--- a/src/HOL/ex/predicate_compile.ML Tue Jun 09 10:23:41 2009 -0700
+++ b/src/HOL/ex/predicate_compile.ML Tue Jun 09 11:12:08 2009 -0700
@@ -7,21 +7,24 @@
signature PREDICATE_COMPILE =
sig
type mode = int list option list * int list
- val prove_equation: string -> mode option -> theory -> theory
- val intro_rule: theory -> string -> mode -> thm
- val elim_rule: theory -> string -> mode -> thm
- val strip_intro_concl: term -> int -> term * (term list * term list)
- val modename_of: theory -> string -> mode -> string
+ val add_equations_of: string list -> theory -> theory
+ val register_predicate : (thm list * thm * int) -> theory -> theory
+ 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 pred_intros: theory -> string -> thm list
- val get_nparams: theory -> string -> int
+ val intros_of: theory -> string -> thm list
+ val nparams_of: theory -> string -> int
val setup: theory -> theory
val code_pred: string -> Proof.context -> Proof.state
val code_pred_cmd: string -> Proof.context -> Proof.state
- val print_alternative_rules: theory -> theory (*FIXME diagnostic command?*)
+(* val print_alternative_rules: theory -> theory (*FIXME diagnostic command?*) *)
val do_proofs: bool ref
val analyze_compr: theory -> term -> term
val eval_ref: (unit -> term Predicate.pred) option ref
+ val add_equations : string -> theory -> theory
end;
structure Predicate_Compile : PREDICATE_COMPILE =
@@ -31,8 +34,6 @@
(* debug stuff *)
-fun makestring _ = "?"; (* FIXME dummy *)
-
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);
@@ -40,6 +41,12 @@
val do_proofs = ref true;
+fun mycheat_tac thy i st =
+ (Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) i) st
+
+(* reference to preprocessing of InductiveSet package *)
+
+val ind_set_codegen_preproc = InductiveSetPackage.codegen_preproc;
(** fundamentals **)
@@ -54,6 +61,10 @@
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;
@@ -61,9 +72,9 @@
| dest_tuple (Const (@{const_name Pair}, _) $ t1 $ t2) = t1 :: (dest_tuple t2)
| dest_tuple t = [t]
-fun mk_pred_enumT T = Type ("Predicate.pred", [T])
+fun mk_pred_enumT T = Type (@{type_name "Predicate.pred"}, [T])
-fun dest_pred_enumT (Type ("Predicate.pred", [T])) = T
+fun dest_pred_enumT (Type (@{type_name "Predicate.pred"}, [T])) = T
| dest_pred_enumT T = raise TYPE ("dest_pred_enumT", [T], []);
fun mk_Enum f =
@@ -98,120 +109,163 @@
fun mk_not_pred t = let val T = mk_pred_enumT HOLogic.unitT
in Const (@{const_name Predicate.not_pred}, T --> T) $ t end
+(* 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 mode = int list option list * int list;
+type mode = int list option list * int list; (*pmode FIMXE*)
+
+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 = Output.tracing ("Inferred modes:\n" ^
+ cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
+ string_of_mode ms)) modes));
-val mode_ord = prod_ord (list_ord (option_ord (list_ord int_ord))) (list_ord int_ord);
+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}
-structure PredModetab = TableFun(
- type key = string * mode
- val ord = prod_ord fast_string_ord mode_ord
-);
+datatype pred_data = PredData of {
+ intros : thm list,
+ elim : thm option,
+ nparams : int,
+ functions : (mode * predfun_data) list
+};
-
-(*FIXME scrap boilerplate*)
-
-structure IndCodegenData = TheoryDataFun
+fun rep_pred_data (PredData data) = data;
+fun mk_pred_data ((intros, elim, nparams), functions) =
+ PredData {intros = intros, elim = elim, nparams = nparams, functions = functions}
+fun map_pred_data f (PredData {intros, elim, nparams, functions}) =
+ mk_pred_data (f ((intros, elim, nparams), 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 = {names : string PredModetab.table,
- modes : mode 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
- }; (*FIXME: better group tables according to key*)
- (* 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};
+ type T = pred_data Graph.T;
+ val empty = Graph.empty;
val copy = I;
val extend = I;
- fun merge _ (r : T * T) = {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 merge _ = Graph.merge eq_pred_data;
);
- 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
+(* queries *)
+
+val lookup_pred_data = try rep_pred_data oo Graph.get_node o PredData.get;
+
+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_pred = is_some oo lookup_pred_data
- 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
+val all_preds_of = Graph.keys o PredData.get
+
+val intros_of = #intros oo the_pred_data
+
+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
+
+val has_elim = is_some o #elim oo the_pred_data;
+
+val nparams_of = #nparams oo the_pred_data
- 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
+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 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 the_predfun_data thy name mode = case lookup_predfun_data thy name mode
+ of NONE => error ("No such mode" ^ string_of_mode mode)
