)
-(*val funT_of : mode -> typ -> typ
-val mk_if_pred : term -> term
-val mk_Eval : term * term -> term*)
-val mk_tupleT : typ list -> typ
-(*  val mk_predT :  typ -> typ *)
-(* temporary for testing of the compilation *)
-datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term |
-GeneratorPrem of term list * term | Generator of (string * typ);
-(* val prepare_intrs: theory -> string list ->
-(string * typ) list * int * string list * string list * (string * mode list) list *
-(string * (term list * indprem list) list) list * (string * (int option list * int)) list*)
-datatype compilation_funs = CompilationFuns of {
-mk_predT : typ -> typ,
-dest_predT : typ -> typ,
-mk_bot : typ -> term,
-mk_single : term -> term,
-mk_bind : term * term -> term,
-mk_sup : term * term -> term,
-mk_if : term -> term,
-mk_not : term -> term,
-mk_map : typ -> typ -> term -> term -> term,
-lift_pred : term -> term
-};
-type moded_clause = term list * (indprem * tmode) list
-type 'a pred_mode_table = (string * (mode * 'a) list) list
-val infer_modes : theory -> (string * mode list) list
--> (string * mode list) list
--> string list
--> (string * (term list * indprem list) list) list
--> (moded_clause list) pred_mode_table
-val infer_modes_with_generator : theory -> (string * mode list) list
--> (string * mode list) list
--> string list
--> (string * (term list * indprem list) list) list
--> (moded_clause list) pred_mode_table
-(*val compile_preds : theory -> compilation_funs -> string list -> string list
--> (string * typ) list -> (moded_clause list) pred_mode_table -> term pred_mode_table
-val rpred_create_definitions :(string * typ) list -> string * mode list
--> theory -> theory
-val split_smode : int list -> term list -> (term list * term list) *)
-val print_moded_clauses :
-theory -> (moded_clause list) pred_mode_table -> unit
-val print_compiled_terms : theory -> term pred_mode_table -> unit
-(*val rpred_prove_preds : theory -> term pred_mode_table -> thm pred_mode_table*)
-val rpred_compfuns : compilation_funs
-val dest_funT : typ -> typ * typ
-(* val depending_preds_of : theory -> thm list -> string list *)
-val add_quickcheck_equations : string list -> theory -> theory
-val add_sizelim_equations : string list -> theory -> theory
-val is_inductive_predicate : theory -> string -> bool
-val terms_vs : term list -> string list
-val subsets : int -> int -> int list list
-val check_mode_clause : bool -> theory -> string list ->
-(string * mode list) list -> (string * mode list) list -> mode -> (term list * indprem list)
--> (term list * (indprem * tmode) list) option
-val string_of_moded_prem : theory -> (indprem * tmode) -> string
-val all_modes_of : theory -> (string * mode list) list
-val all_generator_modes_of : theory -> (string * mode list) list
-val compile_clause : compilation_funs -> term option -> (term list -> term) ->
-theory -> string list -> string list -> mode -> term -> moded_clause -> term
-val preprocess_intro : theory -> thm -> thm
-val is_constrt : theory -> term -> bool
-val is_predT : typ -> bool
-val guess_nparams : typ -> int
-val cprods_subset : 'a list list -> 'a list list
-end;
-structure Predicate_Compile : PREDICATE_COMPILE =
-struct
-(** auxiliary **)
-(* debug stuff *)
-fun tracing s = (if ! Toplevel.debug then Output.tracing s else ());
-fun print_tac s = Seq.single; (*Tactical.print_tac s;*) (* (if ! Toplevel.debug then Tactical.print_tac s else Seq.single); *)
-fun debug_tac msg = Seq.single; (* (fn st => (Output.tracing msg; Seq.single st)); *)
-val do_proofs = ref true;
-fun mycheat_tac thy i st =
-(Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) i) st
-fun remove_last_goal thy st =
-(Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) (nprems_of st)) st
-(* reference to preprocessing of InductiveSet package *)
-val ind_set_codegen_preproc = Inductive_Set.codegen_preproc;
-(** fundamentals **)
-(* syntactic operations *)
-fun mk_eq (x, xs) =
-let fun mk_eqs _ [] = []
-| mk_eqs a (b::cs) =
-HOLogic.mk_eq (Free (a, fastype_of b), b) :: mk_eqs a cs
-in mk_eqs x xs end;
-fun mk_tupleT [] = HOLogic.unitT
-| mk_tupleT Ts = foldr1 HOLogic.mk_prodT Ts;
-fun dest_tupleT (Type (@{type_name Product_Type.unit}, [])) = []
-| dest_tupleT (Type (@{type_name "*"}, [T1, T2])) = T1 :: (dest_tupleT T2)
-| dest_tupleT t = [t]
-fun mk_tuple [] = HOLogic.unit
-| mk_tuple ts = foldr1 HOLogic.mk_prod ts;
-fun dest_tuple (Const (@{const_name Product_Type.Unity}, _)) = []
-| dest_tuple (Const (@{const_name Pair}, _) $ t1 $ t2) = t1 :: (dest_tuple t2)
-| dest_tuple t = [t]
-fun mk_scomp (t, u) =
-let
-val T = fastype_of t
-val U = fastype_of u
-val [A] = binder_types T
-val D = body_type U
-in
-Const (@{const_name "scomp"}, T --> U --> A --> D) $ t $ u
-end;
-fun dest_funT (Type ("fun",[S, T])) = (S, T)
-| dest_funT T = raise TYPE ("dest_funT", [T], [])
-fun mk_fun_comp (t, u) =
-let
-val (_, B) = dest_funT (fastype_of t)
-val (C, A) = dest_funT (fastype_of u)
-in
-Const(@{const_name "Fun.comp"}, (A --> B) --> (C --> A) --> C --> B) $ t $ u
-end;
-fun dest_randomT (Type ("fun", [@{typ Random.seed},
-Type ("*", [Type ("*", [T, @{typ "unit => Code_Eval.term"}]) ,@{typ Random.seed}])])) = T
-| dest_randomT T = raise TYPE ("dest_randomT", [T], [])
-(* destruction of intro rules *)
-(* FIXME: look for other place where this functionality was used before *)
-fun strip_intro_concl nparams intro = let
-val _ $ u = Logic.strip_imp_concl intro
-val (pred, all_args) = strip_comb u
-val (params, args) = chop nparams all_args
-in (pred, (params, args)) end
-(** data structures **)
-type smode = (int * int list option) list;
-type mode = smode option list * smode;
-datatype tmode = Mode of mode * smode * tmode option list;
-fun gen_split_smode (mk_tuple, strip_tuple) smode ts =
-let
-fun split_tuple' _ _ [] = ([], [])
-| split_tuple' is i (t::ts) =
-(if i mem is then apfst else apsnd) (cons t)
-(split_tuple' is (i+1) ts)
-fun split_tuple is t = split_tuple' is 1 (strip_tuple t)
-fun split_smode' _ _ [] = ([], [])
-| split_smode' smode i (t::ts) =
-(if i mem (map fst smode) then
-case (the (AList.lookup (op =) smode i)) of
-NONE => apfst (cons t)
-| SOME is =>
-let
-val (ts1, ts2) = split_tuple is t
-fun cons_tuple ts = if null ts then I else cons (mk_tuple ts)
-in (apfst (cons_tuple ts1)) o (apsnd (cons_tuple ts2)) end
-else apsnd (cons t))
-(split_smode' smode (i+1) ts)
-in split_smode' smode 1 ts end
-val split_smode = gen_split_smode (HOLogic.mk_tuple, HOLogic.strip_tuple)
-val split_smodeT = gen_split_smode (HOLogic.mk_tupleT, HOLogic.strip_tupleT)
-fun gen_split_mode split_smode (iss, is) ts =
-let
-val (t1, t2) = chop (length iss) ts
-in (t1, split_smode is t2) end
-val split_mode = gen_split_mode split_smode
-val split_modeT = gen_split_mode split_smodeT
-fun string_of_smode js =
-commas (map
-(fn (i, is) =>
-string_of_int i ^ (case is of NONE => ""
-| SOME is => "p" ^ enclose "[" "]" (commas (map string_of_int is)))) js)
-fun string_of_mode (iss, is) = space_implode " -> " (map
-(fn NONE => "X"
-| SOME js => enclose "[" "]" (string_of_smode js))
-(iss @ [SOME is]));
-fun string_of_tmode (Mode (predmode, termmode, param_modes)) =
-"predmode: " ^ (string_of_mode predmode) ^
-(if null param_modes then "" else
-"; " ^ "params: " ^ commas (map (the_default "NONE" o Option.map string_of_tmode) param_modes))
-datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term |
-GeneratorPrem of term list * term | Generator of (string * typ);
-type moded_clause = term list * (indprem * tmode) list
-type 'a pred_mode_table = (string * (mode * 'a) list) list
-datatype predfun_data = PredfunData of {
-name : string,
-definition : thm,
-intro : thm,
-elim : thm
-};
-fun rep_predfun_data (PredfunData data) = data;
-fun mk_predfun_data (name, definition, intro, elim) =
-PredfunData {name = name, definition = definition, intro = intro, elim = elim}
-datatype function_data = FunctionData of {
-name : string,
-equation : thm option (* is not used at all? *)
-};
-fun rep_function_data (FunctionData data) = data;
-fun mk_function_data (name, equation) =
-FunctionData {name = name, equation = equation}
-datatype pred_data = PredData of {
-intros : thm list,
-elim : thm option,
-nparams : int,
-functions : (mode * predfun_data) list,
-generators : (mode * function_data) list,
-sizelim_functions : (mode * function_data) list
-};
-fun rep_pred_data (PredData data) = data;
-fun mk_pred_data ((intros, elim, nparams), (functions, generators, sizelim_functions)) =
-PredData {intros = intros, elim = elim, nparams = nparams,
-functions = functions, generators = generators, sizelim_functions = sizelim_functions}
-fun map_pred_data f (PredData {intros, elim, nparams, functions, generators, sizelim_functions}) =
-mk_pred_data (f ((intros, elim, nparams), (functions, generators, sizelim_functions)))
-fun eq_option eq (NONE, NONE) = true
-| eq_option eq (SOME x, SOME y) = eq (x, y)
-| eq_option eq _ = false
-fun eq_pred_data (PredData d1, PredData d2) =
-eq_list (Thm.eq_thm) (#intros d1, #intros d2) andalso
-eq_option (Thm.eq_thm) (#elim d1, #elim d2) andalso
-#nparams d1 = #nparams d2
-structure PredData = TheoryDataFun
-(
-type T = pred_data Graph.T;
-val empty = Graph.empty;
-val copy = I;
-val extend = I;
-fun merge _ = Graph.merge eq_pred_data;
-);
-(* queries *)
-fun lookup_pred_data thy name =
-Option.map rep_pred_data (try (Graph.get_node (PredData.get thy)) name)
-fun the_pred_data thy name = case lookup_pred_data thy name
-of NONE => error ("No such predicate " ^ quote name)
-| SOME data => data;
-val is_registered = is_some oo lookup_pred_data
-val all_preds_of = Graph.keys o PredData.get
-fun intros_of thy = map (Thm.transfer thy) o #intros o the_pred_data thy
-fun the_elim_of thy name = case #elim (the_pred_data thy name)
-of NONE => error ("No elimination rule for predicate " ^ quote name)
-| SOME thm => Thm.transfer thy thm
-val has_elim = is_some o #elim oo the_pred_data;
-val nparams_of = #nparams oo the_pred_data
-val modes_of = (map fst) o #functions oo the_pred_data
-fun all_modes_of thy = map (fn name => (name, modes_of thy name)) (all_preds_of thy)
-val is_compiled = not o null o #functions oo the_pred_data
-fun lookup_predfun_data thy name mode =
-Option.map rep_predfun_data (AList.lookup (op =)
-(#functions (the_pred_data thy name)) mode)
-fun the_predfun_data thy name mode = case lookup_predfun_data thy name mode
-of NONE => error ("No function defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name)
-| SOME data => data;
-val predfun_name_of = #name ooo the_predfun_data
-val predfun_definition_of = #definition ooo the_predfun_data
-val predfun_intro_of = #intro ooo the_predfun_data
