--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/ex/predicate_compile.ML Sun Mar 08 15:25:28 2009 +0100
@@ -0,0 +1,1346 @@
+(* Author: Lukas Bulwahn
+
+(Prototype of) A compiler from predicates specified by intro/elim rules
+to equations.
+*)
+
+signature PREDICATE_COMPILE =
+sig
+ val create_def_equation': string -> (int list option list * int list) option -> theory -> theory
+ val create_def_equation: string -> theory -> theory
+ val intro_rule: theory -> string -> (int list option list * int list) -> thm
+ val elim_rule: theory -> string -> (int list option list * int list) -> thm
+ val strip_intro_concl : term -> int -> (term * (term list * term list))
+ val code_ind_intros_attrib : attribute
+ val code_ind_cases_attrib : attribute
+ val setup : theory -> theory
+ val print_alternative_rules : theory -> theory
+ val do_proofs: bool ref
+end;
+
+structure Predicate_Compile: PREDICATE_COMPILE =
+struct
+
+structure PredModetab = TableFun(
+ type key = (string * (int list option list * int list))
+ val ord = prod_ord fast_string_ord (prod_ord
+ (list_ord (option_ord (list_ord int_ord))) (list_ord int_ord)))
+
+
+structure IndCodegenData = TheoryDataFun
+(
+ type T = {names : string PredModetab.table,
+ modes : ((int list option list * int list) list) Symtab.table,
+ function_defs : Thm.thm Symtab.table,
+ function_intros : Thm.thm Symtab.table,
+ function_elims : Thm.thm Symtab.table,
+ intro_rules : (Thm.thm list) Symtab.table,
+ elim_rules : Thm.thm Symtab.table,
+ nparams : int Symtab.table
+ };
+ (* names: map from inductive predicate and mode to function name (string).
+ modes: map from inductive predicates to modes
+ function_defs: map from function name to definition
+ function_intros: map from function name to intro rule
+ function_elims: map from function name to elim rule
+ intro_rules: map from inductive predicate to alternative intro rules
+ elim_rules: map from inductive predicate to alternative elimination rule
+ nparams: map from const name to number of parameters (* assuming there exist intro and elimination rules *)
+ *)
+ val empty = {names = PredModetab.empty,
+ modes = Symtab.empty,
+ function_defs = Symtab.empty,
+ function_intros = Symtab.empty,
+ function_elims = Symtab.empty,
+ intro_rules = Symtab.empty,
+ elim_rules = Symtab.empty,
+ nparams = Symtab.empty};
+ val copy = I;
+ val extend = I;
+ fun merge _ r = {names = PredModetab.merge (op =) (pairself #names r),
+ modes = Symtab.merge (op =) (pairself #modes r),
+ function_defs = Symtab.merge Thm.eq_thm (pairself #function_defs r),
+ function_intros = Symtab.merge Thm.eq_thm (pairself #function_intros r),
+ function_elims = Symtab.merge Thm.eq_thm (pairself #function_elims r),
+ intro_rules = Symtab.merge ((forall Thm.eq_thm) o (op ~~)) (pairself #intro_rules r),
+ elim_rules = Symtab.merge Thm.eq_thm (pairself #elim_rules r),
+ nparams = Symtab.merge (op =) (pairself #nparams r)};
+);
+
+ fun map_names f thy = IndCodegenData.map
+ (fn x => {names = f (#names x), modes = #modes x, function_defs = #function_defs x,
+ function_intros = #function_intros x, function_elims = #function_elims x,
+ intro_rules = #intro_rules x, elim_rules = #elim_rules x,
+ nparams = #nparams x}) thy
+
+ fun map_modes f thy = IndCodegenData.map
+ (fn x => {names = #names x, modes = f (#modes x), function_defs = #function_defs x,
+ function_intros = #function_intros x, function_elims = #function_elims x,
+ intro_rules = #intro_rules x, elim_rules = #elim_rules x,
+ nparams = #nparams x}) thy
+
+ fun map_function_defs f thy = IndCodegenData.map
+ (fn x => {names = #names x, modes = #modes x, function_defs = f (#function_defs x),
+ function_intros = #function_intros x, function_elims = #function_elims x,
+ intro_rules = #intro_rules x, elim_rules = #elim_rules x,
+ nparams = #nparams x}) thy
+
+ fun map_function_elims f thy = IndCodegenData.map
+ (fn x => {names = #names x, modes = #modes x, function_defs = #function_defs x,
+ function_intros = #function_intros x, function_elims = f (#function_elims x),
+ intro_rules = #intro_rules x, elim_rules = #elim_rules x,
+ nparams = #nparams x}) thy
+
+ fun map_function_intros f thy = IndCodegenData.map
+ (fn x => {names = #names x, modes = #modes x, function_defs = #function_defs x,
+ function_intros = f (#function_intros x), function_elims = #function_elims x,
+ intro_rules = #intro_rules x, elim_rules = #elim_rules x,
+ nparams = #nparams x}) thy
+
+ fun map_intro_rules f thy = IndCodegenData.map
+ (fn x => {names = #names x, modes = #modes x, function_defs = #function_defs x,
+ function_intros = #function_intros x, function_elims = #function_elims x,
+ intro_rules = f (#intro_rules x), elim_rules = #elim_rules x,
+ nparams = #nparams x}) thy
+
+ fun map_elim_rules f thy = IndCodegenData.map
+ (fn x => {names = #names x, modes = #modes x, function_defs = #function_defs x,
+ function_intros = #function_intros x, function_elims = #function_elims x,
+ intro_rules = #intro_rules x, elim_rules = f (#elim_rules x),
+ nparams = #nparams x}) thy
+
+ fun map_nparams f thy = IndCodegenData.map
+ (fn x => {names = #names x, modes = #modes x, function_defs = #function_defs x,
+ function_intros = #function_intros x, function_elims = #function_elims x,