+ | 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 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
+(* replaces print_alternative_rules *)
+(* TODO:
+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;
+*)
+
+(* updaters *)
+
+fun add_predfun name mode data = let
+ val add = apsnd (cons (mode, mk_predfun_data data))
+ in PredData.map (Graph.map_node name (map_pred_data add)) end
- 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
+fun add_intro thm = let
+ val (name, _) = dest_Const (fst (strip_intro_concl 0 (prop_of thm)))
+ fun set (intros, elim, nparams) = (thm::intros, elim, nparams)
+ in PredData.map (Graph.map_node name (map_pred_data (apfst set))) 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
-(* removes first subgoal *)
-fun mycheat_tac thy i st =
- (Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) i) st
-
-(* Lightweight mode analysis **********************************************)
+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
-(**************************************************************************)
-(* source code from old code generator ************************************)
+fun register_predicate (intros, elim, nparams) = let
+ val (name, _) = dest_Const (fst (strip_intro_concl nparams (prop_of (hd intros))))
+ fun set _ = (intros, SOME elim, nparams)
+ in PredData.map (Graph.new_node (name, mk_pred_data ((intros, SOME elim, nparams), []))) end
-(**** check if a term contains only constructor functions ****)
+
+(* Mode analysis *)
+(*** check if a term contains only constructor functions ***)
fun is_constrt thy =
let
val cnstrs = flat (maps
@@ -225,23 +279,11 @@
| _ => false)
in check end;
-(**** check if a type is an equality type (i.e. doesn't contain fun)
- FIXME this is only an approximation ****)
-
+(*** 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;
-(**** 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 = tracing ("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;
@@ -265,16 +307,52 @@
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;
datatype hmode = Mode of mode * int list * hmode option list; (*FIXME don't understand
- why there is another mode type!?*)
+ why there is another mode type tmode !?*)
-fun modes_of_term modes t =
+
+(*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 modes_of_term modes t =
let
val ks = 1 upto length (binder_types (fastype_of t));
val default = [Mode (([], ks), ks, [])];
@@ -301,6 +379,7 @@
(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 _, []) => modes_of_param default modes t
| _ => default)
end
@@ -376,10 +455,7 @@
subsets 1 k))) arities);
-(*****************************************************************************************)
-(**** end of old source code *************************************************************)
-(*****************************************************************************************)
-(**** term construction ****)
+(* term construction *)
(* 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 *)
@@ -400,22 +476,22 @@
fun mk_v (names, vs) s T = (case AList.lookup (op =) vs s of
- NONE => ((names, (s, [])::vs), Free (s, T))
+ NONE => (Free (s, T), (names, (s, [])::vs))
| 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)
+ (v, (s'::names, AList.update (op =) (s, v::xs) vs))
end);
-fun distinct_v (nvs, Free (s, T)) = mk_v nvs s T
- | distinct_v (nvs, t $ u) =
+fun distinct_v (Free (s, T)) nvs = mk_v nvs s T
+ | distinct_v (t $ u) nvs =
let
- val (nvs', t') = distinct_v (nvs, t);
- val (nvs'', u') = distinct_v (nvs', u);
- in (nvs'', t' $ u') end
- | distinct_v x = x;
+ 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 eqs eqs' out_ts success_t =
let
@@ -439,15 +515,6 @@
(v', mk_empty U')]))
end;
-fun modename_of thy name mode = let
- val v = (PredModetab.lookup (#names (IndCodegenData.get thy)) (name, mode))
- in if (is_some v) then the v (*FIXME use case here*)
- else error ("fun modename_of - definition not found: name: " ^ name ^ " mode: " ^ (makestring mode))
- end
-
-fun modes_of thy =
- these o Symtab.lookup ((#modes o IndCodegenData.get) thy);
-
(*FIXME function can be removed*)
fun mk_funcomp f t =
let
@@ -459,20 +526,58 @@
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
+
+
+fun compile_param_ext thy modes (NONE, t) = t
+ | compile_param_ext thy modes (m as SOME (Mode ((iss, is'), is, ms)), t) =
+ let
+ val (vs, u) = strip_abs t
+ val (ivs, ovs) = get_args is vs
+ val (f, args) = strip_comb u
+ val (params, args') = chop (length ms) args
+ val (inargs, outargs) = get_args 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 (get_args 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
+ Const (predfun_name_of 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'))
+ val outTs = dest_tupleT (dest_pred_enumT (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 (mk_tuple (map (fn i => nth out_vs (i - 1)) outp_perm)))
+ val match_t = compile_match thy [] [] out_vs single_t
+ in list_abs (ivs,