-val predfun_elim_of = #elim ooo the_predfun_data
-fun lookup_generator_data thy name mode =
-Option.map rep_function_data (AList.lookup (op =)
-(#generators (the_pred_data thy name)) mode)
-fun the_generator_data thy name mode = case lookup_generator_data thy name mode
-of NONE => error ("No generator defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name)
-| SOME data => data
-val generator_name_of = #name ooo the_generator_data
-val generator_modes_of = (map fst) o #generators oo the_pred_data
-fun all_generator_modes_of thy =
-map (fn name => (name, generator_modes_of thy name)) (all_preds_of thy)
-fun lookup_sizelim_function_data thy name mode =
-Option.map rep_function_data (AList.lookup (op =)
-(#sizelim_functions (the_pred_data thy name)) mode)
-fun the_sizelim_function_data thy name mode = case lookup_sizelim_function_data thy name mode
-of NONE => error ("No size-limited function defined for mode " ^ string_of_mode mode
-^ " of predicate " ^ name)
-| SOME data => data
-val sizelim_function_name_of = #name ooo the_sizelim_function_data
-(*val generator_modes_of = (map fst) o #generators oo the_pred_data*)
-(* diagnostic display functions *)
-fun print_modes modes = Output.tracing ("Inferred modes:\n" ^
-cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
-string_of_mode ms)) modes));
-fun print_pred_mode_table string_of_entry thy pred_mode_table =
-let
-fun print_mode pred (mode, entry) =  "mode : " ^ (string_of_mode mode)
-^ (string_of_entry pred mode entry)
-fun print_pred (pred, modes) =
-"predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes)
-val _ = Output.tracing (cat_lines (map print_pred pred_mode_table))
-in () end;
-fun string_of_moded_prem thy (Prem (ts, p), tmode) =
-(Syntax.string_of_term_global thy (list_comb (p, ts))) ^
-"(" ^ (string_of_tmode tmode) ^ ")"
-| string_of_moded_prem thy (GeneratorPrem (ts, p), Mode (predmode, is, _)) =
-(Syntax.string_of_term_global thy (list_comb (p, ts))) ^
-"(generator_mode: " ^ (string_of_mode predmode) ^ ")"
-| string_of_moded_prem thy (Generator (v, T), _) =
-"Generator for " ^ v ^ " of Type " ^ (Syntax.string_of_typ_global thy T)
-| string_of_moded_prem thy (Negprem (ts, p), Mode (_, is, _)) =
-(Syntax.string_of_term_global thy (list_comb (p, ts))) ^
-"(negative mode: " ^ string_of_smode is ^ ")"
-| string_of_moded_prem thy (Sidecond t, Mode (_, is, _)) =
-(Syntax.string_of_term_global thy t) ^
-"(sidecond mode: " ^ string_of_smode is ^ ")"
-| string_of_moded_prem _ _ = error "string_of_moded_prem: unimplemented"
-fun print_moded_clauses thy =
-let
-fun string_of_clause pred mode clauses =
-cat_lines (map (fn (ts, prems) => (space_implode " --> "
-(map (string_of_moded_prem thy) prems)) ^ " --> " ^ pred ^ " "
-^ (space_implode " " (map (Syntax.string_of_term_global thy) ts))) clauses)
-in print_pred_mode_table string_of_clause thy end;
-fun print_compiled_terms thy =
-print_pred_mode_table (fn _ => fn _ => Syntax.string_of_term_global thy) thy
-fun print_stored_rules thy =
-let
-val preds = (Graph.keys o PredData.get) thy
-fun print pred () = let
-val _ = writeln ("predicate: " ^ pred)
-val _ = writeln ("number of parameters: " ^ string_of_int (nparams_of thy pred))
-val _ = writeln ("introrules: ")
-val _ = fold (fn thm => fn u => writeln (Display.string_of_thm_global thy thm))
-(rev (intros_of thy pred)) ()
-in
-if (has_elim thy pred) then
-writeln ("elimrule: " ^ Display.string_of_thm_global thy (the_elim_of thy pred))
-else
-writeln ("no elimrule defined")
-end
-in
-fold print preds ()
-end;
-fun print_all_modes thy =
-let
-val _ = writeln ("Inferred modes:")
-fun print (pred, modes) u =
-let
-val _ = writeln ("predicate: " ^ pred)
-val _ = writeln ("modes: " ^ (commas (map string_of_mode modes)))
-in u end
-in
-fold print (all_modes_of thy) ()
-end
-(** preprocessing rules **)
-fun imp_prems_conv cv ct =
-case Thm.term_of ct of
-Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct
-| _ => Conv.all_conv ct
-fun Trueprop_conv cv ct =
-case Thm.term_of ct of
-Const ("Trueprop", _) $ _ => Conv.arg_conv cv ct
-| _ => error "Trueprop_conv"
-fun preprocess_intro thy rule =
-Conv.fconv_rule
-(imp_prems_conv
-(Trueprop_conv (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq})))))
-(Thm.transfer thy rule)
-fun preprocess_elim thy nparams elimrule =
-let
-val _ = Output.tracing ("Preprocessing elimination rule "
-^ (Display.string_of_thm_global thy elimrule))
-fun replace_eqs (Const ("Trueprop", _) $ (Const ("op =", T) $ lhs $ rhs)) =
-HOLogic.mk_Trueprop (Const (@{const_name Predicate.eq}, T) $ lhs $ rhs)
-| replace_eqs t = t
-val prems = Thm.prems_of elimrule
-val nargs = length (snd (strip_comb (HOLogic.dest_Trueprop (hd prems)))) - nparams
-fun preprocess_case t =
-let
-val params = Logic.strip_params t
-val (assums1, assums2) = chop nargs (Logic.strip_assums_hyp t)
-val assums_hyp' = assums1 @ (map replace_eqs assums2)
-in
-list_all (params, Logic.list_implies (assums_hyp', Logic.strip_assums_concl t))
-end
-val cases' = map preprocess_case (tl prems)
-val elimrule' = Logic.list_implies ((hd prems) :: cases', Thm.concl_of elimrule)
-(*
-(*val _ =  Output.tracing ("elimrule': "^ (Syntax.string_of_term_global thy elimrule'))*)
-val bigeq = (Thm.symmetric (Conv.implies_concl_conv (MetaSimplifier.rewrite true [@{thm Predicate.eq_is_eq}])
-(cterm_of thy elimrule')))
-val _ = Output.tracing ("bigeq:" ^ (Display.string_of_thm_global thy bigeq))
-val res =
-Thm.equal_elim bigeq
-elimrule
-*)
-val t = (fn {...} => mycheat_tac thy 1)
-val eq = Goal.prove (ProofContext.init thy) [] [] (Logic.mk_equals ((Thm.prop_of elimrule), elimrule')) t
-val _ = Output.tracing "Preprocessed elimination rule"
-in
-Thm.equal_elim eq elimrule
-end;
-(* special case: predicate with no introduction rule *)
-fun noclause thy predname elim = let
-val T = (Logic.unvarifyT o Sign.the_const_type thy) predname
-val Ts = binder_types T
-val names = Name.variant_list []
-(map (fn i => "x" ^ (string_of_int i)) (1 upto (length Ts)))
-val vs = map2 (curry Free) names Ts
-val clausehd = HOLogic.mk_Trueprop (list_comb (Const (predname, T), vs))
-val intro_t = Logic.mk_implies (@{prop False}, clausehd)
-val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT))
-val elim_t = Logic.list_implies ([clausehd, Logic.mk_implies (@{prop False}, P)], P)
-val intro = Goal.prove (ProofContext.init thy) names [] intro_t
-(fn {...} => etac @{thm FalseE} 1)
-val elim = Goal.prove (ProofContext.init thy) ("P" :: names) [] elim_t
-(fn {...} => etac elim 1)
-in
-([intro], elim)
-end
-fun fetch_pred_data thy name =
-case try (Inductive.the_inductive (ProofContext.init thy)) name of
-SOME (info as (_, result)) =>
-let
-fun is_intro_of intro =
-let
-val (const, _) = strip_comb (HOLogic.dest_Trueprop (concl_of intro))
-in (fst (dest_Const const) = name) end;
-val intros = ind_set_codegen_preproc thy ((map (preprocess_intro thy))
-(filter is_intro_of (#intrs result)))
-val pre_elim = nth (#elims result) (find_index (fn s => s = name) (#names (fst info)))
-val nparams = length (Inductive.params_of (#raw_induct result))
-val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim)
-val (intros, elim) = if null intros then noclause thy name elim else (intros, elim)
-in
-mk_pred_data ((intros, SOME elim, nparams), ([], [], []))
-end
-| NONE => error ("No such predicate: " ^ quote name)
-(* updaters *)
-fun apfst3 f (x, y, z) =  (f x, y, z)
-fun apsnd3 f (x, y, z) =  (x, f y, z)
-fun aptrd3 f (x, y, z) =  (x, y, f z)
-fun add_predfun name mode data =
-let
-val add = (apsnd o apfst3 o cons) (mode, mk_predfun_data data)
-in PredData.map (Graph.map_node name (map_pred_data add)) end
-fun is_inductive_predicate thy name =
-is_some (try (Inductive.the_inductive (ProofContext.init thy)) name)
-fun depending_preds_of thy (key, value) =
-let
-val intros = (#intros o rep_pred_data) value
-in
-fold Term.add_const_names (map Thm.prop_of intros) []
-|> filter (fn c => (not (c = key)) andalso (is_inductive_predicate thy c orelse is_registered thy c))
-end;
-(* code dependency graph *)
-(*
-fun dependencies_of thy name =
-let
-val (intros, elim, nparams) = fetch_pred_data thy name
-val data = mk_pred_data ((intros, SOME elim, nparams), ([], [], []))
-val keys = depending_preds_of thy intros
-in
-(data, keys)
-end;
-*)
-(* guessing number of parameters *)
-fun find_indexes pred xs =
-let
-fun find is n [] = is
-| find is n (x :: xs) = find (if pred x then (n :: is) else is) (n + 1) xs;
-in rev (find [] 0 xs) end;
-fun is_predT (T as Type("fun", [_, _])) = (snd (strip_type T) = HOLogic.boolT)
-| is_predT _ = false
-fun guess_nparams T =
-let
-val argTs = binder_types T
-val nparams = fold (curry Int.max)
-(map (fn x => x + 1) (find_indexes is_predT argTs)) 0
-in nparams end;
-fun add_intro thm thy = let
-val (name, T) = dest_Const (fst (strip_intro_concl 0 (prop_of thm)))
-fun cons_intro gr =
-case try (Graph.get_node gr) name of
-SOME pred_data => Graph.map_node name (map_pred_data
-(apfst (fn (intro, elim, nparams) => (thm::intro, elim, nparams)))) gr
-| NONE =>
-let
-val nparams = the_default (guess_nparams T)  (try (#nparams o rep_pred_data o (fetch_pred_data thy)) name)
-in Graph.new_node (name, mk_pred_data (([thm], NONE, nparams), ([], [], []))) gr end;
-in PredData.map cons_intro thy end
-fun set_elim thm = let
-val (name, _) = dest_Const (fst
-(strip_comb (HOLogic.dest_Trueprop (hd (prems_of thm)))))
-fun set (intros, _, nparams) = (intros, SOME thm, nparams)
-in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end
-fun set_nparams name nparams = let
-fun set (intros, elim, _ ) = (intros, elim, nparams)
-in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end
-fun register_predicate (pre_intros, pre_elim, nparams) thy = let
-val (name, _) = dest_Const (fst (strip_intro_concl nparams (prop_of (hd pre_intros))))
-(* preprocessing *)
-val intros = ind_set_codegen_preproc thy (map (preprocess_intro thy) pre_intros)
-val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim)
-in
-PredData.map
-(Graph.new_node (name, mk_pred_data ((intros, SOME elim, nparams), ([], [], [])))) thy
-end
-fun set_generator_name pred mode name =
-let
-val set = (apsnd o apsnd3 o cons) (mode, mk_function_data (name, NONE))
-in
-PredData.map (Graph.map_node pred (map_pred_data set))
-end
-fun set_sizelim_function_name pred mode name =
-let
-val set = (apsnd o aptrd3 o cons) (mode, mk_function_data (name, NONE))
-in
-PredData.map (Graph.map_node pred (map_pred_data set))
-end
-(** data structures for generic compilation for different monads **)
-(* maybe rename functions more generic:
-mk_predT -> mk_monadT; dest_predT -> dest_monadT
-mk_single -> mk_return (?)