+ intro_rules = #intro_rules x, elim_rules = #elim_rules x,
+ nparams = f (#nparams x)}) thy
+
+(* Debug stuff and tactics ***********************************************************)
+
+fun tracing s = (if ! Toplevel.debug then Output.tracing s else ());
+fun print_tac s = (if ! Toplevel.debug then Tactical.print_tac s else Seq.single);
+
+fun debug_tac msg = (fn st =>
+ (tracing msg; Seq.single st));
+
+(* removes first subgoal *)
+fun mycheat_tac thy i st =
+ (Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) i) st
+
+val (do_proofs : bool ref) = ref true;
+
+(* Lightweight mode analysis **********************************************)
+
+(* Hack for message from old code generator *)
+val message = tracing;
+
+
+(**************************************************************************)
+(* source code from old code generator ************************************)
+
+(**** 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 (DatatypePackage.get_datatypes 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) ****)
+
+fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts
+ | is_eqT _ = true;
+
+(**** mode inference ****)
+
+fun string_of_mode (iss, is) = space_implode " -> " (map
+ (fn NONE => "X"
+ | SOME js => enclose "[" "]" (commas (map string_of_int js)))
+ (iss @ [SOME is]));
+
+fun print_modes modes = message ("Inferred modes:\n" ^
+ cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
+ string_of_mode ms)) modes));
+
+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 [];
+
+fun get_args is ts = let
+ fun get_args' _ _ [] = ([], [])
+ | get_args' is i (t::ts) = (if i mem is then apfst else apsnd) (cons t)
+ (get_args' is (i+1) ts)
+in get_args' is 1 ts end
+
+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 [[]];
+
+fun cprod ([], ys) = []
+ | cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys);
+
+fun cprods xss = foldr (map op :: o cprod) [[]] xss;
+
+datatype mode = Mode of (int list option list * int list) * int list * mode option list;
+
+fun modes_of modes t =
+ let
+ val ks = 1 upto length (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 = 1 upto k
+ in
+ if not (is_prefix op = prfx is) then [] else
+ let val is' = map (fn i => i - k) (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 modes arg)))
+ (iss ~~ args1)))
+ 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
+
+datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term;
+
+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) = get_args 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 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 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 check_mode_clause thy param_vs modes (iss, is) (ts, ps) =
+ let
+ val modes' = modes @ List.mapPartial
+ (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
+ (param_vs ~~ iss);
+ fun check_mode_prems vs [] = SOME vs
+ | check_mode_prems vs ps = (case select_mode_prem thy modes' vs ps of
+ NONE => NONE
+ | SOME (x, _) => check_mode_prems
+ (case x of Prem (us, _) => vs union terms_vs us | _ => vs)
+ (filter_out (equal x) ps))
+ val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (get_args is ts));
+ val in_vs = terms_vs in_ts;
+ val concl_vs = terms_vs ts
+ in
+ forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso
+ forall (is_eqT o fastype_of) in_ts' andalso
+ (case check_mode_prems (param_vs union in_vs) ps of
+ NONE => false
+ | SOME vs => concl_vs subset vs)
+ end;
+
+fun check_modes_pred thy param_vs preds modes (p, ms) =
+ let val SOME rs = AList.lookup (op =) preds p
+ in (p, List.filter (fn m => case find_index
+ (not o check_mode_clause thy param_vs modes m) rs of
+ ~1 => true
+ | i => (message ("Clause " ^ string_of_int (i+1) ^ " of " ^
+ p ^ " violates mode " ^ string_of_mode m); false)) ms)
+ end;
+
+fun fixp f (x : (string * (int list option list * int list) list) list) =
+ let val y = f x
+ in if x = y then x else fixp f y end;
+
+fun infer_modes thy extra_modes arities param_vs preds = fixp (fn modes =>
+ map (check_modes_pred thy param_vs preds (modes @ extra_modes)) modes)
+ (map (fn (s, (ks, k)) => (s, cprod (cprods (map
+ (fn NONE => [NONE]
+ | SOME k' => map SOME (subsets 1 k')) ks),
+ subsets 1 k))) arities);
+
+
+(*****************************************************************************************)
+(**** end of old source code *************************************************************)
+(*****************************************************************************************)
+(**** term construction ****)
+
+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_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_tupleT [] = HOLogic.unitT
+ | mk_tupleT Ts = foldr1 HOLogic.mk_prodT Ts;
+
+fun mk_pred_enumT T = Type ("Predicate.pred", [T])
+
+fun dest_pred_enumT (Type ("Predicate.pred", [T])) = T
+ | dest_pred_enumT T = raise TYPE ("dest_pred_enumT", [T], []);
+
+fun mk_single t =
+ let val T = fastype_of t
+ in Const(@{const_name Predicate.single}, T --> mk_pred_enumT T) $ t end;
+
+fun mk_empty T = Const (@{const_name Orderings.bot}, mk_pred_enumT T);
+
+fun mk_if_predenum cond = Const (@{const_name Predicate.if_pred},