+ mk_bind (f_app, match_t))
+ end
+ | compile_param_ext _ _ _ = error "compile params"
+
+and compile_param thy modes (NONE, t) = t
+ | compile_param thy modes (m as SOME (Mode ((iss, is'), is, ms)), t) =
+ (case t of
+ Abs _ => compile_param_ext thy modes (m, 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_of thy name (iss, is'), funT'_of (iss, is') T)
+ Const (predfun_name_of 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"
-
+ 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) =>
@@ -481,8 +586,7 @@
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_of thy name mode
- in list_comb (Const (mode_id, ((map fastype_of params') @ Ts) --->
+ in list_comb (Const (predfun_name_of thy name mode, ((map fastype_of params') @ Ts) --->
mk_pred_enumT (mk_tupleT Us)), params')
end
else error "not a valid inductive expression"
@@ -499,25 +603,25 @@
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
+ 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 ((s::names, HOLogic.mk_eq (v, t)::eqs), v) end;
+ in (v, (s::names, HOLogic.mk_eq (v, t)::eqs)) 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);
+ val (in_ts', (all_vs', eqs)) =
+ fold_map check_constrt in_ts (all_vs, []);
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'');
+ 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
- compile_match thy (snd nvs) (eqs @ eqs') out_ts'''
+ compile_match thy constr_vs (eqs @ eqs') out_ts'''
(mk_single (mk_tuple out_ts))
end
| compile_prems out_ts vs names ps =
@@ -526,16 +630,16 @@
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 (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''') = 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'
+ val rest = compile_prems out_ts''' vs' names'' ps'
in
(u, rest)
end
@@ -543,18 +647,18 @@
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'
+ val rest = compile_prems out_ts''' vs' names'' ps'
in
(mk_not_pred u, rest)
end
| Sidecond t =>
let
- val rest = compile_prems [] vs' (fst nvs) ps';
+ val rest = compile_prems [] vs' names'' ps';
in
(mk_if_predenum t, rest)
end
in
- compile_match thy (snd nvs) eqs out_ts''
+ compile_match thy constr_vs' eqs out_ts''
(mk_bind (compiled_clause, rest))
end
val prem_t = compile_prems in_ts' param_vs all_vs' ps;
@@ -574,7 +678,7 @@
val cl_ts =
map (fn cl => compile_clause thy
all_vs param_vs modes mode cl (mk_tuple xs)) cls;
- val mode_id = modename_of thy s mode
+ val mode_id = predfun_name_of thy s mode
in
HOLogic.mk_Trueprop (HOLogic.mk_eq
(list_comb (Const (mode_id, (Ts1' @ Us1) --->
@@ -588,26 +692,13 @@
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)
+(* 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 ^ ": " ^
@@ -628,7 +719,7 @@
(t, argnames @ names)
end;
-fun create_intro_rule nparams mode defthm mode_id funT pred thy =
+fun create_intro_elim_rule nparams mode defthm mode_id funT pred thy =
let
val Ts = binder_types (fastype_of pred)
val funtrm = Const (mode_id, funT)
@@ -654,11 +745,8 @@
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 (Long_Name.base_name mode_id ^ "I"), introthm) |> snd
- |> PureThy.store_thm (Binding.name (Long_Name.base_name mode_id ^ "E"), elimthm) |> snd
+in
+ (introthm, elimthm)
end;
fun create_definitions preds nparams (name, modes) thy =
@@ -694,12 +782,13 @@
val mode_id = Sign.full_bname thy (Long_Name.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 |>
+ val ([definition], thy') = thy |>
Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_id), funT, NoSyn)] |>
PureThy.add_defs false [((Binding.name (Long_Name.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))
+ val (intro, elim) = create_intro_elim_rule nparams mode definition mode_id funT (Const (name, T)) thy'
+ in thy' |> add_predfun name mode (mode_id, definition, intro, elim)
+ |> PureThy.store_thm (Binding.name (Long_Name.base_name mode_id ^ "I"), intro) |> snd
+ |> PureThy.store_thm (Binding.name (Long_Name.base_name mode_id ^ "E"), elim) |> snd
end;
in
fold create_definition modes thy
@@ -708,29 +797,6 @@
(**************************************************************************************)
(* Proving equivalence of term *)
-
-fun intro_rule thy pred mode = modename_of thy pred mode
- |> Symtab.lookup (#function_intros (IndCodegenData.get thy)) |> the
-
-fun elim_rule thy pred mode = modename_of 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_of thy pred mode |> Symtab.lookup (#function_defs (IndCodegenData.get thy)) |> the
-
fun is_Type (Type _) = true
| is_Type _ = false
@@ -793,11 +859,12 @@
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
+ (@{thm eval_pred}::(predfun_definition_of thy name mode)::
+ @{thm "Product_Type.split_conv"}::[])) 1
| Free _ => all_tac
+ | Abs _ => error "TODO: implement here"
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 *)
@@ -809,25 +876,19 @@
(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 introrule = predfun_intro_of 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