-*)
-datatype compilation_funs = CompilationFuns of {
-mk_predT : typ -> typ,
-dest_predT : typ -> typ,
-mk_bot : typ -> term,
-mk_single : term -> term,
-mk_bind : term * term -> term,
-mk_sup : term * term -> term,
-mk_if : term -> term,
-mk_not : term -> term,
-(*  funT_of : mode -> typ -> typ, *)
-(*  mk_fun_of : theory -> (string * typ) -> mode -> term, *)
-mk_map : typ -> typ -> term -> term -> term,
-lift_pred : term -> term
-};
-fun mk_predT (CompilationFuns funs) = #mk_predT funs
-fun dest_predT (CompilationFuns funs) = #dest_predT funs
-fun mk_bot (CompilationFuns funs) = #mk_bot funs
-fun mk_single (CompilationFuns funs) = #mk_single funs
-fun mk_bind (CompilationFuns funs) = #mk_bind funs
-fun mk_sup (CompilationFuns funs) = #mk_sup funs
-fun mk_if (CompilationFuns funs) = #mk_if funs
-fun mk_not (CompilationFuns funs) = #mk_not funs
-(*fun funT_of (CompilationFuns funs) = #funT_of funs*)
-(*fun mk_fun_of (CompilationFuns funs) = #mk_fun_of funs*)
-fun mk_map (CompilationFuns funs) = #mk_map funs
-fun lift_pred (CompilationFuns funs) = #lift_pred funs
-fun funT_of compfuns (iss, is) T =
-let
-val Ts = binder_types T
-val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts
-val paramTs' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss paramTs
-in
-(paramTs' @ inargTs) ---> (mk_predT compfuns (mk_tupleT outargTs))
-end;
-fun sizelim_funT_of compfuns (iss, is) T =
-let
-val Ts = binder_types T
-val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts
-val paramTs' = map2 (fn SOME is => sizelim_funT_of compfuns ([], is) | NONE => I) iss paramTs
-in
-(paramTs' @ inargTs @ [@{typ "code_numeral"}]) ---> (mk_predT compfuns (mk_tupleT outargTs))
-end;
-fun mk_fun_of compfuns thy (name, T) mode =
-Const (predfun_name_of thy name mode, funT_of compfuns mode T)
-fun mk_sizelim_fun_of compfuns thy (name, T) mode =
-Const (sizelim_function_name_of thy name mode, sizelim_funT_of compfuns mode T)
-fun mk_generator_of compfuns thy (name, T) mode =
-Const (generator_name_of thy name mode, sizelim_funT_of compfuns mode T)
-structure PredicateCompFuns =
-struct
-fun mk_predT T = Type (@{type_name "Predicate.pred"}, [T])
-fun dest_predT (Type (@{type_name "Predicate.pred"}, [T])) = T
-| dest_predT T = raise TYPE ("dest_predT", [T], []);
-fun mk_bot T = Const (@{const_name Orderings.bot}, mk_predT T);
-fun mk_single t =
-let val T = fastype_of t
-in Const(@{const_name Predicate.single}, T --> mk_predT T) $ t end;
-fun mk_bind (x, f) =
-let val T as Type ("fun", [_, U]) = fastype_of f
-in
-Const (@{const_name Predicate.bind}, fastype_of x --> T --> U) $ x $ f
-end;
-val mk_sup = HOLogic.mk_binop @{const_name sup};
-fun mk_if cond = Const (@{const_name Predicate.if_pred},
-HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond;
-fun mk_not t = let val T = mk_predT HOLogic.unitT
-in Const (@{const_name Predicate.not_pred}, T --> T) $ t end
-fun mk_Enum f =
-let val T as Type ("fun", [T', _]) = fastype_of f
-in
-Const (@{const_name Predicate.Pred}, T --> mk_predT T') $ f
-end;
-fun mk_Eval (f, x) =
-let
-val T = fastype_of x
-in
-Const (@{const_name Predicate.eval}, mk_predT T --> T --> HOLogic.boolT) $ f $ x
-end;
-fun mk_map T1 T2 tf tp = Const (@{const_name Predicate.map},
-(T1 --> T2) --> mk_predT T1 --> mk_predT T2) $ tf $ tp;
-val lift_pred = I
-val compfuns = CompilationFuns {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot,
-mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not,
-mk_map = mk_map, lift_pred = lift_pred};
-end;
-(* termify_code:
-val termT = Type ("Code_Eval.term", []);
-fun termifyT T = HOLogic.mk_prodT (T, HOLogic.unitT --> termT)
-*)
-(*
-fun lift_random random =
-let
-val T = dest_randomT (fastype_of random)
-in
-mk_scomp (random,
-mk_fun_comp (HOLogic.pair_const (PredicateCompFuns.mk_predT T) @{typ Random.seed},
-mk_fun_comp (Const (@{const_name Predicate.single}, T --> (PredicateCompFuns.mk_predT T)),
-Const (@{const_name "fst"}, HOLogic.mk_prodT (T, @{typ "unit => term"}) --> T))))
-end;
-*)
-structure RPredCompFuns =
-struct
-fun mk_rpredT T =
-@{typ "Random.seed"} --> HOLogic.mk_prodT (PredicateCompFuns.mk_predT T, @{typ "Random.seed"})
-fun dest_rpredT (Type ("fun", [_,
-Type (@{type_name "*"}, [Type (@{type_name "Predicate.pred"}, [T]), _])])) = T
-| dest_rpredT T = raise TYPE ("dest_rpredT", [T], []);
-fun mk_bot T = Const(@{const_name RPred.bot}, mk_rpredT T)
-fun mk_single t =
-let
-val T = fastype_of t
-in
-Const (@{const_name RPred.return}, T --> mk_rpredT T) $ t
-end;
-fun mk_bind (x, f) =
-let
-val T as (Type ("fun", [_, U])) = fastype_of f
-in
-Const (@{const_name RPred.bind}, fastype_of x --> T --> U) $ x $ f
-end
-val mk_sup = HOLogic.mk_binop @{const_name RPred.supp}
-fun mk_if cond = Const (@{const_name RPred.if_rpred},
-HOLogic.boolT --> mk_rpredT HOLogic.unitT) $ cond;
-fun mk_not t = error "Negation is not defined for RPred"
-fun mk_map t = error "FIXME" (*FIXME*)
-fun lift_pred t =
-let
-val T = PredicateCompFuns.dest_predT (fastype_of t)
-val lift_predT = PredicateCompFuns.mk_predT T --> mk_rpredT T
-in
-Const (@{const_name "RPred.lift_pred"}, lift_predT) $ t
-end;
-val compfuns = CompilationFuns {mk_predT = mk_rpredT, dest_predT = dest_rpredT, mk_bot = mk_bot,
-mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not,
-mk_map = mk_map, lift_pred = lift_pred};
-end;
-(* for external use with interactive mode *)
-val rpred_compfuns = RPredCompFuns.compfuns;
-fun lift_random random =
-let
-val T = dest_randomT (fastype_of random)
-in
-Const (@{const_name lift_random}, (@{typ Random.seed} -->
-HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) -->
-RPredCompFuns.mk_rpredT T) $ random
-end;
-(* Mode analysis *)
-(*** check if a term contains only constructor functions ***)
-fun is_constrt thy =
-let
-val cnstrs = flat (maps
-(map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
-(Symtab.dest (Datatype.get_all thy)));
-fun check t = (case strip_comb t of
-(Free _, []) => true
-| (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of
-(SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts
-| _ => false)
-| _ => false)
-in check end;
-(*** check if a type is an equality type (i.e. doesn't contain fun)
-FIXME this is only an approximation ***)
-fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts
-| is_eqT _ = true;
-fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm [];
-val terms_vs = distinct (op =) o maps term_vs;
-(** collect all Frees in a term (with duplicates!) **)
-fun term_vTs tm =
-fold_aterms (fn Free xT => cons xT | _ => I) tm [];
-(*FIXME this function should not be named merge... make it local instead*)
-fun merge xs [] = xs
-| merge [] ys = ys
-| merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys)
-else y::merge (x::xs) ys;
-fun subsets i j = if i <= j then
-let val is = subsets (i+1) j
-in merge (map (fn ks => i::ks) is) is end
-else [[]];
-(* FIXME: should be in library - map_prod *)
-fun cprod ([], ys) = []
-| cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys);
-fun cprods xss = foldr (map op :: o cprod) [[]] xss;
-fun cprods_subset [] = [[]]
-| cprods_subset (xs :: xss) =
-let
-val yss = (cprods_subset xss)
-in maps (fn ys => map (fn x => cons x ys) xs) yss @ yss end
-(*TODO: cleanup function and put together with modes_of_term *)
-(*
-fun modes_of_param default modes t = let
-val (vs, t') = strip_abs t
-val b = length vs
-fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) =>
-let
-val (args1, args2) =
-if length args < length iss then
-error ("Too few arguments for inductive predicate " ^ name)
-else chop (length iss) args;
-val k = length args2;
-val perm = map (fn i => (find_index_eq (Bound (b - i)) args2) + 1)
-(1 upto b)
-val partial_mode = (1 upto k) \\ perm
-in
-if not (partial_mode subset is) then [] else
-let
-val is' =
-(fold_index (fn (i, j) => if j mem is then cons (i + 1) else I) perm [])
-|> fold (fn i => if i > k then cons (i - k + b) else I) is
-val res = map (fn x => Mode (m, is', x)) (cprods (map
-(fn (NONE, _) => [NONE]
-| (SOME js, arg) => map SOME (filter
-(fn Mode (_, js', _) => js=js') (modes_of_term modes arg)))
-(iss ~~ args1)))
-in res end
-end)) (AList.lookup op = modes name)
-in case strip_comb t' of
-(Const (name, _), args) => the_default default (mk_modes name args)
-| (Var ((name, _), _), args) => the (mk_modes name args)
-| (Free (name, _), args) => the (mk_modes name args)
-| _ => default end
-and
-*)
-fun modes_of_term modes t =
-let
-val ks = map_index (fn (i, T) => (i, NONE)) (binder_types (fastype_of t));
-val default = [Mode (([], ks), ks, [])];
-fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) =>
-let
-val (args1, args2) =
-if length args < length iss then
-error ("Too few arguments for inductive predicate " ^ name)
-else chop (length iss) args;
-val k = length args2;
-val prfx = map (rpair NONE) (1 upto k)
-in
-if not (is_prefix op = prfx is) then [] else
-let val is' = List.drop (is, k)
-in map (fn x => Mode (m, is', x)) (cprods (map
-(fn (NONE, _) => [NONE]
-| (SOME js, arg) => map SOME (filter
-(fn Mode (_, js', _) => js=js') (modes_of_term modes arg)))
-(iss ~~ args1)))
-end
-end)) (AList.lookup op = modes name)
-in
-case strip_comb (Envir.eta_contract t) of
-(Const (name, _), args) => the_default default (mk_modes name args)
-| (Var ((name, _), _), args) => the (mk_modes name args)
-| (Free (name, _), args) => the (mk_modes name args)
-| (Abs _, []) => error "Abs at param position" (* modes_of_param default modes t *)
-| _ => default
-end
-fun select_mode_prem thy modes vs ps =
-find_first (is_some o snd) (ps ~~ map
-(fn Prem (us, t) => find_first (fn Mode (_, is, _) =>
-let
-val (in_ts, out_ts) = split_smode is us;
-val (out_ts', in_ts') = List.partition (is_constrt thy) out_ts;
-val vTs = maps term_vTs out_ts';
-val dupTs = map snd (duplicates (op =) vTs) @
-List.mapPartial (AList.lookup (op =) vTs) vs;
-in
-terms_vs (in_ts @ in_ts') subset vs andalso
-forall (is_eqT o fastype_of) in_ts' andalso
-term_vs t subset vs andalso
-forall is_eqT dupTs
-end)
-(modes_of_term modes t handle Option =>
-error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))
-| Negprem (us, t) => find_first (fn Mode (_, is, _) =>
-length us = length is andalso
-terms_vs us subset vs andalso
-term_vs t subset vs)
-(modes_of_term modes t handle Option =>
-error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))
-| Sidecond t => if term_vs t subset vs then SOME (Mode (([], []), [], []))
-else NONE
-) ps);
-fun fold_prem f (Prem (args, _)) = fold f args
-| fold_prem f (Negprem (args, _)) = fold f args
-| fold_prem f (Sidecond t) = f t
-fun all_subsets [] = [[]]
-| all_subsets (x::xs) = let val xss' = all_subsets xs in xss' @ (map (cons x) xss') end