+ HOLogic.boolT --> mk_pred_enumT HOLogic.unitT)
+ $ cond
+
+fun mk_not_pred t = let val T = mk_pred_enumT HOLogic.unitT
+ in Const (@{const_name Predicate.not_pred}, T --> 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;
+
+fun mk_Enum f =
+ let val T as Type ("fun", [T', _]) = fastype_of f
+ in
+ Const (@{const_name Predicate.Pred}, T --> mk_pred_enumT T') $ f
+ end;
+
+fun mk_Eval (f, x) =
+ let val T = fastype_of x
+ in
+ Const (@{const_name Predicate.eval}, mk_pred_enumT T --> T --> HOLogic.boolT) $ f $ x
+ end;
+
+fun mk_Eval' f =
+ let val T = fastype_of f
+ in
+ Const (@{const_name Predicate.eval}, T --> dest_pred_enumT T --> HOLogic.boolT) $ f
+ end;
+
+val mk_sup = HOLogic.mk_binop @{const_name sup};
+
+(* for simple modes (e.g. parameters) only: better call it param_funT *)
+(* or even better: remove it and only use funT'_of - some modifications to funT'_of necessary *)
+fun funT_of T NONE = T
+ | funT_of T (SOME mode) = let
+ val Ts = binder_types T;
+ val (Us1, Us2) = get_args mode Ts
+ in Us1 ---> (mk_pred_enumT (mk_tupleT Us2)) end;
+
+fun funT'_of (iss, is) T = let
+ val Ts = binder_types T
+ val (paramTs, argTs) = chop (length iss) Ts
+ val paramTs' = map2 (fn SOME is => funT'_of ([], is) | NONE => I) iss paramTs
+ val (inargTs, outargTs) = get_args is argTs
+ in
+ (paramTs' @ inargTs) ---> (mk_pred_enumT (mk_tupleT outargTs))
+ end;
+
+
+fun mk_v (names, vs) s T = (case AList.lookup (op =) vs s of
+ NONE => ((names, (s, [])::vs), Free (s, T))
+ | SOME xs =>
+ let
+ val s' = Name.variant names s;
+ val v = Free (s', T)
+ in
+ ((s'::names, AList.update (op =) (s, v::xs) vs), v)
+ end);
+
+fun distinct_v (nvs, Free (s, T)) = mk_v nvs s T
+ | distinct_v (nvs, t $ u) =
+ let
+ val (nvs', t') = distinct_v (nvs, t);
+ val (nvs'', u') = distinct_v (nvs', u);
+ in (nvs'', t' $ u') end
+ | distinct_v x = x;
+
+fun compile_match thy 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_pred_enumT U;
+ val v = Free (name, T);
+ val v' = Free (name', T);
+ in
+ lambda v (fst (DatatypePackage.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_empty U'),
+ (v', mk_empty U')]))
+ end;
+
+fun modename thy name mode = let
+ val v = (PredModetab.lookup (#names (IndCodegenData.get thy)) (name, mode))
+ in if (is_some v) then the v
+ else error ("fun modename - definition not found: name: " ^ name ^ " mode: " ^ (makestring mode))
+ end
+
+(* 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 thy modes (NONE, t) = t
+ | compile_param thy modes (m as SOME (Mode ((iss, is'), is, ms)), t) = let
+ val (f, args) = strip_comb t
+ val (params, args') = chop (length ms) args
+ val params' = map (compile_param thy modes) (ms ~~ params)
+ val f' = case f of
+ Const (name, T) =>
+ if AList.defined op = modes name then
+ Const (modename thy name (iss, is'), funT'_of (iss, is') T)
+ else error "compile param: Not an inductive predicate with correct mode"
+ | Free (name, T) => Free (name, funT_of T (SOME is'))
+ in list_comb (f', params' @ args') end
+ | compile_param _ _ _ = error "compile params"
+
+fun compile_expr thy modes (SOME (Mode (mode, is, ms)), t) =
+ (case strip_comb t of
+ (Const (name, T), params) =>
+ if AList.defined op = modes name then
+ let
+ val (Ts, Us) = get_args is
+ (curry Library.drop (length ms) (fst (strip_type T)))
+ val params' = map (compile_param thy modes) (ms ~~ params)
+ val mode_id = modename thy name mode
+ in list_comb (Const (mode_id, ((map fastype_of params') @ Ts) --->
+ mk_pred_enumT (mk_tupleT Us)), params')
+ end
+ else error "not a valid inductive expression"
+ | (Free (name, T), args) =>
+ (*if name mem param_vs then *)
+ (* Higher order mode call *)
+ let val r = Free (name, funT_of T (SOME is))
+ in list_comb (r, args) end)
+ | compile_expr _ _ _ = error "not a valid inductive expression"
+
+
+fun compile_clause thy all_vs param_vs modes (iss, is) (ts, ps) inp =
+ let
+ val modes' = modes @ List.mapPartial
+ (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
+ (param_vs ~~ iss);
+ fun check_constrt ((names, eqs), t) =
+ if is_constrt thy t then ((names, eqs), t) else
+ let
+ val s = Name.variant names "x";
+ val v = Free (s, fastype_of t)
+ in ((s::names, HOLogic.mk_eq (v, t)::eqs), v) end;
+
+ val (in_ts, out_ts) = get_args is ts;
+ val ((all_vs', eqs), in_ts') =
+ (*FIXME*) Library.foldl_map check_constrt ((all_vs, []), in_ts);
+
+ fun compile_prems out_ts' vs names [] =
+ let
+ val ((names', eqs'), out_ts'') =
+ (*FIXME*) Library.foldl_map check_constrt ((names, []), out_ts');
+ val (nvs, out_ts''') = (*FIXME*) Library.foldl_map distinct_v
+ ((names', map (rpair []) vs), out_ts'');
+ in
+ compile_match thy (snd nvs) (eqs @ eqs') out_ts'''
+ (mk_single (mk_tuple out_ts))
+ end
+ | compile_prems out_ts vs names ps =
+ let
+ val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
+ val SOME (p, mode as SOME (Mode (_, js, _))) =
+ select_mode_prem thy modes' vs' ps
+ val ps' = filter_out (equal p) ps
+ val ((names', eqs), out_ts') =
+ (*FIXME*) Library.foldl_map check_constrt ((names, []), out_ts)
+ val (nvs, out_ts'') = (*FIXME*) Library.foldl_map distinct_v
+ ((names', map (rpair []) vs), out_ts')
+ val (compiled_clause, rest) = case p of