@@ -854,9 +915,8 @@
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
+ 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))))
@@ -866,26 +926,22 @@
(* 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_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 ([], (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 @{thm not_False_eq_True} :: @{thm eval_pred} :: defs) 1
+ (* need better control here! *)
+ end
fun prove_clause thy nargs all_vs param_vs modes (iss, is) (ts, ps) = let
val modes' = modes @ List.mapPartial
@@ -932,13 +988,10 @@
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
+ rtac @{thm bindI} 1
THEN (if (is_some name) then
- simp_tac (HOL_basic_ss addsimps [function_definition thy (the name) (iss, js)]) 1
+ simp_tac (HOL_basic_ss addsimps [predfun_definition_of 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
@@ -967,43 +1020,17 @@
| select_sup _ 1 = [rtac @{thm supI1}]
| select_sup n i = (rtac @{thm supI2})::(select_sup (n - 1) (i - 1));
-(* FIXME: This function relies on the derivation of an induction rule *)
-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_of 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 nargs = length (binder_types T) - nparams_of thy pred
val pred_case_rule = singleton (ind_set_codegen_preproc thy)
- (preprocess_elim thy nargs (pred_elim thy pred))
+ (preprocess_elim thy nargs (the_elim_of 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 (predfun_elim_of thy pred mode) 1
THEN etac pred_case_rule 1
THEN (EVERY (map
(fn i => EVERY' (select_sup (length clauses) i) i)
@@ -1027,8 +1054,7 @@
| _ => 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)
+ (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))
@@ -1049,11 +1075,11 @@
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
+ (@{thm eval_pred}::(predfun_definition_of thy name mode)
+ :: @{thm "Product_Type.split_conv"}::[])) 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 *)
@@ -1066,23 +1092,21 @@
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 (etac (predfun_elim_of 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)))))
+ (fn (pred, T) => predfun_definition_of thy pred ([], (1 upto (length (binder_types T)))))
preds
in
(* only simplify the one assumption *)
@@ -1101,7 +1125,7 @@
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)
+ val pred_intro_rule = nth (intros_of 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}]) *)
@@ -1146,7 +1170,7 @@
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
+ full_simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, js)]) 1
THEN etac @{thm not_predE} 1
THEN (EVERY (map (prove_param2 thy modes) (param_modes ~~ params)))
else
@@ -1180,7 +1204,7 @@
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 (rtac (predfun_intro_of thy pred mode) 1)
THEN (EVERY (map prove_clause (clauses ~~ (1 upto (length clauses)))))
end;
@@ -1202,25 +1226,6 @@
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
@@ -1231,137 +1236,110 @@
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
+ val intro = 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)
+ val elim = Goal.prove (ProofContext.init thy) ("P" :: names) [] elim_t
+ (fn {...} => etac (the_elim_of thy predname) 1)
in
- add_intro_thm intro_thm thy
- |> add_elim_thm elim_thm
+ add_intro intro thy
+ |> set_elim elim
end
-(*************************************************************************************)
-(* main function *********************************************************************)
-(*************************************************************************************)
-
-fun prove_equation ind_name mode thy =
-let
- val _ = tracing ("starting prove_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 =
- (*FIXME use member instead of infix mem*)
- if not (name mem (Symtab.keys (#modes (IndCodegenData.get thy)))) then
- prove_equation name NONE 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 =
+fun prepare_intrs thy prednames =
+ let
+ val intrs = map (preprocess_intro thy) (maps (intros_of 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 nparams = nparams_of thy (hd prednames)
+ val preds = distinct (op =) (map (dest_Const o fst o (strip_intro_concl nparams)) intrs)
+ val extra_modes = all_modes_of thy |> filter_out (fn (name, _) => member (op =) prednames 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)))
+ | 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_ind_pred thy'' s then
- let val (ts1, ts2) = chop (get_nparams thy'' s) ts
+ if is_pred 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
+ 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)
+ end;
+ val (clauses, arities) = fold add_clause intrs ([], []);
+ in (preds, nparams, all_vs, param_vs, extra_modes, clauses, arities) end;
+
+fun arrange kvs =
+ let
+ fun add (key, value) table =
+ AList.update op = (key, these (AList.lookup op = table key) @ [value]) table
+ in fold add kvs [] end;
+