-fun generator vTs v =
-let
-val T = the (AList.lookup (op =) vTs v)
-in
-(Generator (v, T), Mode (([], []), [], []))
-end;
-fun gen_prem (Prem (us, t)) = GeneratorPrem (us, t)
-| gen_prem _ = error "gen_prem : invalid input for gen_prem"
-fun param_gen_prem param_vs (p as Prem (us, t as Free (v, _))) =
-if member (op =) param_vs v then
-GeneratorPrem (us, t)
-else p
-| param_gen_prem param_vs p = p
-fun check_mode_clause with_generator thy param_vs modes gen_modes (iss, is) (ts, ps) =
-let
-val modes' = modes @ List.mapPartial
-(fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
-(param_vs ~~ iss);
-val gen_modes' = gen_modes @ List.mapPartial
-(fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
-(param_vs ~~ iss);
-val vTs = distinct (op =) ((fold o fold_prem) Term.add_frees ps (fold Term.add_frees ts []))
-val prem_vs = distinct (op =) ((fold o fold_prem) Term.add_free_names ps [])
-fun check_mode_prems acc_ps vs [] = SOME (acc_ps, vs)
-| check_mode_prems acc_ps vs ps = (case select_mode_prem thy modes' vs ps of
-NONE =>
-(if with_generator then
-(case select_mode_prem thy gen_modes' vs ps of
-SOME (p, SOME mode) => check_mode_prems ((gen_prem p, mode) :: acc_ps)
-(case p of Prem (us, _) => vs union terms_vs us | _ => vs)
-(filter_out (equal p) ps)
-| NONE =>
-let
-val all_generator_vs = all_subsets (prem_vs \\ vs) |> sort (int_ord o (pairself length))
-in
-case (find_first (fn generator_vs => is_some
-(select_mode_prem thy modes' (vs union generator_vs) ps)) all_generator_vs) of
-SOME generator_vs => check_mode_prems ((map (generator vTs) generator_vs) @ acc_ps)
-(vs union generator_vs) ps
-| NONE => NONE
-end)
-else
-NONE)
-| SOME (p, SOME mode) => check_mode_prems ((if with_generator then param_gen_prem param_vs p else p, mode) :: acc_ps)
-(case p of Prem (us, _) => vs union terms_vs us | _ => vs)
-(filter_out (equal p) ps))
-val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (split_smode is ts));
-val in_vs = terms_vs in_ts;
-val concl_vs = terms_vs ts
-in
-if forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso
-forall (is_eqT o fastype_of) in_ts' then
-case check_mode_prems [] (param_vs union in_vs) ps of
-NONE => NONE
-| SOME (acc_ps, vs) =>
-if with_generator then
-SOME (ts, (rev acc_ps) @ (map (generator vTs) (concl_vs \\ vs)))
-else
-if concl_vs subset vs then SOME (ts, rev acc_ps) else NONE
-else NONE
-end;
-fun check_modes_pred with_generator thy param_vs clauses modes gen_modes (p, ms) =
-let val SOME rs = AList.lookup (op =) clauses p
-in (p, List.filter (fn m => case find_index
-(is_none o check_mode_clause with_generator thy param_vs modes gen_modes m) rs of
-~1 => true
-| i => (Output.tracing ("Clause " ^ string_of_int (i + 1) ^ " of " ^
-p ^ " violates mode " ^ string_of_mode m);
-Output.tracing (commas (map (Syntax.string_of_term_global thy) (fst (nth rs i)))); false)) ms)
-end;
-fun get_modes_pred with_generator thy param_vs clauses modes gen_modes (p, ms) =
-let
-val SOME rs = AList.lookup (op =) clauses p
-in
-(p, map (fn m =>
-(m, map (the o check_mode_clause with_generator thy param_vs modes gen_modes m) rs)) ms)
-end;
-fun fixp f (x : (string * mode list) list) =
-let val y = f x
-in if x = y then x else fixp f y end;
-fun infer_modes thy extra_modes all_modes param_vs clauses =
-let
-val modes =
-fixp (fn modes =>
-map (check_modes_pred false thy param_vs clauses (modes @ extra_modes) []) modes)
-all_modes
-in
-map (get_modes_pred false thy param_vs clauses (modes @ extra_modes) []) modes
-end;
-fun remove_from rem [] = []
-| remove_from rem ((k, vs) :: xs) =
-(case AList.lookup (op =) rem k of
-NONE => (k, vs)
-| SOME vs' => (k, vs \\ vs'))
-:: remove_from rem xs
-fun infer_modes_with_generator thy extra_modes all_modes param_vs clauses =
-let
-val prednames = map fst clauses
-val extra_modes = all_modes_of thy
-val gen_modes = all_generator_modes_of thy
-|> filter_out (fn (name, _) => member (op =) prednames name)
-val starting_modes = remove_from extra_modes all_modes
-val modes =
-fixp (fn modes =>
-map (check_modes_pred true thy param_vs clauses extra_modes (gen_modes @ modes)) modes)
-starting_modes
-in
-map (get_modes_pred true thy param_vs clauses extra_modes (gen_modes @ modes)) modes
-end;
-(* term construction *)
-fun mk_v (names, vs) s T = (case AList.lookup (op =) vs s of
-NONE => (Free (s, T), (names, (s, [])::vs))
-| SOME xs =>
-let
-val s' = Name.variant names s;
-val v = Free (s', T)
-in
-(v, (s'::names, AList.update (op =) (s, v::xs) vs))
-end);
-fun distinct_v (Free (s, T)) nvs = mk_v nvs s T
-| distinct_v (t $ u) nvs =
-let
-val (t', nvs') = distinct_v t nvs;
-val (u', nvs'') = distinct_v u nvs';
-in (t' $ u', nvs'') end
-| distinct_v x nvs = (x, nvs);
-fun compile_match thy compfuns eqs eqs' out_ts success_t =
-let
-val eqs'' = maps mk_eq eqs @ eqs'
-val names = fold Term.add_free_names (success_t :: eqs'' @ out_ts) [];
-val name = Name.variant names "x";
-val name' = Name.variant (name :: names) "y";
-val T = mk_tupleT (map fastype_of out_ts);
-val U = fastype_of success_t;
-val U' = dest_predT compfuns U;
-val v = Free (name, T);
-val v' = Free (name', T);
-in
-lambda v (fst (Datatype.make_case
-(ProofContext.init thy) false [] v
-[(mk_tuple out_ts,
-if null eqs'' then success_t
-else Const (@{const_name HOL.If}, HOLogic.boolT --> U --> U --> U) $
-foldr1 HOLogic.mk_conj eqs'' $ success_t $
-mk_bot compfuns U'),
-(v', mk_bot compfuns U')]))
-end;
-(*FIXME function can be removed*)
-fun mk_funcomp f t =
-let
-val names = Term.add_free_names t [];
-val Ts = binder_types (fastype_of t);
-val vs = map Free
-(Name.variant_list names (replicate (length Ts) "x") ~~ Ts)
-in
-fold_rev lambda vs (f (list_comb (t, vs)))
-end;
-(*
-fun compile_param_ext thy compfuns modes (NONE, t) = t
-| compile_param_ext thy compfuns modes (m as SOME (Mode ((iss, is'), is, ms)), t) =
-let
-val (vs, u) = strip_abs t
-val (ivs, ovs) = split_mode is vs
-val (f, args) = strip_comb u
-val (params, args') = chop (length ms) args
-val (inargs, outargs) = split_mode is' args'
-val b = length vs
-val perm = map (fn i => (find_index_eq (Bound (b - i)) args') + 1) (1 upto b)
-val outp_perm =
-snd (split_mode is perm)
-|> map (fn i => i - length (filter (fn x => x < i) is'))
-val names = [] -- TODO
-val out_names = Name.variant_list names (replicate (length outargs) "x")
-val f' = case f of
-Const (name, T) =>
-if AList.defined op = modes name then
-mk_predfun_of thy compfuns (name, T) (iss, is')
-else error "compile param: Not an inductive predicate with correct mode"
-| Free (name, T) => Free (name, param_funT_of compfuns T (SOME is'))
-val outTs = dest_tupleT (dest_predT compfuns (body_type (fastype_of f')))
-val out_vs = map Free (out_names ~~ outTs)
-val params' = map (compile_param thy modes) (ms ~~ params)
-val f_app = list_comb (f', params' @ inargs)
-val single_t = (mk_single compfuns (mk_tuple (map (fn i => nth out_vs (i - 1)) outp_perm)))
-val match_t = compile_match thy compfuns [] [] out_vs single_t
-in list_abs (ivs,
-mk_bind compfuns (f_app, match_t))
-end
-| compile_param_ext _ _ _ _ = error "compile params"
-*)
-fun compile_param size thy compfuns (NONE, t) = t
-| compile_param size thy compfuns (m as SOME (Mode ((iss, is'), is, ms)), t) =
-let
-val (f, args) = strip_comb (Envir.eta_contract t)
-val (params, args') = chop (length ms) args
-val params' = map (compile_param size thy compfuns) (ms ~~ params)
-val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of
-val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of
-val f' =
-case f of
-Const (name, T) =>
-mk_fun_of compfuns thy (name, T) (iss, is')
-| Free (name, T) => Free (name, funT_of compfuns (iss, is') T)
-| _ => error ("PredicateCompiler: illegal parameter term")
-in list_comb (f', params' @ args') end
-fun compile_expr size thy ((Mode (mode, is, ms)), t) =
-case strip_comb t of
-(Const (name, T), params) =>
-let
-val params' = map (compile_param size thy PredicateCompFuns.compfuns) (ms ~~ params)
-val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of
-in
-list_comb (mk_fun_of PredicateCompFuns.compfuns thy (name, T) mode, params')
-end
-| (Free (name, T), args) =>
-let
-val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of
-in
-list_comb (Free (name, funT_of PredicateCompFuns.compfuns ([], is) T), args)
-end;
-fun compile_gen_expr size thy compfuns ((Mode (mode, is, ms)), t) =
-case strip_comb t of
-(Const (name, T), params) =>
-let
-val params' = map (compile_param size thy compfuns) (ms ~~ params)
-in
-list_comb (mk_generator_of compfuns thy (name, T) mode, params')
-end
-| (Free (name, T), args) =>
-list_comb (Free (name, sizelim_funT_of RPredCompFuns.compfuns ([], is) T), args)
-(** specific rpred functions -- move them to the correct place in this file *)
-(* uncommented termify code; causes more trouble than expected at first *)
-(*
-fun mk_valtermify_term (t as Const (c, T)) = HOLogic.mk_prod (t, Abs ("u", HOLogic.unitT, HOLogic.reflect_term t))
-| mk_valtermify_term (Free (x, T)) = Free (x, termifyT T)
-| mk_valtermify_term (t1 $ t2) =
-let
-val T = fastype_of t1
-val (T1, T2) = dest_funT T
-val t1' = mk_valtermify_term t1
-val t2' = mk_valtermify_term t2
-in
-Const ("Code_Eval.valapp", termifyT T --> termifyT T1 --> termifyT T2) $ t1' $ t2'
-end
-| mk_valtermify_term _ = error "Not a valid term for mk_valtermify_term"
-*)
-fun compile_clause compfuns size final_term thy all_vs param_vs (iss, is) inp (ts, moded_ps) =
-let
-fun check_constrt t (names, eqs) =
-if is_constrt thy t then (t, (names, eqs)) else
-let
-val s = Name.variant names "x";
-val v = Free (s, fastype_of t)
-in (v, (s::names, HOLogic.mk_eq (v, t)::eqs)) end;
-val (in_ts, out_ts) = split_smode is ts;
-val (in_ts', (all_vs', eqs)) =
-fold_map check_constrt in_ts (all_vs, []);
-fun compile_prems out_ts' vs names [] =
-let
-val (out_ts'', (names', eqs')) =
-fold_map check_constrt out_ts' (names, []);
-val (out_ts''', (names'', constr_vs)) = fold_map distinct_v
-out_ts'' (names', map (rpair []) vs);
-in
-(* termify code:
-compile_match thy compfuns constr_vs (eqs @ eqs') out_ts'''
-(mk_single compfuns (mk_tuple (map mk_valtermify_term out_ts)))
-*)
-compile_match thy compfuns constr_vs (eqs @ eqs') out_ts'''
-(final_term out_ts)
-end
-| compile_prems out_ts vs names ((p, mode as Mode ((_, is), _, _)) :: ps) =
-let
-val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
-val (out_ts', (names', eqs)) =
-fold_map check_constrt out_ts (names, [])
-val (out_ts'', (names'', constr_vs')) = fold_map distinct_v
-out_ts' ((names', map (rpair []) vs))
-val (compiled_clause, rest) = case p of
-Prem (us, t) =>
-let