+ Prem (us, t) =>
+ let
+ val (in_ts, out_ts''') = get_args js us;
+ val u = list_comb (compile_expr thy modes (mode, t), in_ts)
+ val rest = compile_prems out_ts''' vs' (fst nvs) ps'
+ in
+ (u, rest)
+ end
+ | Negprem (us, t) =>
+ let
+ val (in_ts, out_ts''') = get_args js us
+ val u = list_comb (compile_expr thy modes (mode, t), in_ts)
+ val rest = compile_prems out_ts''' vs' (fst nvs) ps'
+ in
+ (mk_not_pred u, rest)
+ end
+ | Sidecond t =>
+ let
+ val rest = compile_prems [] vs' (fst nvs) ps';
+ in
+ (mk_if_predenum t, rest)
+ end
+ in
+ compile_match thy (snd nvs) eqs out_ts''
+ (mk_bind (compiled_clause, rest))
+ end
+ val prem_t = compile_prems in_ts' param_vs all_vs' ps;
+ in
+ mk_bind (mk_single inp, prem_t)
+ end
+
+fun compile_pred thy all_vs param_vs modes s T cls mode =
+ let
+ val Ts = binder_types T;
+ val (Ts1, Ts2) = chop (length param_vs) Ts;
+ val Ts1' = map2 funT_of Ts1 (fst mode)
+ val (Us1, Us2) = get_args (snd mode) Ts2;
+ val xnames = Name.variant_list param_vs
+ (map (fn i => "x" ^ string_of_int i) (snd mode));
+ val xs = map2 (fn s => fn T => Free (s, T)) xnames Us1;
+ val cl_ts =
+ map (fn cl => compile_clause thy
+ all_vs param_vs modes mode cl (mk_tuple xs)) cls;
+ val mode_id = modename thy s mode
+ in
+ HOLogic.mk_Trueprop (HOLogic.mk_eq
+ (list_comb (Const (mode_id, (Ts1' @ Us1) --->
+ mk_pred_enumT (mk_tupleT Us2)),
+ map2 (fn s => fn T => Free (s, T)) param_vs Ts1' @ xs),
+ foldr1 mk_sup cl_ts))
+ end;
+
+fun compile_preds thy all_vs param_vs modes preds =
+ map (fn (s, (T, cls)) =>
+ map (compile_pred thy all_vs param_vs modes s T cls)
+ ((the o AList.lookup (op =) modes) s)) preds;
+
+(* end of term construction ******************************************************)
+
+(* special setup for simpset *)
+val HOL_basic_ss' = HOL_basic_ss setSolver
+ (mk_solver "all_tac_solver" (fn _ => fn _ => all_tac))
+
+
+(* misc: constructing and proving tupleE rules ***********************************)
+
+
+(* Creating definitions of functional programs
+ and proving intro and elim rules **********************************************)
+
+fun is_ind_pred thy c =
+ (can (InductivePackage.the_inductive (ProofContext.init thy)) c) orelse
+ (c mem_string (Symtab.keys (#intro_rules (IndCodegenData.get thy))))
+
+fun get_name_of_ind_calls_of_clauses thy preds intrs =
+ fold Term.add_consts intrs [] |> map fst
+ |> filter_out (member (op =) preds) |> filter (is_ind_pred thy)
+
+fun print_arities arities = message ("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) = get_args mode args
+ val r = mk_Eval (list_comb (x, inargs), mk_tuple outargs)
+ val t = fold_rev lambda args r
+in
+ (t, argnames @ names)
+end;
+
+fun create_intro_rule nparams mode defthm mode_id funT pred thy =
+let
+ val Ts = binder_types (fastype_of pred)
+ val funtrm = Const (mode_id, funT)
+ val argnames = Name.variant_list []
+ (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
+ val (Ts1, Ts2) = chop nparams Ts;
+ val Ts1' = map2 funT_of Ts1 (fst mode)
+ val args = map Free (argnames ~~ (Ts1' @ Ts2))
+ val (params, io_args) = chop nparams args
+ val (inargs, outargs) = get_args (snd mode) io_args
+ val (params', names) = fold_map mk_Eval_of ((params ~~ Ts1) ~~ (fst mode)) []
+ val predprop = HOLogic.mk_Trueprop (list_comb (pred, params' @ io_args))
+ val funargs = params @ inargs
+ val funpropE = HOLogic.mk_Trueprop (mk_Eval (list_comb (funtrm, funargs),
+ if null outargs then Free("y", HOLogic.unitT) else mk_tuple outargs))
+ val funpropI = HOLogic.mk_Trueprop (mk_Eval (list_comb (funtrm, funargs),
+ mk_tuple outargs))
+ val introtrm = Logic.mk_implies (predprop, funpropI)
+ val simprules = [defthm, @{thm eval_pred},
+ @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}]
+ val unfolddef_tac = (Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps simprules) 1)
+ val introthm = Goal.prove (ProofContext.init thy) (argnames @ ["y"]) [] introtrm (fn {...} => unfolddef_tac)
+ val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT));
+ val elimtrm = Logic.list_implies ([funpropE, Logic.mk_implies (predprop, P)], P)
+ val elimthm = Goal.prove (ProofContext.init thy) (argnames @ ["y", "P"]) [] elimtrm (fn {...} => unfolddef_tac)
+in
+ map_function_intros (Symtab.update_new (mode_id, introthm)) thy
+ |> map_function_elims (Symtab.update_new (mode_id, elimthm))
+ |> PureThy.store_thm (Binding.name (NameSpace.base_name mode_id ^ "I"), introthm) |> snd
+ |> PureThy.store_thm (Binding.name (NameSpace.base_name mode_id ^ "E"), elimthm) |> snd
+end;
+
+fun create_definitions preds nparams (name, modes) thy =
+ let
+ val _ = tracing "create definitions"
+ val T = AList.lookup (op =) preds name |> the
+ fun create_definition mode thy = let
+ fun string_of_mode mode = if null mode then "0"
+ else space_implode "_" (map string_of_int mode)
+ val HOmode = let
+ fun string_of_HOmode m s = case m of NONE => s | SOME mode => s ^ "__" ^ (string_of_mode mode)
+ in (fold string_of_HOmode (fst mode) "") end;
+ val mode_id = name ^ (if HOmode = "" then "_" else HOmode ^ "___")
+ ^ (string_of_mode (snd mode))
+ val Ts = binder_types T;
+ val (Ts1, Ts2) = chop nparams Ts;
+ val Ts1' = map2 funT_of Ts1 (fst mode)
+ val (Us1, Us2) = get_args (snd mode) Ts2;