+(* main function *)
+
+fun add_equations_of prednames thy =
+let
+ val _ = tracing ("starting add_equations with " ^ commas prednames ^ "...")
+ (* null clause handling *)
+ (*
+ val thy' = fold (fn pred as (predname, T) => fn thy =>
+ if null (intros_of thy predname) then noclause pred thy else thy) preds thy
+ *)
+ val (preds, nparams, all_vs, param_vs, extra_modes, clauses, arities) =
+ prepare_intrs thy prednames
+ val _ = tracing "Infering modes..."
+ val modes = infer_modes thy extra_modes arities param_vs clauses
+ val _ = tracing "Defining executable functions..."
+ val thy' = fold (create_definitions preds nparams) modes thy
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.qualify true (Long_Name.base_name ind_name) (Binding.name "equation"), result_thms),
- [Attrib.attribute_i thy''' Code.add_default_eqn_attrib]) thy'''
+ val _ = tracing "Compiling equations..."
+ val ts = compile_preds thy' all_vs param_vs (extra_modes @ modes) clauses'
+ val pred_mode =
+ maps (fn (s, (T, _)) => map (pair (s, T)) ((the o AList.lookup (op =) modes) s)) clauses'
+ val _ = tracing "Proving equations..."
+ val result_thms =
+ prove_preds thy' all_vs param_vs (extra_modes @ modes) clauses (pred_mode ~~ (flat ts))
+ val thy'' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss
+ [((Binding.qualify true (Long_Name.base_name name) (Binding.name "equation"), result_thms),
+ [Attrib.attribute_i thy Code.add_default_eqn_attrib])] thy))
+ (arrange ((map (fn ((name, _), _) => name) pred_mode) ~~ result_thms)) thy'
in
- thy''''
+ thy''
end
-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;
-
-
(* generation of case rules from user-given introduction rules *)
fun mk_casesrule introrules nparams ctxt =
let
val intros = map prop_of introrules
- val (pred, (params, args)) = strip_intro_concl (hd intros) nparams
+ 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 = map Free (argnames ~~ (map fastype_of args))
- (*FIXME map2*)
+ val argvs = map2 (curry Free) argnames (map fastype_of args)
fun mk_case intro = let
- val (_, (_, args)) = strip_intro_concl intro nparams
+ 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)
@@ -1376,6 +1354,46 @@
ctxt2
in (pred, prop, ctxt3) end;
+(* code dependency graph *)
+
+fun fetch_pred_data thy name =
+ case try (InductivePackage.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 = filter is_intro_of (#intrs result)
+ val elim = nth (#elims result) (find_index (fn s => s = name) (#names (fst info)))
+ val nparams = length (InductivePackage.params_of (#raw_induct result))
+ in mk_pred_data ((intros, SOME elim, nparams), []) end
+ | NONE => error ("No such predicate: " ^ quote name)
+
+fun dependencies_of (thy : theory) name =
+ let
+ fun is_inductive_predicate thy name =
+ is_some (try (InductivePackage.the_inductive (ProofContext.init thy)) name)
+ val data = fetch_pred_data thy name
+ val intros = map Thm.prop_of (#intros (rep_pred_data data))
+ val keys = fold Term.add_consts intros [] |> map fst
+ |> filter (is_inductive_predicate thy)
+ in
+ (data, keys)
+ end;
+
+fun add_equations name thy =
+ let
+ val thy' = PredData.map (Graph.extend (dependencies_of thy) [name]) thy;
+ (*val preds = Graph.all_preds (PredData.get thy') [name] |> filter_out (has_elim thy') *)
+ 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') [name]
+ val thy'' = fold_rev
+ (fn preds => fn thy =>
+ if forall (null o modes_of thy) preds then add_equations_of preds thy else thy)
+ scc thy'
+ in thy'' end
(** user interface **)
@@ -1383,26 +1401,47 @@
fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I);
-val add_elim_attrib = attrib add_elim_thm;
+(*
+val add_elim_attrib = attrib set_elim;
+*)
+
+(* TODO: make TheoryDataFun to GenericDataFun & remove duplication of local theory and theory *)
+(* TODO: must create state to prove multiple cases *)
fun generic_code_pred prep_const raw_const lthy =
let
- val thy = ProofContext.theory_of lthy
+ val thy = (ProofContext.theory_of lthy)
val const = prep_const thy raw_const
- val nparams = get_nparams thy const
- val intro_rules = pred_intros thy const
- val (((tfrees, frees), fact), lthy') =
- Variable.import_thms true intro_rules lthy;
- val (pred, prop, lthy'') = mk_casesrule fact nparams lthy'
- val (predname, _) = dest_Const pred
- fun after_qed [[th]] lthy'' =
- lthy''
+ val lthy' = lthy
+ val thy' = PredData.map (Graph.extend (dependencies_of thy) [const]) thy
+ val preds = Graph.all_preds (PredData.get thy') [const] |> filter_out (has_elim thy')
+ val _ = Output.tracing ("preds: " ^ commas preds)
+ (*
+ fun mk_elim pred =
+ let
+ val nparams = nparams_of thy pred
+ val intros = intros_of thy pred
+ val (((tfrees, frees), fact), lthy'') =
+ Variable.import_thms true intros lthy';
+ val (pred, prop, lthy''') = mk_casesrule fact nparams lthy''
+ in (pred, prop, lthy''') end;
+
+ val (predname, _) = dest_Const pred
+ *)
+ val nparams = nparams_of thy' const
+ val intros = intros_of thy' const