-val (in_ts, out_ts''') = split_smode is us;
-val args = case size of
-NONE => in_ts
-| SOME size_t => in_ts @ [size_t]
-val u = lift_pred compfuns
-(list_comb (compile_expr size thy (mode, t), args))
-val rest = compile_prems out_ts''' vs' names'' ps
-in
-(u, rest)
-end
-| Negprem (us, t) =>
-let
-val (in_ts, out_ts''') = split_smode is us
-val u = lift_pred compfuns
-(mk_not PredicateCompFuns.compfuns (list_comb (compile_expr NONE thy (mode, t), in_ts)))
-val rest = compile_prems out_ts''' vs' names'' ps
-in
-(u, rest)
-end
-| Sidecond t =>
-let
-val rest = compile_prems [] vs' names'' ps;
-in
-(mk_if compfuns t, rest)
-end
-| GeneratorPrem (us, t) =>
-let
-val (in_ts, out_ts''') = split_smode is us;
-val args = case size of
-NONE => in_ts
-| SOME size_t => in_ts @ [size_t]
-val u = list_comb (compile_gen_expr size thy compfuns (mode, t), args)
-val rest = compile_prems out_ts''' vs' names'' ps
-in
-(u, rest)
-end
-| Generator (v, T) =>
-let
-val u = lift_random (HOLogic.mk_random T @{term "1::code_numeral"})
-val rest = compile_prems [Free (v, T)]  vs' names'' ps;
-in
-(u, rest)
-end
-in
-compile_match thy compfuns constr_vs' eqs out_ts''
-(mk_bind compfuns (compiled_clause, rest))
-end
-val prem_t = compile_prems in_ts' param_vs all_vs' moded_ps;
-in
-mk_bind compfuns (mk_single compfuns inp, prem_t)
-end
-fun compile_pred compfuns mk_fun_of use_size thy all_vs param_vs s T mode moded_cls =
-let
-	  val (Ts1, Ts2) = chop (length (fst mode)) (binder_types T)
-val (Us1, Us2) = split_smodeT (snd mode) Ts2
-val funT_of = if use_size then sizelim_funT_of else funT_of
-val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) (fst mode) Ts1
-val size_name = Name.variant (all_vs @ param_vs) "size"
-	fun mk_input_term (i, NONE) =
-		    [Free (Name.variant (all_vs @ param_vs) ("x" ^ string_of_int i), nth Ts2 (i - 1))]
-		  | mk_input_term (i, SOME pis) = case HOLogic.strip_tupleT (nth Ts2 (i - 1)) of
-						   [] => error "strange unit input"
-					   | [T] => [Free (Name.variant (all_vs @ param_vs) ("x" ^ string_of_int i), nth Ts2 (i - 1))]
-						 | Ts => let
-							 val vnames = Name.variant_list (all_vs @ param_vs)
-								(map (fn j => "x" ^ string_of_int i ^ "p" ^ string_of_int j)
-									pis)
-						 in if null pis then []
-						   else [HOLogic.mk_tuple (map Free (vnames ~~ map (fn j => nth Ts (j - 1)) pis))] end
-		val in_ts = maps mk_input_term (snd mode)
-val params = map2 (fn s => fn T => Free (s, T)) param_vs Ts1'
-val size = Free (size_name, @{typ "code_numeral"})
-val decr_size =
-if use_size then
-SOME (Const ("HOL.minus_class.minus", @{typ "code_numeral => code_numeral => code_numeral"})
-$ size $ Const ("HOL.one_class.one", @{typ "Code_Numeral.code_numeral"}))
-else
-NONE
-val cl_ts =
-map (compile_clause compfuns decr_size (fn out_ts => mk_single compfuns (mk_tuple out_ts))
-thy all_vs param_vs mode (mk_tuple in_ts)) moded_cls;
-val t = foldr1 (mk_sup compfuns) cl_ts
-val T' = mk_predT compfuns (mk_tupleT Us2)
-val size_t = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')
-$ HOLogic.mk_eq (size, @{term "0 :: code_numeral"})
-$ mk_bot compfuns (dest_predT compfuns T') $ t
-val fun_const = mk_fun_of compfuns thy (s, T) mode
-val eq = if use_size then
-(list_comb (fun_const, params @ in_ts @ [size]), size_t)
-else
-(list_comb (fun_const, params @ in_ts), t)
-in
-HOLogic.mk_Trueprop (HOLogic.mk_eq eq)
-end;
-(* special setup for simpset *)
-val HOL_basic_ss' = HOL_basic_ss addsimps (@{thms "HOL.simp_thms"} @ [@{thm Pair_eq}])
-setSolver (mk_solver "all_tac_solver" (fn _ => fn _ => all_tac))
-	setSolver (mk_solver "True_solver" (fn _ => rtac @{thm TrueI}))
-(* Definition of executable functions and their intro and elim rules *)
-fun print_arities arities = tracing ("Arities:\n" ^
-cat_lines (map (fn (s, (ks, k)) => s ^ ": " ^
-space_implode " -> " (map
-(fn NONE => "X" | SOME k' => string_of_int k')
-(ks @ [SOME k]))) arities));
-fun mk_Eval_of ((x, T), NONE) names = (x, names)
-| mk_Eval_of ((x, T), SOME mode) names =
-	let
-val Ts = binder_types T
-(*val argnames = Name.variant_list names
-(map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
-val args = map Free (argnames ~~ Ts)
-val (inargs, outargs) = split_smode mode args*)
-		fun mk_split_lambda [] t = lambda (Free (Name.variant names "x", HOLogic.unitT)) t
-			| mk_split_lambda [x] t = lambda x t
-			| mk_split_lambda xs t =
-			let
-				fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t))
-					| mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t))
-			in
-				mk_split_lambda' xs t
-			end;
-	fun mk_arg (i, T) =
-		  let
-	  	  val vname = Name.variant names ("x" ^ string_of_int i)
-		    val default = Free (vname, T)
-		  in
-		    case AList.lookup (op =) mode i of
-		      NONE => (([], [default]), [default])
-			  | SOME NONE => (([default], []), [default])
-			  | SOME (SOME pis) =>
-				  case HOLogic.strip_tupleT T of
-						[] => error "pair mode but unit tuple" (*(([default], []), [default])*)
-					| [_] => error "pair mode but not a tuple" (*(([default], []), [default])*)
-					| Ts =>
-					  let
-							val vnames = Name.variant_list names
-								(map (fn j => "x" ^ string_of_int i ^ "p" ^ string_of_int j)
-									(1 upto length Ts))
-							val args = map Free (vnames ~~ Ts)
-							fun split_args (i, arg) (ins, outs) =
-							  if member (op =) pis i then
-							    (arg::ins, outs)
-								else
-								  (ins, arg::outs)
-							val (inargs, outargs) = fold_rev split_args ((1 upto length Ts) ~~ args) ([], [])
-							fun tuple args = if null args then [] else [HOLogic.mk_tuple args]
-						in ((tuple inargs, tuple outargs), args) end
-			end
-		val (inoutargs, args) = split_list (map mk_arg (1 upto (length Ts) ~~ Ts))
-val (inargs, outargs) = pairself flat (split_list inoutargs)
-		val r = PredicateCompFuns.mk_Eval (list_comb (x, inargs), mk_tuple outargs)
-val t = fold_rev mk_split_lambda args r
-in
-(t, names)
-end;
-fun create_intro_elim_rule (mode as (iss, is)) defthm mode_id funT pred thy =
-let
-val Ts = binder_types (fastype_of pred)
-val funtrm = Const (mode_id, funT)
-val (Ts1, Ts2) = chop (length iss) Ts;
-val Ts1' = map2 (fn NONE => I | SOME is => funT_of (PredicateCompFuns.compfuns) ([], is)) iss Ts1
-	val param_names = Name.variant_list []
-(map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1)));
-val params = map Free (param_names ~~ Ts1')
-	fun mk_args (i, T) argnames =
-let
-		  val vname = Name.variant (param_names @ argnames) ("x" ^ string_of_int (length Ts1' + i))
-		  val default = (Free (vname, T), vname :: argnames)
-	  in
-	  case AList.lookup (op =) is i of
-						 NONE => default
-					 | SOME NONE => default
-	 | SOME (SOME pis) =>
-					   case HOLogic.strip_tupleT T of
-						   [] => default
-					   | [_] => default
-						 | Ts =>
-						let
-							val vnames = Name.variant_list (param_names @ argnames)
-								(map (fn j => "x" ^ string_of_int (length Ts1' + i) ^ "p" ^ string_of_int j)
-									(1 upto (length Ts)))
-						 in (HOLogic.mk_tuple (map Free (vnames ~~ Ts)), vnames  @ argnames) end
-		end
-	val (args, argnames) = fold_map mk_args (1 upto (length Ts2) ~~ Ts2) []
-val (inargs, outargs) = split_smode is args
-val param_names' = Name.variant_list (param_names @ argnames)
-(map (fn i => "p" ^ string_of_int i) (1 upto (length iss)))
-val param_vs = map Free (param_names' ~~ Ts1)
-val (params', names) = fold_map mk_Eval_of ((params ~~ Ts1) ~~ iss) []
-val predpropI = HOLogic.mk_Trueprop (list_comb (pred, param_vs @ args))
-val predpropE = HOLogic.mk_Trueprop (list_comb (pred, params' @ args))
-val param_eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (param_vs ~~ params')
-val funargs = params @ inargs
-val funpropE = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs),
-if null outargs then Free("y", HOLogic.unitT) else mk_tuple outargs))
-val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs),
-mk_tuple outargs))
-val introtrm = Logic.list_implies (predpropI :: param_eqs, funpropI)
-val simprules = [defthm, @{thm eval_pred},
-	  @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}, @{thm pair_collapse}]
-val unfolddef_tac = Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps simprules) 1
-val introthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ param_names' @ ["y"]) [] introtrm (fn {...} => unfolddef_tac)
-val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT));
-val elimtrm = Logic.list_implies ([funpropE, Logic.mk_implies (predpropE, P)], P)
-val elimthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ param_names' @ ["y", "P"]) [] elimtrm (fn {...} => unfolddef_tac)
-	val _ = Output.tracing (Display.string_of_thm_global thy elimthm)
-	val _ = Output.tracing (Display.string_of_thm_global thy introthm)
-in
-(introthm, elimthm)
-end;
-fun create_constname_of_mode thy prefix name mode =
-let
-fun string_of_mode mode = if null mode then "0"
-else space_implode "_" (map (fn (i, NONE) => string_of_int i | (i, SOME pis) => string_of_int i ^ "p"
-^ space_implode "p" (map string_of_int pis)) mode)
-val HOmode = space_implode "_and_"
-(fold (fn NONE => I | SOME mode => cons (string_of_mode mode)) (fst mode) [])
-in
-(Sign.full_bname thy (prefix ^ (Long_Name.base_name name))) ^
-(if HOmode = "" then "_" else "_for_" ^ HOmode ^ "_yields_") ^ (string_of_mode (snd mode))
-end;
-fun split_tupleT is T =
-	let
-		fun split_tuple' _ _ [] = ([], [])
-			| split_tuple' is i (T::Ts) =
-			(if i mem is then apfst else apsnd) (cons T)
-				(split_tuple' is (i+1) Ts)
-	in
-	  split_tuple' is 1 (HOLogic.strip_tupleT T)
-end
-fun mk_arg xin xout pis T =
-let
-	  val n = length (HOLogic.strip_tupleT T)
-		val ni = length pis
-	  fun mk_proj i j t =
-		  (if i = j then I else HOLogic.mk_fst)
-			  (funpow (i - 1) HOLogic.mk_snd t)
-	  fun mk_arg' i (si, so) = if i mem pis then
-		    (mk_proj si ni xin, (si+1, so))
-		  else
-			  (mk_proj so (n - ni) xout, (si, so+1))
-	  val (args, _) = fold_map mk_arg' (1 upto n) (1, 1)
-	in
-	  HOLogic.mk_tuple args
-	end
-fun create_definitions preds (name, modes) thy =
-let
-val compfuns = PredicateCompFuns.compfuns
-val T = AList.lookup (op =) preds name |> the
-fun create_definition (mode as (iss, is)) thy = let
-val mode_cname = create_constname_of_mode thy "" name mode
-val mode_cbasename = Long_Name.base_name mode_cname
-val Ts = binder_types T
-val (Ts1, Ts2) = chop (length iss) Ts
-val (Us1, Us2) =  split_smodeT is Ts2
-val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss Ts1
-val funT = (Ts1' @ Us1) ---> (mk_predT compfuns (mk_tupleT Us2))
-val names = Name.variant_list []
-(map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