+ val names = Name.variant_list []
+ (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
+ val xs = map Free (names ~~ (Ts1' @ Ts2));
+ val (xparams, xargs) = chop nparams xs;
+ val (xparams', names') = fold_map mk_Eval_of ((xparams ~~ Ts1) ~~ (fst mode)) names
+ val (xins, xouts) = get_args (snd mode) 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 = mk_Enum (mk_split_lambda xouts (list_comb (Const (name, T), xparams' @ xargs)))
+ val funT = (Ts1' @ Us1) ---> (mk_pred_enumT (mk_tupleT Us2))
+ val mode_id = Sign.full_bname thy (NameSpace.base_name mode_id)
+ val lhs = list_comb (Const (mode_id, funT), xparams @ xins)
+ val def = Logic.mk_equals (lhs, predterm)
+ val ([defthm], thy') = thy |>
+ Sign.add_consts_i [(NameSpace.base_name mode_id, funT, NoSyn)] |>
+ PureThy.add_defs false [((Binding.name (NameSpace.base_name mode_id ^ "_def"), def), [])]
+ in thy' |> map_names (PredModetab.update_new ((name, mode), mode_id))
+ |> map_function_defs (Symtab.update_new (mode_id, defthm))
+ |> create_intro_rule nparams mode defthm mode_id funT (Const (name, T))
+ end;
+ in
+ fold create_definition modes thy
+ end;
+
+(**************************************************************************************)
+(* Proving equivalence of term *)
+
+
+fun intro_rule thy pred mode = modename thy pred mode
+ |> Symtab.lookup (#function_intros (IndCodegenData.get thy)) |> the
+
+fun elim_rule thy pred mode = modename thy pred mode
+ |> Symtab.lookup (#function_elims (IndCodegenData.get thy)) |> the
+
+fun pred_intros thy predname = let
+ fun is_intro_of pred intro = let
+ val const = fst (strip_comb (HOLogic.dest_Trueprop (concl_of intro)))
+ in (fst (dest_Const const) = pred) end;
+ val d = IndCodegenData.get thy
+ in
+ if (Symtab.defined (#intro_rules d) predname) then
+ rev (Symtab.lookup_list (#intro_rules d) predname)
+ else
+ InductivePackage.the_inductive (ProofContext.init thy) predname
+ |> snd |> #intrs |> filter (is_intro_of predname)
+ end
+
+fun function_definition thy pred mode =
+ modename thy pred mode |> Symtab.lookup (#function_defs (IndCodegenData.get thy)) |> the
+
+fun is_Type (Type _) = true
+ | is_Type _ = false
+
+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 = Thm.transfer thy rule (*FIXME preprocessor
+ 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 nargs elimrule = (*FIXME preprocessor -- let
+ 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
+ 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 prems = Thm.prems_of elimrule
+ val cases' = map preprocess_case (tl prems)
+ val elimrule' = Logic.list_implies ((hd prems) :: cases', Thm.concl_of elimrule)
+ in
+ Thm.equal_elim
+ (Thm.symmetric (Conv.implies_concl_conv (MetaSimplifier.rewrite true [@ {thm eq_is_eq}])
+ (cterm_of thy elimrule')))
+ elimrule
+ end*) elimrule;
+
+
+(* 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 DatatypePackage.get_datatype 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 modes (NONE, t) = all_tac
+ | prove_param thy modes (m as SOME (Mode (mode, is, ms)), t) = let
+ val (f, args) = strip_comb 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}::function_definition thy name mode::[]) 1
+ | Free _ => all_tac
+ in
+ print_tac "before simplification in prove_args:"
+ THEN debug_tac ("mode" ^ (makestring mode))
+ THEN f_tac
+ THEN print_tac "after simplification in prove_args"
+ (* work with parameter arguments *)
+ THEN (EVERY (map (prove_param thy modes) (ms ~~ params)))
+ THEN (REPEAT_DETERM (atac 1))
+ end
+
+fun prove_expr thy modes (SOME (Mode (mode, is, ms)), t, us) (premposition : int) =
+ (case strip_comb t of
+ (Const (name, T), args) =>
+ if AList.defined op = modes name then (let
+ val introrule = intro_rule thy name mode
+ (*val (in_args, out_args) = get_args is us
+ val (pred, rargs) = strip_comb (HOLogic.dest_Trueprop
+ (hd (Logic.strip_imp_prems (prop_of introrule))))
+ val nparams = length ms (* get_nparams thy (fst (dest_Const pred)) *)
+ val (_, args) = chop nparams rargs
+ val _ = tracing ("args: " ^ (makestring args))
+ val subst = map (pairself (cterm_of thy)) (args ~~ us)
+ val _ = tracing ("subst: " ^ (makestring subst))
+ val inst_introrule = Drule.cterm_instantiate subst introrule*)
+ (* the next line is old and probably wrong *)
+ val (args1, args2) = chop (length ms) args
+ val _ = tracing ("premposition: " ^ (makestring premposition))
+ in
+ rtac @{thm bindI} 1
+ THEN print_tac "before intro rule:"
+ THEN debug_tac ("mode" ^ (makestring mode))
+ THEN debug_tac (makestring introrule)
+ THEN debug_tac ("premposition: " ^ (makestring premposition))
+ (* for the right assumption in first position *)
+ THEN rotate_tac premposition 1
+ THEN rtac introrule 1
+ THEN print_tac "after intro rule"
+ (* work with parameter arguments *)
+ THEN (EVERY (map (prove_param thy modes) (ms ~~ args1)))
+ THEN (REPEAT_DETERM (atac 1)) end)
+ else error "Prove expr if case not implemented"
+ | _ => rtac @{thm bindI} 1
+ THEN atac 1)
+ | prove_expr _ _ _ _ = error "Prove expr not implemented"
+
+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 (DatatypePackage.the_datatype 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