+ val (((tfrees, frees), fact), lthy'') =
+ Variable.import_thms true intros lthy';
+ val (pred, prop, lthy''') = mk_casesrule fact nparams lthy''
+ val (predname, _) = dest_Const pred
+ fun after_qed [[th]] lthy''' =
+ lthy'''
|> LocalTheory.note Thm.generatedK
- ((Binding.empty, [Attrib.internal (K add_elim_attrib)]), [th])
+ ((Binding.empty, []), [th])
|> snd
- |> LocalTheory.theory (prove_equation predname NONE)
+ |> LocalTheory.theory (add_equations_of [predname])
in
- Proof.theorem_i NONE after_qed [[(prop, [])]] lthy''
+ Proof.theorem_i NONE after_qed [[(prop, [])]] lthy'''
end;
structure P = OuterParse
@@ -1412,14 +1451,15 @@
val code_pred = generic_code_pred (K I);
val code_pred_cmd = generic_code_pred Code.read_const
-val setup =
- Attrib.setup @{binding code_ind_intros} (Scan.succeed (attrib add_intro_thm))
- "adding alternative introduction rules for code generation of inductive predicates" #>
- Attrib.setup @{binding code_ind_cases} (Scan.succeed add_elim_attrib)
+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 atribute for cases?*)
+ (*FIXME why distinguished attribute for cases?*)
val _ = OuterSyntax.local_theory_to_proof "code_pred"
"prove equations for predicate specified by intro/elim rules"
@@ -1443,21 +1483,20 @@
val (body, Ts, fp) = HOLogic.strip_split split;
(*FIXME former order of tuple positions must be restored*)
val (pred as Const (name, T), all_args) = strip_comb body
- val (params, args) = chop (get_nparams thy name) all_args
+ 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 (inargs, _) = get_args user_mode args;
- val all_modes = Symtab.dest (#modes (IndCodegenData.get thy));
val modes = filter (fn Mode (_, is, _) => is = user_mode)
- (modes_of_term all_modes (list_comb (pred, params)));
+ (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 t_eval = list_comb (compile_expr thy all_modes (SOME m, list_comb (pred, params)),
+ val t_eval = list_comb (compile_expr thy (all_modes_of thy) (SOME m, list_comb (pred, params)),
inargs)
in t_eval end;
--- a/src/Provers/Arith/fast_lin_arith.ML Tue Jun 09 10:23:41 2009 -0700
+++ b/src/Provers/Arith/fast_lin_arith.ML Tue Jun 09 11:12:08 2009 -0700
@@ -1,6 +1,6 @@
(* Title: Provers/Arith/fast_lin_arith.ML
ID: $Id$
- Author: Tobias Nipkow and Tjark Weber
+ Author: Tobias Nipkow and Tjark Weber and Sascha Boehme
A generic linear arithmetic package. It provides two tactics
(cut_lin_arith_tac, lin_arith_tac) and a simplification procedure
@@ -21,6 +21,7 @@
val not_lessD : thm (* ~(m < n) ==> n <= m *)
val not_leD : thm (* ~(m <= n) ==> n < m *)
val sym : thm (* x = y ==> y = x *)
+ val trueI : thm (* True *)
val mk_Eq : thm -> thm
val atomize : thm -> thm list
val mk_Trueprop : term -> term
@@ -56,7 +57,6 @@
(*preprocessing, performed on the goal -- must do the same as 'pre_decomp':*)
val pre_tac: Proof.context -> int -> tactic
- val mk_number: typ -> int -> term
(*the limit on the number of ~= allowed; because each ~= is split
into two cases, this can lead to an explosion*)
@@ -90,9 +90,11 @@
val lin_arith_tac: Proof.context -> bool -> int -> tactic
val lin_arith_simproc: simpset -> term -> thm option
val map_data: ({add_mono_thms: thm list, mult_mono_thms: thm list, inj_thms: thm list,
- lessD: thm list, neqE: thm list, simpset: Simplifier.simpset}
+ lessD: thm list, neqE: thm list, simpset: Simplifier.simpset,
+ number_of : serial * (theory -> typ -> int -> cterm)}
-> {add_mono_thms: thm list, mult_mono_thms: thm list, inj_thms: thm list,
- lessD: thm list, neqE: thm list, simpset: Simplifier.simpset})
+ lessD: thm list, neqE: thm list, simpset: Simplifier.simpset,
+ number_of : serial * (theory -> typ -> int -> cterm)})
-> Context.generic -> Context.generic
val trace: bool ref
val warning_count: int ref;
@@ -105,6 +107,8 @@
(** theory data **)
+fun no_number_of _ _ _ = raise CTERM ("number_of", [])
+
structure Data = GenericDataFun
(
type T =
@@ -113,22 +117,27 @@
inj_thms: thm list,
lessD: thm list,
neqE: thm list,
- simpset: Simplifier.simpset};
+ simpset: Simplifier.simpset,
+ number_of : serial * (theory -> typ -> int -> cterm)};
val empty = {add_mono_thms = [], mult_mono_thms = [], inj_thms = [],
- lessD = [], neqE = [], simpset = Simplifier.empty_ss};
+ lessD = [], neqE = [], simpset = Simplifier.empty_ss,
+ number_of = (serial (), no_number_of) };
val extend = I;
fun merge _
({add_mono_thms= add_mono_thms1, mult_mono_thms= mult_mono_thms1, inj_thms= inj_thms1,
- lessD = lessD1, neqE=neqE1, simpset = simpset1},
+ lessD = lessD1, neqE=neqE1, simpset = simpset1,
+ number_of = (number_of1 as (s1, _))},
{add_mono_thms= add_mono_thms2, mult_mono_thms= mult_mono_thms2, inj_thms= inj_thms2,
- lessD = lessD2, neqE=neqE2, simpset = simpset2}) =
+ lessD = lessD2, neqE=neqE2, simpset = simpset2,
+ number_of = (number_of2 as (s2, _))}) =
{add_mono_thms = Thm.merge_thms (add_mono_thms1, add_mono_thms2),
mult_mono_thms = Thm.merge_thms (mult_mono_thms1, mult_mono_thms2),