-			(* old *)
-			(*
-		  val xs = map Free (names ~~ (Ts1' @ Ts2))
-val (xparams, xargs) = chop (length iss) xs
-val (xins, xouts) = split_smode is xargs
-			*)
-			(* new *)
-			val param_names = Name.variant_list []
-			  (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1')))
-		  val xparams = map Free (param_names ~~ Ts1')
-fun mk_vars (i, T) names =
-			  let
-				  val vname = Name.variant names ("x" ^ string_of_int (length Ts1' + i))
-				in
-					case AList.lookup (op =) is i of
-						 NONE => ((([], [Free (vname, T)]), Free (vname, T)), vname :: names)
-					 | SOME NONE => ((([Free (vname, T)], []), Free (vname, T)), vname :: names)
-	 | SOME (SOME pis) =>
-					   let
-						   val (Tins, Touts) = split_tupleT pis T
-							 val name_in = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "in")
-							 val name_out = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "out")
-						   val xin = Free (name_in, HOLogic.mk_tupleT Tins)
-							 val xout = Free (name_out, HOLogic.mk_tupleT Touts)
-							 val xarg = mk_arg xin xout pis T
-						 in (((if null Tins then [] else [xin], if null Touts then [] else [xout]), xarg), name_in :: name_out :: names) end
-						(* HOLogic.strip_tupleT T of
-						[] =>
-							in (Free (vname, T), vname :: names) end
-					| [_] => let val vname = Name.variant names ("x" ^ string_of_int (length Ts1' + i))
-							in (Free (vname, T), vname :: names) end
-					| Ts =>
-						let
-							val vnames = Name.variant_list names
-								(map (fn j => "x" ^ string_of_int (length Ts1' + i) ^ "p" ^ string_of_int j)
-									(1 upto (length Ts)))
-						 in (HOLogic.mk_tuple (map Free (vnames ~~ Ts)), vnames @ names) end *)
-				end
-	  val (xinoutargs, names) = fold_map mk_vars ((1 upto (length Ts2)) ~~ Ts2) param_names
-val (xinout, xargs) = split_list xinoutargs
-			val (xins, xouts) = pairself flat (split_list xinout)
-			(*val (xins, xouts) = split_smode is xargs*)
-			val (xparams', names') = fold_map mk_Eval_of ((xparams ~~ Ts1) ~~ iss) names
-			val _ = Output.tracing ("xargs:" ^ commas (map (Syntax.string_of_term_global thy) xargs))
-fun mk_split_lambda [] t = lambda (Free (Name.variant names' "x", HOLogic.unitT)) t
-| mk_split_lambda [x] t = lambda x t
-| mk_split_lambda xs t =
-let
-fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t))
-| mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t))
-in
-mk_split_lambda' xs t
-end;
-val predterm = PredicateCompFuns.mk_Enum (mk_split_lambda xouts
-(list_comb (Const (name, T), xparams' @ xargs)))
-val lhs = list_comb (Const (mode_cname, funT), xparams @ xins)
-val def = Logic.mk_equals (lhs, predterm)
-			val _ = Output.tracing ("def:" ^ (Syntax.string_of_term_global thy def))
-val ([definition], thy') = thy |>
-Sign.add_consts_i [(Binding.name mode_cbasename, funT, NoSyn)] |>
-PureThy.add_defs false [((Binding.name (mode_cbasename ^ "_def"), def), [])]
-val (intro, elim) =
-create_intro_elim_rule mode definition mode_cname funT (Const (name, T)) thy'
-			val _ = Output.tracing (Display.string_of_thm_global thy' definition)
-in thy'
-			  |> add_predfun name mode (mode_cname, definition, intro, elim)
-|> PureThy.store_thm (Binding.name (mode_cbasename ^ "I"), intro) |> snd
-|> PureThy.store_thm (Binding.name (mode_cbasename ^ "E"), elim)  |> snd
-|> Theory.checkpoint
-end;
-in
-fold create_definition modes thy
-end;
-fun sizelim_create_definitions preds (name, modes) thy =
-let
-val T = AList.lookup (op =) preds name |> the
-fun create_definition mode thy =
-let
-val mode_cname = create_constname_of_mode thy "sizelim_" name mode
-val funT = sizelim_funT_of PredicateCompFuns.compfuns mode T
-in
-thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]
-|> set_sizelim_function_name name mode mode_cname
-end;
-in
-fold create_definition modes thy
-end;
-fun rpred_create_definitions preds (name, modes) thy =
-let
-val T = AList.lookup (op =) preds name |> the
-fun create_definition mode thy =
-let
-val mode_cname = create_constname_of_mode thy "gen_" name mode
-val funT = sizelim_funT_of RPredCompFuns.compfuns mode T
-in
-thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]
-|> set_generator_name name mode mode_cname
-end;
-in
-fold create_definition modes thy
-end;
-(* Proving equivalence of term *)
-fun is_Type (Type _) = true
-| is_Type _ = false
-(* returns true if t is an application of an datatype constructor *)
-(* which then consequently would be splitted *)
-(* else false *)
-fun is_constructor thy t =
-if (is_Type (fastype_of t)) then
-(case Datatype.get_info thy ((fst o dest_Type o fastype_of) t) of
-NONE => false
-| SOME info => (let
-val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info)
-val (c, _) = strip_comb t
-in (case c of
-Const (name, _) => name mem_string constr_consts
-| _ => false) end))
-else false
-(* MAJOR FIXME:  prove_params should be simple
-- different form of introrule for parameters ? *)
-fun prove_param thy (NONE, t) = TRY (rtac @{thm refl} 1)
-| prove_param thy (m as SOME (Mode (mode, is, ms)), t) =
-let
-val  (f, args) = strip_comb (Envir.eta_contract t)
-val (params, _) = chop (length ms) args
-val f_tac = case f of
-Const (name, T) => simp_tac (HOL_basic_ss addsimps
-([@{thm eval_pred}, (predfun_definition_of thy name mode),
-@{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"},
-				 @{thm "snd_conv"}, @{thm pair_collapse}, @{thm "Product_Type.split_conv"}])) 1
-| Free _ => TRY (rtac @{thm refl} 1)
-| Abs _ => error "prove_param: No valid parameter term"
-in
-REPEAT_DETERM (etac @{thm thin_rl} 1)
-THEN REPEAT_DETERM (rtac @{thm ext} 1)
-THEN print_tac "prove_param"
-THEN f_tac
-THEN print_tac "after simplification in prove_args"
-THEN (EVERY (map (prove_param thy) (ms ~~ params)))
-THEN (REPEAT_DETERM (atac 1))
-end
-fun prove_expr thy (Mode (mode, is, ms), t, us) (premposition : int) =
-case strip_comb t of
-(Const (name, T), args) =>
-let
-val introrule = predfun_intro_of thy name mode
-val (args1, args2) = chop (length ms) args
-in
-rtac @{thm bindI} 1
-THEN print_tac "before intro rule:"
-(* for the right assumption in first position *)
-THEN rotate_tac premposition 1
-THEN debug_tac (Display.string_of_thm (ProofContext.init thy) introrule)
-THEN rtac introrule 1
-THEN print_tac "after intro rule"
-(* work with parameter arguments *)
-THEN (atac 1)
-THEN (print_tac "parameter goal")
-THEN (EVERY (map (prove_param thy) (ms ~~ args1)))
-THEN (REPEAT_DETERM (atac 1))
-end
-| _ => rtac @{thm bindI} 1
-	  THEN asm_full_simp_tac
-		  (HOL_basic_ss' addsimps [@{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"},
-				 @{thm "snd_conv"}, @{thm pair_collapse}]) 1
-	  THEN (atac 1)
-	  THEN print_tac "after prove parameter call"
-fun SOLVED tac st = FILTER (fn st' => nprems_of st' = nprems_of st - 1) tac st;
-fun SOLVEDALL tac st = FILTER (fn st' => nprems_of st' = 0) tac st
-fun prove_match thy (out_ts : term list) = let
-fun get_case_rewrite t =
-if (is_constructor thy t) then let
-val case_rewrites = (#case_rewrites (Datatype.the_info thy
-((fst o dest_Type o fastype_of) t)))
-in case_rewrites @ (flat (map get_case_rewrite (snd (strip_comb t)))) end
-else []
-val simprules = @{thm "unit.cases"} :: @{thm "prod.cases"} :: (flat (map get_case_rewrite out_ts))
-(* replace TRY by determining if it necessary - are there equations when calling compile match? *)
-in
-(* make this simpset better! *)
-asm_full_simp_tac (HOL_basic_ss' addsimps simprules) 1
-THEN print_tac "after prove_match:"
-THEN (DETERM (TRY (EqSubst.eqsubst_tac (ProofContext.init thy) [0] [@{thm "HOL.if_P"}] 1
-THEN (REPEAT_DETERM (rtac @{thm conjI} 1 THEN (SOLVED (asm_simp_tac HOL_basic_ss 1))))
-THEN (SOLVED (asm_simp_tac HOL_basic_ss 1)))))
-THEN print_tac "after if simplification"
-end;
-(* corresponds to compile_fun -- maybe call that also compile_sidecond? *)
-fun prove_sidecond thy modes t =
-let
-fun preds_of t nameTs = case strip_comb t of
-(f as Const (name, T), args) =>
-if AList.defined (op =) modes name then (name, T) :: nameTs
-else fold preds_of args nameTs
-| _ => nameTs
-val preds = preds_of t []
-val defs = map
-(fn (pred, T) => predfun_definition_of thy pred
-([], map (rpair NONE) (1 upto (length (binder_types T)))))
-preds
-in
-(* remove not_False_eq_True when simpset in prove_match is better *)
-simp_tac (HOL_basic_ss addsimps
-(@{thms "HOL.simp_thms"} @ (@{thm not_False_eq_True} :: @{thm eval_pred} :: defs))) 1
-(* need better control here! *)
-end
-fun prove_clause thy nargs modes (iss, is) (_, clauses) (ts, moded_ps) =
-let
-val (in_ts, clause_out_ts) = split_smode is ts;
-fun prove_prems out_ts [] =
-(prove_match thy out_ts)
-			THEN print_tac "before simplifying assumptions"
-THEN asm_full_simp_tac HOL_basic_ss' 1
-			THEN print_tac "before single intro rule"
-THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1)
-| prove_prems out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) =
-let
-val premposition = (find_index (equal p) clauses) + nargs
-val rest_tac = (case p of Prem (us, t) =>
-let
-val (_, out_ts''') = split_smode is us
-val rec_tac = prove_prems out_ts''' ps
-in
-print_tac "before clause:"
-THEN asm_simp_tac HOL_basic_ss 1
-THEN print_tac "before prove_expr:"
-THEN prove_expr thy (mode, t, us) premposition
-THEN print_tac "after prove_expr:"
-THEN rec_tac
-end
-| Negprem (us, t) =>
-let
-val (_, out_ts''') = split_smode is us
-val rec_tac = prove_prems out_ts''' ps
-val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
-val (_, params) = strip_comb t
-in
-rtac @{thm bindI} 1
-THEN (if (is_some name) then
-simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1
-THEN rtac @{thm not_predI} 1
-THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
-THEN (REPEAT_DETERM (atac 1))
-(* FIXME: work with parameter arguments *)
-THEN (EVERY (map (prove_param thy) (param_modes ~~ params)))
-else
-rtac @{thm not_predI'} 1)
-THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
-THEN rec_tac
-end
-| Sidecond t =>
-rtac @{thm bindI} 1
-THEN rtac @{thm if_predI} 1
-THEN print_tac "before sidecond:"
-THEN prove_sidecond thy modes t
-THEN print_tac "after sidecond:"
-THEN prove_prems [] ps)
-in (prove_match thy out_ts)
-THEN rest_tac
-end;
-val prems_tac = prove_prems in_ts moded_ps
-in
-rtac @{thm bindI} 1
-THEN rtac @{thm singleI} 1
-THEN prems_tac
-end;
-fun select_sup 1 1 = []
-| select_sup _ 1 = [rtac @{thm supI1}]
-| select_sup n i = (rtac @{thm supI2})::(select_sup (n - 1) (i - 1));
-fun prove_one_direction thy clauses preds modes pred mode moded_clauses =
-let
-val T = the (AList.lookup (op =) preds pred)
-val nargs = length (binder_types T) - nparams_of thy pred
-val pred_case_rule = the_elim_of thy pred