+ print_tac ("before prove_match rewriting: simprules = " ^ (makestring simprules))
+ (* make this simpset better! *)
+ THEN asm_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
+ val _ = tracing ("prove_sidecond:" ^ (makestring t))
+ 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 _ = tracing ("preds: " ^ (makestring preds))
+ val defs = map
+ (fn (pred, T) => function_definition thy pred ([], (1 upto (length (binder_types T)))))
+ preds
+ val _ = tracing ("defs: " ^ (makestring defs))
+in
+ (* remove not_False_eq_True when simpset in prove_match is better *)
+ simp_tac (HOL_basic_ss addsimps @{thm not_False_eq_True} :: @{thm eval_pred} :: defs) 1
+ (* need better control here! *)
+ THEN print_tac "after sidecond simplification"
+ end
+
+fun prove_clause thy nargs all_vs param_vs modes (iss, is) (ts, ps) = let
+ val modes' = modes @ List.mapPartial
+ (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
+ (param_vs ~~ iss);
+ fun check_constrt ((names, eqs), t) =
+ if is_constrt thy t then ((names, eqs), t) else
+ let
+ val s = Name.variant names "x";
+ val v = Free (s, fastype_of t)
+ in ((s::names, HOLogic.mk_eq (v, t)::eqs), v) end;
+
+ val (in_ts, clause_out_ts) = get_args is ts;
+ val ((all_vs', eqs), in_ts') =
+ (*FIXME*) Library.foldl_map check_constrt ((all_vs, []), in_ts);
+ fun prove_prems out_ts vs [] =
+ (prove_match thy out_ts)
+ THEN asm_simp_tac HOL_basic_ss' 1
+ THEN print_tac "before the last rule of singleI:"
+ THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1)
+ | prove_prems out_ts vs rps =
+ let
+ val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
+ val SOME (p, mode as SOME (Mode ((iss, js), _, param_modes))) =
+ select_mode_prem thy modes' vs' rps;
+ val premposition = (find_index (equal p) ps) + nargs
+ val rps' = filter_out (equal p) rps;
+ val rest_tac = (case p of Prem (us, t) =>
+ let
+ val (in_ts, out_ts''') = get_args js us
+ val rec_tac = prove_prems out_ts''' vs' rps'
+ in
+ print_tac "before clause:"
+ THEN asm_simp_tac HOL_basic_ss 1
+ THEN print_tac "before prove_expr:"
+ THEN prove_expr thy modes (mode, t, us) premposition
+ THEN print_tac "after prove_expr:"
+ THEN rec_tac
+ end
+ | Negprem (us, t) =>
+ let
+ val (in_ts, out_ts''') = get_args js us
+ val rec_tac = prove_prems out_ts''' vs' rps'
+ val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
+ val (_, params) = strip_comb t
+ in
+ print_tac "before negated clause:"
+ THEN rtac @{thm bindI} 1
+ THEN (if (is_some name) then
+ simp_tac (HOL_basic_ss addsimps [function_definition thy (the name) (iss, js)]) 1
+ THEN rtac @{thm not_predI} 1
+ THEN print_tac "after neg. intro rule"
+ THEN print_tac ("t = " ^ (makestring t))
+ (* FIXME: work with parameter arguments *)
+ THEN (EVERY (map (prove_param thy modes) (param_modes ~~ params)))
+ else
+ rtac @{thm not_predI'} 1)
+ THEN (REPEAT_DETERM (atac 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 [] vs' rps')
+ in (prove_match thy out_ts)
+ THEN rest_tac
+ end;
+ val prems_tac = prove_prems in_ts' param_vs 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 get_nparams thy s = let
+ val _ = tracing ("get_nparams: " ^ s)
+ in
+ if Symtab.defined (#nparams (IndCodegenData.get thy)) s then
+ the (Symtab.lookup (#nparams (IndCodegenData.get thy)) s)
+ else
+ case try (InductivePackage.the_inductive (ProofContext.init thy)) s of
+ SOME info => info |> snd |> #raw_induct |> Thm.unvarify
+ |> InductivePackage.params_of |> length
+ | NONE => 0 (* default value *)
+ end
+
+val ind_set_codegen_preproc = InductiveSetPackage.codegen_preproc;
+
+fun pred_elim thy predname =
+ if (Symtab.defined (#elim_rules (IndCodegenData.get thy)) predname) then
+ the (Symtab.lookup (#elim_rules (IndCodegenData.get thy)) predname)
+ else
+ (let
+ val ind_result = InductivePackage.the_inductive (ProofContext.init thy) predname
+ val index = find_index (fn s => s = predname) (#names (fst ind_result))
+ in nth (#elims (snd ind_result)) index end)
+
+fun prove_one_direction thy all_vs param_vs modes clauses ((pred, T), mode) = let
+ val elim_rule = the (Symtab.lookup (#function_elims (IndCodegenData.get thy)) (modename thy pred mode))
+(* val ind_result = InductivePackage.the_inductive (ProofContext.init thy) pred
+ val index = find_index (fn s => s = pred) (#names (fst ind_result))
+ val (_, T) = dest_Const (nth (#preds (snd ind_result)) index) *)
+ val nargs = length (binder_types T) - get_nparams thy pred
+ val pred_case_rule = singleton (ind_set_codegen_preproc thy)
+ (preprocess_elim thy nargs (pred_elim thy pred))
+ (* FIXME preprocessor |> Simplifier.full_simplify (HOL_basic_ss addsimps [@ {thm Predicate.memb_code}])*)
+ val _ = tracing ("pred_case_rule " ^ (makestring pred_case_rule))
+in
+ REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))
+ THEN etac elim_rule 1
+ THEN etac pred_case_rule 1
+ THEN (EVERY (map
+ (fn i => EVERY' (select_sup (length clauses) i) i)
+ (1 upto (length clauses))))
+ THEN (EVERY (map (prove_clause thy nargs all_vs param_vs modes mode) clauses))
+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 = DatatypePackage.the_datatype 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
+ print_tac ("splitting with t = " ^ (makestring t))