inj_thms = Thm.merge_thms (inj_thms1, inj_thms2),
lessD = Thm.merge_thms (lessD1, lessD2),
neqE = Thm.merge_thms (neqE1, neqE2),
- simpset = Simplifier.merge_ss (simpset1, simpset2)};
+ simpset = Simplifier.merge_ss (simpset1, simpset2),
+ number_of = if s1 > s2 then number_of1 else number_of2};
);
val map_data = Data.map;
@@ -154,7 +163,6 @@
| NotLeD of injust
| NotLeDD of injust
| Multiplied of int * injust
- | Multiplied2 of int * injust
| Added of injust * injust;
datatype lineq = Lineq of int * lineq_type * int list * injust;
@@ -320,7 +328,7 @@
else (m1,m2)
val (p1,p2) = if ty1=Eq andalso ty2=Eq andalso (n1 = ~1 orelse n2 = ~1)
then (~n1,~n2) else (n1,n2)
- in add_ineq (multiply_ineq n1 i1) (multiply_ineq n2 i2) end;
+ in add_ineq (multiply_ineq p1 i1) (multiply_ineq p2 i2) end;
(* ------------------------------------------------------------------------- *)
(* The main refutation-finding code. *)
@@ -328,7 +336,7 @@
fun is_trivial (Lineq(_,_,l,_)) = forall (fn i => i=0) l;
-fun is_answer (ans as Lineq(k,ty,l,_)) =
+fun is_contradictory (ans as Lineq(k,ty,l,_)) =
case ty of Eq => k <> 0 | Le => k > 0 | Lt => k >= 0;
fun calc_blowup l =
@@ -347,13 +355,10 @@
(* blowup (number of consequences generated) and eliminates it. *)
(* ------------------------------------------------------------------------- *)
-fun allpairs f xs ys =
- maps (fn x => map (fn y => f x y) ys) xs;
-
fun extract_first p =
- let fun extract xs (y::ys) = if p y then (SOME y,xs@ys)
- else extract (y::xs) ys
- | extract xs [] = (NONE,xs)
+ let
+ fun extract xs (y::ys) = if p y then (y, xs @ ys) else extract (y::xs) ys
+ | extract xs [] = raise Empty
in extract [] end;
fun print_ineqs ineqs =
@@ -368,10 +373,10 @@
datatype result = Success of injust | Failure of history;
fun elim (ineqs, hist) =
- let val dummy = print_ineqs ineqs
+ let val _ = print_ineqs ineqs
val (triv, nontriv) = List.partition is_trivial ineqs in
if not (null triv)
- then case Library.find_first is_answer triv of
+ then case Library.find_first is_contradictory triv of
NONE => elim (nontriv, hist)
| SOME(Lineq(_,_,_,j)) => Success j
else
@@ -379,11 +384,12 @@
else
let val (eqs, noneqs) = List.partition (fn (Lineq(_,ty,_,_)) => ty=Eq) nontriv in
if not (null eqs) then
- let val clist = Library.foldl (fn (cs,Lineq(_,_,l,_)) => l union cs) ([],eqs)
- val sclist = sort (fn (x,y) => int_ord (abs x, abs y))
- (List.filter (fn i => i<>0) clist)
- val c = hd sclist
- val (SOME(eq as Lineq(_,_,ceq,_)),othereqs) =
+ let val c =
+ fold (fn Lineq(_,_,l,_) => fn cs => l union cs) eqs []
+ |> filter (fn i => i <> 0)
+ |> sort (int_ord o pairself abs)
+ |> hd
+ val (eq as Lineq(_,_,ceq,_),othereqs) =
extract_first (fn Lineq(_,_,l,_) => c mem l) eqs
val v = find_index_eq c ceq
val (ioth,roth) = List.partition (fn (Lineq(_,_,l,_)) => nth l v = 0)
@@ -402,7 +408,7 @@
let val (c,v) = hd(sort (fn (x,y) => int_ord(fst(x),fst(y))) nziblows)
val (no,yes) = List.partition (fn (Lineq(_,_,l,_)) => nth l v = 0) ineqs
val (pos,neg) = List.partition(fn (Lineq(_,_,l,_)) => nth l v > 0) yes
- in elim(no @ allpairs (elim_var v) pos neg, (v,nontriv)::hist) end
+ in elim(no @ map_product (elim_var v) pos neg, (v,nontriv)::hist) end
end
end
end;
@@ -427,11 +433,12 @@
val union_bterm = curry (gen_union
(fn ((b:bool, t), (b', t')) => b = b' andalso Pattern.aeconv (t, t')));
-(* FIXME OPTIMIZE!!!! (partly done already)
- Addition/Multiplication need i*t representation rather than t+t+...
- Get rid of Mulitplied(2). For Nat LA_Data.mk_number should return Suc^n
- because Numerals are not known early enough.
+fun add_atoms (lhs, _, _, rhs, _, _) =
+ union_term (map fst lhs) o union_term (map fst rhs);
+fun atoms_of ds = fold add_atoms ds [];
+
+(*
Simplification may detect a contradiction 'prematurely' due to type
information: n+1 <= 0 is simplified to False and does not need to be crossed
with 0 <= n.
@@ -444,58 +451,77 @@
let
val ctxt = Simplifier.the_context ss;
val thy = ProofContext.theory_of ctxt;
- val {add_mono_thms, mult_mono_thms, inj_thms, lessD, simpset, ...} = get_data ctxt;
+ val {add_mono_thms, mult_mono_thms, inj_thms, lessD, simpset,
+ number_of = (_, num_of), ...} = get_data ctxt;
val simpset' = Simplifier.inherit_context ss simpset;
- val atoms = Library.foldl (fn (ats, (lhs,_,_,rhs,_,_)) =>
- union_term (map fst lhs) (union_term (map fst rhs) ats))
- ([], List.mapPartial (fn thm => if Thm.no_prems thm
- then LA_Data.decomp ctxt (Thm.concl_of thm)
- else NONE) asms)
+ fun only_concl f thm =
+ if Thm.no_prems thm then f (Thm.concl_of thm) else NONE;
+ val atoms = atoms_of (map_filter (only_concl (LA_Data.decomp ctxt)) asms);
+
+ fun use_first rules thm =
+ get_first (fn th => SOME (thm RS th) handle THM _ => NONE) rules
+
+ fun add2 thm1 thm2 =
+ use_first add_mono_thms (thm1 RS (thm2 RS LA_Logic.conjI));
+ fun try_add thms thm = get_first (fn th => add2 th thm) thms;
- fun add2 thm1 thm2 =
- let val conj = thm1 RS (thm2 RS LA_Logic.conjI)