-in
-REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))
-		THEN print_tac "before applying elim rule"
-THEN etac (predfun_elim_of thy pred mode) 1
-THEN etac pred_case_rule 1
-THEN (EVERY (map
-(fn i => EVERY' (select_sup (length moded_clauses) i) i)
-(1 upto (length moded_clauses))))
-THEN (EVERY (map2 (prove_clause thy nargs modes mode) clauses moded_clauses))
-THEN print_tac "proved one direction"
-end;
-(** Proof in the other direction **)
-fun prove_match2 thy out_ts = let
-fun split_term_tac (Free _) = all_tac
-| split_term_tac t =
-if (is_constructor thy t) then let
-val info = Datatype.the_info thy ((fst o dest_Type o fastype_of) t)
-val num_of_constrs = length (#case_rewrites info)
-(* special treatment of pairs -- because of fishing *)
-val split_rules = case (fst o dest_Type o fastype_of) t of
-"*" => [@{thm prod.split_asm}]
-| _ => PureThy.get_thms thy (((fst o dest_Type o fastype_of) t) ^ ".split_asm")
-val (_, ts) = strip_comb t
-in
-(Splitter.split_asm_tac split_rules 1)
-(*        THEN (Simplifier.asm_full_simp_tac HOL_basic_ss 1)
-THEN (DETERM (TRY (etac @{thm Pair_inject} 1))) *)
-THEN (REPEAT_DETERM_N (num_of_constrs - 1) (etac @{thm botE} 1 ORELSE etac @{thm botE} 2))
-THEN (EVERY (map split_term_tac ts))
-end
-else all_tac
-in
-split_term_tac (mk_tuple out_ts)
-THEN (DETERM (TRY ((Splitter.split_asm_tac [@{thm "split_if_asm"}] 1) THEN (etac @{thm botE} 2))))
-end
-(* VERY LARGE SIMILIRATIY to function prove_param
--- join both functions
-*)
-(* TODO: remove function *)
-fun prove_param2 thy (NONE, t) = all_tac
-| prove_param2 thy (m as SOME (Mode (mode, is, ms)), t) = let
-val  (f, args) = strip_comb (Envir.eta_contract t)
-val (params, _) = chop (length ms) args
-val f_tac = case f of
-Const (name, T) => full_simp_tac (HOL_basic_ss addsimps
-(@{thm eval_pred}::(predfun_definition_of thy name mode)
-:: @{thm "Product_Type.split_conv"}::[])) 1
-| Free _ => all_tac
-| _ => error "prove_param2: illegal parameter term"
-in
-print_tac "before simplification in prove_args:"
-THEN f_tac
-THEN print_tac "after simplification in prove_args"
-THEN (EVERY (map (prove_param2 thy) (ms ~~ params)))
-end
-fun prove_expr2 thy (Mode (mode, is, ms), t) =
-(case strip_comb t of
-(Const (name, T), args) =>
-etac @{thm bindE} 1
-THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})))
-THEN print_tac "prove_expr2-before"
-THEN (debug_tac (Syntax.string_of_term_global thy
-(prop_of (predfun_elim_of thy name mode))))
-THEN (etac (predfun_elim_of thy name mode) 1)
-THEN print_tac "prove_expr2"
-THEN (EVERY (map (prove_param2 thy) (ms ~~ args)))
-THEN print_tac "finished prove_expr2"
-| _ => etac @{thm bindE} 1)
-(* FIXME: what is this for? *)
-(* replace defined by has_mode thy pred *)
-(* TODO: rewrite function *)
-fun prove_sidecond2 thy modes t = let
-fun preds_of t nameTs = case strip_comb t of
-(f as Const (name, T), args) =>
-if AList.defined (op =) modes name then (name, T) :: nameTs
-else fold preds_of args nameTs
-| _ => nameTs
-val preds = preds_of t []
-val defs = map
-(fn (pred, T) => predfun_definition_of thy pred
-([], map (rpair NONE) (1 upto (length (binder_types T)))))
-preds
-in
-(* only simplify the one assumption *)
-full_simp_tac (HOL_basic_ss' addsimps @{thm eval_pred} :: defs) 1
-(* need better control here! *)
-THEN print_tac "after sidecond2 simplification"
-end
-fun prove_clause2 thy modes pred (iss, is) (ts, ps) i =
-let
-val pred_intro_rule = nth (intros_of thy pred) (i - 1)
-val (in_ts, clause_out_ts) = split_smode is ts;
-fun prove_prems2 out_ts [] =
-print_tac "before prove_match2 - last call:"
-THEN prove_match2 thy out_ts
-THEN print_tac "after prove_match2 - last call:"
-THEN (etac @{thm singleE} 1)
-THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1))
-THEN (asm_full_simp_tac HOL_basic_ss' 1)
-THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1))
-THEN (asm_full_simp_tac HOL_basic_ss' 1)
-THEN SOLVED (print_tac "state before applying intro rule:"
-THEN (rtac pred_intro_rule 1)
-(* How to handle equality correctly? *)
-THEN (print_tac "state before assumption matching")
-THEN (REPEAT (atac 1 ORELSE
-(CHANGED (asm_full_simp_tac (HOL_basic_ss' addsimps
-					 [@{thm split_eta}, @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}, @{thm pair_collapse}]) 1)
-THEN print_tac "state after simp_tac:"))))
-| prove_prems2 out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) =
-let
-val rest_tac = (case p of
-Prem (us, t) =>
-let
-val (_, out_ts''') = split_smode is us
-val rec_tac = prove_prems2 out_ts''' ps
-in
-(prove_expr2 thy (mode, t)) THEN rec_tac
-end
-| Negprem (us, t) =>
-let
-val (_, out_ts''') = split_smode is us
-val rec_tac = prove_prems2 out_ts''' ps
-val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
-val (_, params) = strip_comb t
-in
-print_tac "before neg prem 2"
-THEN etac @{thm bindE} 1
-THEN (if is_some name then
-full_simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1
-THEN etac @{thm not_predE} 1
-THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
-THEN (EVERY (map (prove_param2 thy) (param_modes ~~ params)))
-else
-etac @{thm not_predE'} 1)
-THEN rec_tac
-end
-| Sidecond t =>
-etac @{thm bindE} 1
-THEN etac @{thm if_predE} 1
-THEN prove_sidecond2 thy modes t
-THEN prove_prems2 [] ps)
-in print_tac "before prove_match2:"
-THEN prove_match2 thy out_ts
-THEN print_tac "after prove_match2:"
-THEN rest_tac
-end;
-val prems_tac = prove_prems2 in_ts ps
-in
-print_tac "starting prove_clause2"
-THEN etac @{thm bindE} 1
-THEN (etac @{thm singleE'} 1)
-THEN (TRY (etac @{thm Pair_inject} 1))
-THEN print_tac "after singleE':"
-THEN prems_tac
-end;
-fun prove_other_direction thy modes pred mode moded_clauses =
-let
-fun prove_clause clause i =
-(if i < length moded_clauses then etac @{thm supE} 1 else all_tac)
-THEN (prove_clause2 thy modes pred mode clause i)
-in
-(DETERM (TRY (rtac @{thm unit.induct} 1)))
-THEN (REPEAT_DETERM (CHANGED (rewtac @{thm split_paired_all})))
-THEN (rtac (predfun_intro_of thy pred mode) 1)
-THEN (REPEAT_DETERM (rtac @{thm refl} 2))
-THEN (EVERY (map2 prove_clause moded_clauses (1 upto (length moded_clauses))))
-end;
-(** proof procedure **)
-fun prove_pred thy clauses preds modes pred mode (moded_clauses, compiled_term) =
-let
-val ctxt = ProofContext.init thy
-val clauses = the (AList.lookup (op =) clauses pred)
-in
-Goal.prove ctxt (Term.add_free_names compiled_term []) [] compiled_term
-(if !do_proofs then
-(fn _ =>
-rtac @{thm pred_iffI} 1
-				THEN print_tac "after pred_iffI"
-THEN prove_one_direction thy clauses preds modes pred mode moded_clauses
-THEN print_tac "proved one direction"
-THEN prove_other_direction thy modes pred mode moded_clauses
-THEN print_tac "proved other direction")
-else (fn _ => mycheat_tac thy 1))
-end;
-(* composition of mode inference, definition, compilation and proof *)
-(** auxillary combinators for table of preds and modes **)
-fun map_preds_modes f preds_modes_table =
-map (fn (pred, modes) =>
-(pred, map (fn (mode, value) => (mode, f pred mode value)) modes)) preds_modes_table
-fun join_preds_modes table1 table2 =
-map_preds_modes (fn pred => fn mode => fn value =>
-(value, the (AList.lookup (op =) (the (AList.lookup (op =) table2 pred)) mode))) table1
-fun maps_modes preds_modes_table =
-map (fn (pred, modes) =>
-(pred, map (fn (mode, value) => value) modes)) preds_modes_table
-fun compile_preds compfuns mk_fun_of use_size thy all_vs param_vs preds moded_clauses =
-map_preds_modes (fn pred => compile_pred compfuns mk_fun_of use_size thy all_vs param_vs pred
-(the (AList.lookup (op =) preds pred))) moded_clauses
-fun prove thy clauses preds modes moded_clauses compiled_terms =
-map_preds_modes (prove_pred thy clauses preds modes)
-(join_preds_modes moded_clauses compiled_terms)
-fun prove_by_skip thy _ _ _ _ compiled_terms =
-map_preds_modes (fn pred => fn mode => fn t => Drule.standard (SkipProof.make_thm thy t))
-compiled_terms
-fun prepare_intrs thy prednames =
-let
-val intrs = maps (intros_of thy) prednames
-|> map (Logic.unvarify o prop_of)
-val nparams = nparams_of thy (hd prednames)
-val extra_modes = all_modes_of thy |> filter_out (fn (name, _) => member (op =) prednames name)
-val preds = distinct (op =) (map (dest_Const o fst o (strip_intro_concl nparams)) intrs)
-val _ $ u = Logic.strip_imp_concl (hd intrs);
-val params = List.take (snd (strip_comb u), nparams);
-val param_vs = maps term_vs params
-val all_vs = terms_vs intrs
-fun dest_prem t =
-(case strip_comb t of
-(v as Free _, ts) => if v mem params then Prem (ts, v) else Sidecond t
-| (c as Const (@{const_name Not}, _), [t]) => (case dest_prem t of
-Prem (ts, t) => Negprem (ts, t)
-| Negprem _ => error ("Double negation not allowed in premise: " ^ (Syntax.string_of_term_global thy (c $ t)))
-| Sidecond t => Sidecond (c $ t))
-| (c as Const (s, _), ts) =>
-if is_registered thy s then
-let val (ts1, ts2) = chop (nparams_of thy s) ts
-in Prem (ts2, list_comb (c, ts1)) end
-else Sidecond t
-| _ => Sidecond t)
-fun add_clause intr (clauses, arities) =
-let
-val _ $ t = Logic.strip_imp_concl intr;
-val (Const (name, T), ts) = strip_comb t;
-val (ts1, ts2) = chop nparams ts;
-val prems = map (dest_prem o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr);
-val (Ts, Us) = chop nparams (binder_types T)
-in
-(AList.update op = (name, these (AList.lookup op = clauses name) @
-[(ts2, prems)]) clauses,
-AList.update op = (name, (map (fn U => (case strip_type U of
-(Rs as _ :: _, Type ("bool", [])) => SOME (length Rs)
-| _ => NONE)) Ts,
-length Us)) arities)
-end;
-val (clauses, arities) = fold add_clause intrs ([], []);
-fun modes_of_arities arities =
-(map (fn (s, (ks, k)) => (s, cprod (cprods (map
-(fn NONE => [NONE]
-| SOME k' => map SOME (map (map (rpair NONE)) (subsets 1 k'))) ks),
-map (map (rpair NONE)) (subsets 1 k)))) arities)
-fun modes_of_typ T =
-let
-val (Ts, Us) = chop nparams (binder_types T)
-fun all_smodes_of_typs Ts = cprods_subset (
-map_index (fn (i, U) =>
-case HOLogic.strip_tupleT U of
-[] => [(i + 1, NONE)]
-| [U] => [(i + 1, NONE)]
-	    | Us =>  map (pair (i + 1) o SOME) ((subsets 1 (length Us)) \\ [[], 1 upto (length Us)]))
-Ts)
-in
-cprod (cprods (map (fn T => case strip_type T of
-(Rs as _ :: _, Type ("bool", [])) => map SOME (all_smodes_of_typs Rs) | _ => [NONE]) Ts),
-all_smodes_of_typs Us)
-end
-val all_modes = map (fn (s, T) => (s, modes_of_typ T)) preds
-in (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) end;
-(** main function of predicate compiler **)
-fun add_equations_of steps prednames thy =
-let
-val _ = Output.tracing ("Starting predicate compiler for predicates " ^ commas prednames ^ "...")