+ THEN (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
+*)
+fun prove_param2 thy modes (NONE, t) = all_tac
+ | prove_param2 thy modes (m as SOME (Mode (mode, is, ms)), t) = let
+ val (f, args) = strip_comb 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}::function_definition thy name mode::[]) 1
+ | Free _ => all_tac
+ in
+ print_tac "before simplification in prove_args:"
+ THEN debug_tac ("function : " ^ (makestring f) ^ " - mode" ^ (makestring mode))
+ THEN f_tac
+ THEN print_tac "after simplification in prove_args"
+ (* work with parameter arguments *)
+ THEN (EVERY (map (prove_param2 thy modes) (ms ~~ params)))
+ end
+
+fun prove_expr2 thy modes (SOME (Mode (mode, is, ms)), t) =
+ (case strip_comb t of
+ (Const (name, T), args) =>
+ if AList.defined op = modes name then
+ etac @{thm bindE} 1
+ THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})))
+ THEN (etac (elim_rule thy name mode) 1)
+ THEN (EVERY (map (prove_param2 thy modes) (ms ~~ args)))
+ else error "Prove expr2 if case not implemented"
+ | _ => etac @{thm bindE} 1)
+ | prove_expr2 _ _ _ = error "Prove expr2 not implemented"
+
+fun prove_sidecond2 thy modes t = let
+ val _ = tracing ("prove_sidecond:" ^ (makestring t))
+ 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 _ = tracing ("preds: " ^ (makestring preds))
+ val defs = map
+ (fn (pred, T) => function_definition thy pred ([], (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 all_vs param_vs modes (iss, is) (ts, ps) pred i = let
+ val modes' = modes @ List.mapPartial
+ (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
+ (param_vs ~~ iss);
+ fun check_constrt ((names, eqs), t) =
+ if is_constrt thy t then ((names, eqs), t) else
+ let
+ val s = Name.variant names "x";
+ val v = Free (s, fastype_of t)
+ in ((s::names, HOLogic.mk_eq (v, t)::eqs), v) end;
+ val pred_intro_rule = nth (pred_intros thy pred) (i - 1)
+ |> preprocess_intro thy
+ |> (fn thm => hd (ind_set_codegen_preproc thy [thm]))
+ (* FIXME preprocess |> Simplifier.full_simplify (HOL_basic_ss addsimps [@ {thm Predicate.memb_code}]) *)
+ val (in_ts, clause_out_ts) = get_args is ts;
+ val ((all_vs', eqs), in_ts') =
+ (*FIXME*) Library.foldl_map check_constrt ((all_vs, []), in_ts);
+ fun prove_prems2 out_ts vs [] =
+ 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' 1)
+ THEN print_tac "state after simp_tac:"))))
+ | prove_prems2 out_ts vs ps = let
+ val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
+ val SOME (p, mode as SOME (Mode ((iss, js), _, param_modes))) =
+ select_mode_prem thy modes' vs' ps;
+ val ps' = filter_out (equal p) ps;
+ val rest_tac = (case p of Prem (us, t) =>
+ let
+ val (in_ts, out_ts''') = get_args js us
+ val rec_tac = prove_prems2 out_ts''' vs' ps'
+ in
+ (prove_expr2 thy modes (mode, t)) THEN rec_tac
+ end
+ | Negprem (us, t) =>
+ let
+ val (in_ts, out_ts''') = get_args js us
+ val rec_tac = prove_prems2 out_ts''' vs' 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 [function_definition thy (the name) (iss, js)]) 1
+ THEN etac @{thm not_predE} 1
+ THEN (EVERY (map (prove_param2 thy modes) (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 [] vs' 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' param_vs 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 all_vs param_vs modes clauses (pred, mode) = let
+ fun prove_clause (clause, i) =
+ (if i < length clauses then etac @{thm supE} 1 else all_tac)
+ THEN (prove_clause2 thy all_vs param_vs modes mode clause pred i)
+in
+ (DETERM (TRY (rtac @{thm unit.induct} 1)))
+ THEN (REPEAT_DETERM (CHANGED (rewtac @{thm split_paired_all})))
+ THEN (rtac (intro_rule thy pred mode) 1)
+ THEN (EVERY (map prove_clause (clauses ~~ (1 upto (length clauses)))))
+end;
+
+fun prove_pred thy all_vs param_vs modes clauses (((pred, T), mode), t) = let
+ val ctxt = ProofContext.init thy
+ val clauses' = the (AList.lookup (op =) clauses pred)
+in
+ Goal.prove ctxt (Term.fold_aterms (fn Free (x, _) => insert (op =) x | _ => I) t []) [] t
+ (if !do_proofs then
+ (fn _ =>
+ rtac @{thm pred_iffI} 1
+ THEN prove_one_direction thy all_vs param_vs modes clauses' ((pred, T), mode)
+ THEN print_tac "proved one direction"
+ THEN prove_other_direction thy all_vs param_vs modes clauses' (pred, mode)
+ THEN print_tac "proved other direction")
+ else (fn _ => mycheat_tac thy 1))
+end;
+
+fun prove_preds thy all_vs param_vs modes clauses pmts =
+ map (prove_pred thy all_vs param_vs modes clauses) pmts
+
+(* look for other place where this functionality was used before *)
+fun strip_intro_concl intro nparams = 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
+
+(* setup for alternative introduction and elimination rules *)
+
+fun add_intro_thm thm thy = let
+ val (pred, _) = dest_Const (fst (strip_intro_concl (prop_of thm) 0))
+ in map_intro_rules (Symtab.insert_list Thm.eq_thm (pred, thm)) thy end
+
+fun add_elim_thm thm thy = let
+ val (pred, _) = dest_Const (fst
+ (strip_comb (HOLogic.dest_Trueprop (hd (prems_of thm)))))
+ in map_elim_rules (Symtab.update (pred, thm)) thy end
+
+
+(* special case: inductive predicate with no clauses *)
+fun noclause (predname, T) thy = let
+ val Ts = binder_types T
+ val names = Name.variant_list []