- in get_first (fn th => SOME(conj RS th) handle THM _ => NONE) add_mono_thms
- end;
- fun try_add [] _ = NONE
- | try_add (thm1::thm1s) thm2 = case add2 thm1 thm2 of
- NONE => try_add thm1s thm2 | some => some;
+ fun add_thms thm1 thm2 =
+ (case add2 thm1 thm2 of
+ NONE =>
+ (case try_add ([thm1] RL inj_thms) thm2 of
+ NONE =>
+ (the (try_add ([thm2] RL inj_thms) thm1)
+ handle Option =>
+ (trace_thm "" thm1; trace_thm "" thm2;
+ sys_error "Linear arithmetic: failed to add thms"))
+ | SOME thm => thm)
+ | SOME thm => thm);
+
+ fun mult_by_add n thm =
+ let fun mul i th = if i = 1 then th else mul (i - 1) (add_thms thm th)
+ in mul n thm end;
- fun addthms thm1 thm2 =
- case add2 thm1 thm2 of
- NONE => (case try_add ([thm1] RL inj_thms) thm2 of
- NONE => ( the (try_add ([thm2] RL inj_thms) thm1)
- handle Option =>
- (trace_thm "" thm1; trace_thm "" thm2;
- sys_error "Linear arithmetic: failed to add thms")
- )
- | SOME thm => thm)
- | SOME thm => thm;
-
- fun multn(n,thm) =
- let fun mul(i,th) = if i=1 then th else mul(i-1, addthms thm th)
- in if n < 0 then mul(~n,thm) RS LA_Logic.sym else mul(n,thm) end;
+ val rewr = Simplifier.rewrite simpset';
+ val rewrite_concl = Conv.fconv_rule (Conv.concl_conv ~1 (Conv.arg_conv
+ (Conv.binop_conv rewr)));
+ fun discharge_prem thm = if Thm.nprems_of thm = 0 then thm else
+ let val cv = Conv.arg1_conv (Conv.arg_conv rewr)
+ in Thm.implies_elim (Conv.fconv_rule cv thm) LA_Logic.trueI end
- fun multn2(n,thm) =
- let val SOME(mth) =
- get_first (fn th => SOME(thm RS th) handle THM _ => NONE) mult_mono_thms
- fun cvar(th,_ $ (_ $ _ $ var)) = cterm_of (Thm.theory_of_thm th) var;
- val cv = cvar(mth, hd(prems_of mth));
- val ct = cterm_of thy (LA_Data.mk_number (#T (rep_cterm cv)) n)
- in instantiate ([],[(cv,ct)]) mth end
+ fun mult n thm =
+ (case use_first mult_mono_thms thm of
+ NONE => mult_by_add n thm
+ | SOME mth =>
+ let
+ val cv = mth |> Thm.cprop_of |> Drule.strip_imp_concl
+ |> Thm.dest_arg |> Thm.dest_arg1 |> Thm.dest_arg1
+ val T = #T (Thm.rep_cterm cv)
+ in
+ mth
+ |> Thm.instantiate ([], [(cv, num_of thy T n)])
+ |> rewrite_concl
+ |> discharge_prem
+ handle CTERM _ => mult_by_add n thm
+ | THM _ => mult_by_add n thm
+ end);
- fun simp thm =
- let val thm' = trace_thm "Simplified:" (full_simplify simpset' thm)
- in if LA_Logic.is_False thm' then raise FalseE thm' else thm' end
+ fun mult_thm (n, thm) =
+ if n = ~1 then thm RS LA_Logic.sym
+ else if n < 0 then mult (~n) thm RS LA_Logic.sym
+ else mult n thm;
+
+ fun simp thm =
+ let val thm' = trace_thm "Simplified:" (full_simplify simpset' thm)
+ in if LA_Logic.is_False thm' then raise FalseE thm' else thm' end;
- fun mk (Asm i) = trace_thm ("Asm " ^ string_of_int i) (nth asms i)
- | mk (Nat i) = trace_thm ("Nat " ^ string_of_int i) (LA_Logic.mk_nat_thm thy (nth atoms i))
- | mk (LessD j) = trace_thm "L" (hd ([mk j] RL lessD))
- | mk (NotLeD j) = trace_thm "NLe" (mk j RS LA_Logic.not_leD)
- | mk (NotLeDD j) = trace_thm "NLeD" (hd ([mk j RS LA_Logic.not_leD] RL lessD))
- | mk (NotLessD j) = trace_thm "NL" (mk j RS LA_Logic.not_lessD)
- | mk (Added (j1, j2)) = simp (trace_thm "+" (addthms (mk j1) (mk j2)))
- | mk (Multiplied (n, j)) = (trace_msg ("*" ^ string_of_int n); trace_thm "*" (multn (n, mk j)))
- | mk (Multiplied2 (n, j)) = simp (trace_msg ("**" ^ string_of_int n); trace_thm "**" (multn2 (n, mk j)))
+ fun mk (Asm i) = trace_thm ("Asm " ^ string_of_int i) (nth asms i)
+ | mk (Nat i) = trace_thm ("Nat " ^ string_of_int i) (LA_Logic.mk_nat_thm thy (nth atoms i))
+ | mk (LessD j) = trace_thm "L" (hd ([mk j] RL lessD))
+ | mk (NotLeD j) = trace_thm "NLe" (mk j RS LA_Logic.not_leD)
+ | mk (NotLeDD j) = trace_thm "NLeD" (hd ([mk j RS LA_Logic.not_leD] RL lessD))
+ | mk (NotLessD j) = trace_thm "NL" (mk j RS LA_Logic.not_lessD)
+ | mk (Added (j1, j2)) = simp (trace_thm "+" (add_thms (mk j1) (mk j2)))
+ | mk (Multiplied (n, j)) = (trace_msg ("*" ^ string_of_int n); trace_thm "*" (mult_thm (n, mk j)))
in
let
@@ -542,7 +568,7 @@
val diff = map2 (curry (op -)) rhsa lhsa
val c = i-j
val just = Asm k
- fun lineq(c,le,cs,j) = Lineq(c,le,cs, if m=1 then j else Multiplied2(m,j))
+ fun lineq(c,le,cs,j) = Lineq(c,le,cs, if m=1 then j else Multiplied(m,j))
in case rel of
"<=" => lineq(c,Le,diff,just)
| "~<=" => if discrete
@@ -676,9 +702,6 @@
result
end;
-fun add_atoms (ats : term list, ((lhs,_,_,rhs,_,_) : LA_Data.decomp, _)) : term list =
- union_term (map fst lhs) (union_term (map fst rhs) ats);
-
fun add_datoms (dats : (bool * term) list, ((lhs,_,_,rhs,_,d) : LA_Data.decomp, _)) :
(bool * term) list =
union_bterm (map (pair d o fst) lhs) (union_bterm (map (pair d o fst) rhs) dats);
@@ -691,7 +714,7 @@
let
fun refute ((Ts, initems : (LA_Data.decomp * int) list) :: initemss) (js: injust list) =
let
- val atoms = Library.foldl add_atoms ([], initems)
+ val atoms = atoms_of (map fst initems)
val n = length atoms
val mkleq = mklineq n atoms
val ixs = 0 upto (n - 1)