-val (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) =
-prepare_intrs thy prednames
-val _ = Output.tracing "Infering modes..."
-val moded_clauses = #infer_modes steps thy extra_modes all_modes param_vs clauses
-val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses
-val _ = print_modes modes
-val _ = print_moded_clauses thy moded_clauses
-val _ = Output.tracing "Defining executable functions..."
-val thy' = fold (#create_definitions steps preds) modes thy
-|> Theory.checkpoint
-val _ = Output.tracing "Compiling equations..."
-val compiled_terms =
-(#compile_preds steps) thy' all_vs param_vs preds moded_clauses
-val _ = print_compiled_terms thy' compiled_terms
-val _ = Output.tracing "Proving equations..."
-val result_thms = #prove steps thy' clauses preds (extra_modes @ modes)
-moded_clauses compiled_terms
-val qname = #qname steps
-(* val attrib = gn thy => Attrib.attribute_i thy Code.add_eqn_attrib *)
-val attrib = fn thy => Attrib.attribute_i thy (Attrib.internal (K (Thm.declaration_attribute
-(fn thm => Context.mapping (Code.add_eqn thm) I))))
-val thy'' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss
-[((Binding.qualify true (Long_Name.base_name name) (Binding.name qname), result_thms),
-[attrib thy ])] thy))
-(maps_modes result_thms) thy'
-|> Theory.checkpoint
-in
-thy''
-end
-fun extend' value_of edges_of key (G, visited) =
-let
-val (G', v) = case try (Graph.get_node G) key of
-SOME v => (G, v)
-| NONE => (Graph.new_node (key, value_of key) G, value_of key)
-val (G'', visited') = fold (extend' value_of edges_of) (edges_of (key, v) \\ visited)
-(G', key :: visited)
-in
-(fold (Graph.add_edge o (pair key)) (edges_of (key, v)) G'', visited')
-end;
-fun extend value_of edges_of key G = fst (extend' value_of edges_of key (G, []))
-fun gen_add_equations steps names thy =
-let
-val thy' = PredData.map (fold (extend (fetch_pred_data thy) (depending_preds_of thy)) names) thy
-|> Theory.checkpoint;
-fun strong_conn_of gr keys =
-Graph.strong_conn (Graph.subgraph (member (op =) (Graph.all_succs gr keys)) gr)
-val scc = strong_conn_of (PredData.get thy') names
-val thy'' = fold_rev
-(fn preds => fn thy =>
-if #are_not_defined steps thy preds then add_equations_of steps preds thy else thy)
-scc thy' |> Theory.checkpoint
-in thy'' end
-(* different instantiantions of the predicate compiler *)
-val add_equations = gen_add_equations
-{infer_modes = infer_modes,
-create_definitions = create_definitions,
-compile_preds = compile_preds PredicateCompFuns.compfuns mk_fun_of false,
-prove = prove,
-are_not_defined = (fn thy => forall (null o modes_of thy)),
-qname = "equation"}
-val add_sizelim_equations = gen_add_equations
-{infer_modes = infer_modes,
-create_definitions = sizelim_create_definitions,
-compile_preds = compile_preds PredicateCompFuns.compfuns mk_sizelim_fun_of true,
-prove = prove_by_skip,
-are_not_defined = (fn thy => fn preds => true), (* TODO *)
-qname = "sizelim_equation"
-}
-val add_quickcheck_equations = gen_add_equations
-{infer_modes = infer_modes_with_generator,
-create_definitions = rpred_create_definitions,
-compile_preds = compile_preds RPredCompFuns.compfuns mk_generator_of true,
-prove = prove_by_skip,
-are_not_defined = (fn thy => fn preds => true), (* TODO *)
-qname = "rpred_equation"}
-(** user interface **)
-(* generation of case rules from user-given introduction rules *)
-fun mk_casesrule ctxt nparams introrules =
-let
-val intros = map (Logic.unvarify o prop_of) introrules
-val (pred, (params, args)) = strip_intro_concl nparams (hd intros)
-val ([propname], ctxt1) = Variable.variant_fixes ["thesis"] ctxt
-val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT))
-val (argnames, ctxt2) = Variable.variant_fixes
-(map (fn i => "a" ^ string_of_int i) (1 upto (length args))) ctxt1
-val argvs = map2 (curry Free) argnames (map fastype_of args)
-fun mk_case intro =
-let
-val (_, (_, args)) = strip_intro_concl nparams intro
-val prems = Logic.strip_imp_prems intro
-val eqprems = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (argvs ~~ args)
-val frees = (fold o fold_aterms)
-(fn t as Free _ =>
-if member (op aconv) params t then I else insert (op aconv) t
-| _ => I) (args @ prems) []
-in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end
-val assm = HOLogic.mk_Trueprop (list_comb (pred, params @ argvs))
-val cases = map mk_case intros
-in Logic.list_implies (assm :: cases, prop) end;
-(* code_pred_intro attribute *)
-fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I);
-val code_pred_intros_attrib = attrib add_intro;
-local
-(* TODO: make TheoryDataFun to GenericDataFun & remove duplication of local theory and theory *)
-fun generic_code_pred prep_const raw_const lthy =
-let
-val thy = ProofContext.theory_of lthy
-val const = prep_const thy raw_const
-val lthy' = LocalTheory.theory (PredData.map
-(extend (fetch_pred_data thy) (depending_preds_of thy) const)) lthy
-|> LocalTheory.checkpoint
-val thy' = ProofContext.theory_of lthy'
-val preds = Graph.all_preds (PredData.get thy') [const] |> filter_out (has_elim thy')
-fun mk_cases const =
-let
-val nparams = nparams_of thy' const
-val intros = intros_of thy' const
-in mk_casesrule lthy' nparams intros end
-val cases_rules = map mk_cases preds
-val cases =
-map (fn case_rule => RuleCases.Case {fixes = [],
-assumes = [("", Logic.strip_imp_prems case_rule)],
-binds = [], cases = []}) cases_rules
-val case_env = map2 (fn p => fn c => (Long_Name.base_name p, SOME c)) preds cases
-val lthy'' = lthy'
-|> fold Variable.auto_fixes cases_rules
-|> ProofContext.add_cases true case_env
-fun after_qed thms goal_ctxt =
-let
-val global_thms = ProofContext.export goal_ctxt
-(ProofContext.init (ProofContext.theory_of goal_ctxt)) (map the_single thms)
-in
-goal_ctxt |> LocalTheory.theory (fold set_elim global_thms #> add_equations [const])
-end
-in
-Proof.theorem_i NONE after_qed (map (single o (rpair [])) cases_rules) lthy''
-end;
-structure P = OuterParse
-in
-val code_pred = generic_code_pred (K I);
-val code_pred_cmd = generic_code_pred Code.read_const
-val setup = PredData.put (Graph.empty) #>
-Attrib.setup @{binding code_pred_intros} (Scan.succeed (attrib add_intro))
-"adding alternative introduction rules for code generation of inductive predicates"
-(*  Attrib.setup @{binding code_ind_cases} (Scan.succeed add_elim_attrib)
-"adding alternative elimination rules for code generation of inductive predicates";
-*)
-(*FIXME name discrepancy in attribs and ML code*)
-(*FIXME intros should be better named intro*)
-(*FIXME why distinguished attribute for cases?*)
-val _ = OuterSyntax.local_theory_to_proof "code_pred"
-"prove equations for predicate specified by intro/elim rules"
-OuterKeyword.thy_goal (P.term_group >> code_pred_cmd)
-end
-(*FIXME
-- Naming of auxiliary rules necessary?
-- add default code equations P x y z = P_i_i_i x y z
-*)
-(* transformation for code generation *)
-val eval_ref = ref (NONE : (unit -> term Predicate.pred) option);
-(*FIXME turn this into an LCF-guarded preprocessor for comprehensions*)
-fun analyze_compr thy t_compr =
-let
-val split = case t_compr of (Const (@{const_name Collect}, _) $ t) => t
-| _ => error ("Not a set comprehension: " ^ Syntax.string_of_term_global thy t_compr);
-val (body, Ts, fp) = HOLogic.strip_psplits split;
-val (pred as Const (name, T), all_args) = strip_comb body;
-val (params, args) = chop (nparams_of thy name) all_args;
-val user_mode = map_filter I (map_index
-(fn (i, t) => case t of Bound j => if j < length Ts then NONE
-else SOME (i+1) | _ => SOME (i+1)) args); (*FIXME dangling bounds should not occur*)
-val user_mode' = map (rpair NONE) user_mode
-val modes = filter (fn Mode (_, is, _) => is = user_mode')
-(modes_of_term (all_modes_of thy) (list_comb (pred, params)));
-val m = case modes
-of [] => error ("No mode possible for comprehension "
-^ Syntax.string_of_term_global thy t_compr)
-| [m] => m
-| m :: _ :: _ => (warning ("Multiple modes possible for comprehension "
-^ Syntax.string_of_term_global thy t_compr); m);
-val (inargs, outargs) = split_smode user_mode' args;
-val t_pred = list_comb (compile_expr NONE thy (m, list_comb (pred, params)), inargs);
-val t_eval = if null outargs then t_pred else let
-val outargs_bounds = map (fn Bound i => i) outargs;
-val outargsTs = map (nth Ts) outargs_bounds;
-val T_pred = HOLogic.mk_tupleT outargsTs;
-val T_compr = HOLogic.mk_ptupleT fp Ts;
-val arrange_bounds = map_index I outargs_bounds
-|> sort (prod_ord (K EQUAL) int_ord)
-|> map fst;
-val arrange = funpow (length outargs_bounds - 1) HOLogic.mk_split
-(Term.list_abs (map (pair "") outargsTs,
-HOLogic.mk_ptuple fp T_compr (map Bound arrange_bounds)))
-in mk_map PredicateCompFuns.compfuns T_pred T_compr arrange t_pred end
-in t_eval end;
-fun eval thy t_compr =
-let
-val t = analyze_compr thy t_compr;
-val T = dest_predT PredicateCompFuns.compfuns (fastype_of t);
-val t' = mk_map PredicateCompFuns.compfuns T HOLogic.termT (HOLogic.term_of_const T) t;
-in (T, Code_ML.eval NONE ("Predicate_Compile.eval_ref", eval_ref) Predicate.map thy t' []) end;
-fun values ctxt k t_compr =
-let
-val thy = ProofContext.theory_of ctxt;
-val (T, t) = eval thy t_compr;
-val setT = HOLogic.mk_setT T;
-val (ts, _) = Predicate.yieldn k t;
-val elemsT = HOLogic.mk_set T ts;
-in if k = ~1 orelse length ts < k then elemsT
-else Const (@{const_name Set.union}, setT --> setT --> setT) $ elemsT $ t_compr
-end;
-fun values_cmd modes k raw_t state =
-let
-val ctxt = Toplevel.context_of state;
-val t = Syntax.read_term ctxt raw_t;
-val t' = values ctxt k t;
-val ty' = Term.type_of t';
-val ctxt' = Variable.auto_fixes t' ctxt;
-val p = PrintMode.with_modes modes (fn () =>
-Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk,
-Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) ();
-in Pretty.writeln p end;
-local structure P = OuterParse in
-val opt_modes = Scan.optional (P.$$$ "(" |-- P.!!! (Scan.repeat1 P.xname --| P.$$$ ")")) [];
-val _ = OuterSyntax.improper_command "values" "enumerate and print comprehensions" OuterKeyword.diag
-(opt_modes -- Scan.optional P.nat ~1 -- P.term
->> (fn ((modes, k), t) => Toplevel.no_timing o Toplevel.keep
-(values_cmd modes k t)));
-end;
-end;

changeset 32667	09546e654222
parent 32666	fd96d5f49d59
child 32668	b2de45007537