+ (map (fn i => "x" ^ (string_of_int i)) (1 upto (length Ts)))
+ val vs = map 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_thm = Goal.prove (ProofContext.init thy) names [] intro_t
+ (fn {...} => etac @{thm FalseE} 1)
+ val elim_thm = Goal.prove (ProofContext.init thy) ("P" :: names) [] elim_t
+ (fn {...} => etac (pred_elim thy predname) 1)
+in
+ add_intro_thm intro_thm thy
+ |> add_elim_thm elim_thm
+end
+
+(*************************************************************************************)
+(* main function *********************************************************************)
+(*************************************************************************************)
+
+fun create_def_equation' ind_name (mode : (int list option list * int list) option) thy =
+let
+ val _ = tracing ("starting create_def_equation' with " ^ ind_name)
+ val (prednames, preds) =
+ case (try (InductivePackage.the_inductive (ProofContext.init thy)) ind_name) of
+ SOME info => let val preds = info |> snd |> #preds
+ in (map (fst o dest_Const) preds, map ((apsnd Logic.unvarifyT) o dest_Const) preds) end
+ | NONE => let
+ val pred = Symtab.lookup (#intro_rules (IndCodegenData.get thy)) ind_name
+ |> the |> hd |> prop_of
+ |> Logic.strip_imp_concl |> HOLogic.dest_Trueprop |> strip_comb
+ |> fst |> dest_Const |> apsnd Logic.unvarifyT
+ in ([ind_name], [pred]) end
+ val thy' = fold (fn pred as (predname, T) => fn thy =>
+ if null (pred_intros thy predname) then noclause pred thy else thy) preds thy
+ val intrs = map (preprocess_intro thy') (maps (pred_intros thy') prednames)
+ |> ind_set_codegen_preproc thy' (*FIXME preprocessor
+ |> map (Simplifier.full_simplify (HOL_basic_ss addsimps [@ {thm Predicate.memb_code}]))*)
+ |> map (Logic.unvarify o prop_of)
+ val _ = tracing ("preprocessed intro rules:" ^ (makestring (map (cterm_of thy') intrs)))
+ val name_of_calls = get_name_of_ind_calls_of_clauses thy' prednames intrs
+ val _ = tracing ("calling preds: " ^ makestring name_of_calls)
+ val _ = tracing "starting recursive compilations"
+ fun rec_call name thy =
+ if not (name mem (Symtab.keys (#modes (IndCodegenData.get thy)))) then
+ create_def_equation name thy else thy
+ val thy'' = fold rec_call name_of_calls thy'
+ val _ = tracing "returning from recursive calls"
+ val _ = tracing "starting mode inference"
+ val extra_modes = Symtab.dest (#modes (IndCodegenData.get thy''))
+ val nparams = get_nparams thy'' ind_name
+ 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: " ^ (makestring (c $ t)))
+ | Sidecond t => Sidecond (c $ t))
+ | (c as Const (s, _), ts) =>
+ if is_ind_pred thy'' s then
+ let val (ts1, ts2) = chop (get_nparams 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 ([], []);
+ val modes = infer_modes thy'' extra_modes arities param_vs clauses
+ val _ = print_arities arities;
+ val _ = print_modes modes;
+ val modes = if (is_some mode) then AList.update (op =) (ind_name, [the mode]) modes else modes
+ val _ = print_modes modes
+ val thy''' = fold (create_definitions preds nparams) modes thy''
+ |> map_modes (fold Symtab.update_new modes)
+ val clauses' = map (fn (s, cls) => (s, (the (AList.lookup (op =) preds s), cls))) clauses
+ val _ = tracing "compiling predicates..."
+ val ts = compile_preds thy''' all_vs param_vs (extra_modes @ modes) clauses'
+ val _ = tracing "returned term from compile_preds"
+ val pred_mode = maps (fn (s, (T, _)) => map (pair (s, T)) ((the o AList.lookup (op =) modes) s)) clauses'
+ val _ = tracing "starting proof"
+ val result_thms = prove_preds thy''' all_vs param_vs (extra_modes @ modes) clauses (pred_mode ~~ (flat ts))
+ val (_, thy'''') = yield_singleton PureThy.add_thmss
+ ((Binding.name (NameSpace.base_name ind_name ^ "_codegen" (*FIXME other suffix*)), result_thms),
+ [Attrib.attribute_i thy''' Code.add_default_eqn_attrib]) thy'''
+in
+ thy''''
+end
+and create_def_equation ind_name thy = create_def_equation' ind_name NONE thy
+
+fun set_nparams (pred, nparams) thy = map_nparams (Symtab.update (pred, nparams)) thy
+
+fun print_alternative_rules thy = let
+ val d = IndCodegenData.get thy
+ val preds = (Symtab.keys (#intro_rules d)) union (Symtab.keys (#elim_rules d))
+ val _ = tracing ("preds: " ^ (makestring preds))
+ fun print pred = let
+ val _ = tracing ("predicate: " ^ pred)
+ val _ = tracing ("introrules: ")
+ val _ = fold (fn thm => fn u => tracing (makestring thm))
+ (rev (Symtab.lookup_list (#intro_rules d) pred)) ()
+ val _ = tracing ("casesrule: ")
+ val _ = tracing (makestring (Symtab.lookup (#elim_rules d) pred))
+ in () end
+ val _ = map print preds
+ in thy end;
+
+fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I)
+
+val code_ind_intros_attrib = attrib add_intro_thm
+
+val code_ind_cases_attrib = attrib add_elim_thm
+
+val setup = Attrib.add_attributes
+ [("code_ind_intros", Attrib.no_args code_ind_intros_attrib,
+ "adding alternative introduction rules for code generation of inductive predicates"),
+ ("code_ind_cases", Attrib.no_args code_ind_cases_attrib,
+ "adding alternative elimination rules for code generation of inductive predicates")]
+
+end;
+
+fun pred_compile name thy = Predicate_Compile.create_def_equation
+ (Sign.intern_const thy name) thy;