(* Title: Tools/Code/code_preproc.ML Author: Florian Haftmann, TU Muenchen
Preprocessing code equations into a well-sorted system in a graph with explicit dependencies.
*)
signature CODE_PREPROC = sig val map_pre: (Proof.context -> Proof.context) -> theory -> theory val map_post: (Proof.context -> Proof.context) -> theory -> theory val add_functrans: string * (Proof.context -> (thm * bool) list -> (thm * bool) listoption) -> theory -> theory val del_functrans: string -> theory -> theory val simple_functrans: (Proof.context -> thm list -> thm listoption)
-> Proof.context -> (thm * bool) list -> (thm * bool) listoption val print_codeproc: Proof.context -> unit
type code_algebra type code_graph val cert: code_graph -> string -> Code.cert val sortargs: code_graph -> string -> sort list valall: code_graph -> stringlist val pretty: Proof.context -> code_graph -> Pretty.T val obtain: bool -> { ctxt: Proof.context, consts: stringlist, terms: term list } ->
{ algebra: code_algebra, eqngr: code_graph } val dynamic_conv: Proof.context
-> (code_algebra -> code_graph -> term -> conv) -> conv val dynamic_value: Proof.context -> ((term -> term) -> 'a -> 'b)
-> (code_algebra -> code_graph -> term -> 'a) -> term -> 'b val static_conv: { ctxt: Proof.context, consts: stringlist }
-> ({ algebra: code_algebra, eqngr: code_graph } -> Proof.context -> term -> conv)
-> Proof.context -> conv val static_value: { ctxt: Proof.context, lift_postproc: ((term -> term) -> 'a -> 'b), consts: stringlist }
-> ({ algebra: code_algebra, eqngr: code_graph } -> Proof.context -> term -> 'a)
-> Proof.context -> term -> 'b
val trace_none: Context.generic -> Context.generic val trace_all: Context.generic -> Context.generic val trace_only: stringlist -> Context.generic -> Context.generic val trace_only_ext: stringlist -> Context.generic -> Context.generic
val timing: bool Config.T val timed: string -> ('a -> Proof.context) -> ('a -> 'b) -> 'a -> 'b val timed_exec: string -> (unit -> 'a) -> Proof.context -> 'a val timed_conv: string -> (Proof.context -> conv) -> Proof.context -> conv val timed_value: string -> (Proof.context -> term -> 'a) -> Proof.context -> term -> 'a end
structure Code_Preproc : CODE_PREPROC = struct
(** timing **)
val timing = Attrib.setup_config_bool \<^binding>\<open>code_timing\<close> (K false);
fun timed msg ctxt_of f x = if Config.get (ctxt_of x) timing then timeap_msg msg f x else f x;
fun timed_exec msg f ctxt = if Config.get ctxt timing then timeap_msg msg f () else f ();
fun timed' msg f ctxt x = if Config.get ctxt timing then timeap_msg msg (f ctxt) x else f ctxt x;
val timed_conv = timed'; val timed_value = timed';
(** preprocessor administration **)
(* theory data *)
datatype thmproc = Thmproc of {
pre: simpset,
post: simpset,
functrans: (string * (serial * (Proof.context -> (thm * bool) list -> (thm * bool) listoption))) list
};
fun make_thmproc ((pre, post), functrans) =
Thmproc { pre = pre, post = post, functrans = functrans }; fun map_thmproc f (Thmproc { pre, post, functrans }) =
make_thmproc (f ((pre, post), functrans)); fun merge_thmproc (Thmproc { pre = pre1, post = post1, functrans = functrans1 },
Thmproc { pre = pre2, post = post2, functrans = functrans2 }) = let val pre = Simplifier.merge_ss (pre1, pre2); val post = Simplifier.merge_ss (post1, post2); val functrans = AList.merge (op =) (eq_fst (op =)) (functrans1, functrans2) handle AList.DUP => error ("Duplicate function transformer"); in make_thmproc ((pre, post), functrans) end;
structure Code_Preproc_Data = Theory_Data
( type T = thmproc; val empty = make_thmproc ((Simplifier.empty_ss, Simplifier.empty_ss), []); val merge = merge_thmproc;
);
fun the_thmproc thy = case Code_Preproc_Data.get thy of Thmproc x => x;
fun delete_force msg key xs = if AList.defined (op =) xs key then AList.delete (op =) key xs else error ("No such " ^ msg ^ ": " ^ quote key);
val map_data = Code_Preproc_Data.map o map_thmproc;
val map_pre_post = map_data o apfst;
fun map_simpset which f thy =
map_pre_post (which (simpset_map (Proof_Context.init_global thy) f)) thy; val map_pre = map_simpset apfst; val map_post = map_simpset apsnd;
fun process_unfold add_del = map_pre o add_del; fun process_post add_del = map_post o add_del;
fun process_abbrev add_del raw_thm thy = let val ctxt = Proof_Context.init_global thy; val thm = Local_Defs.meta_rewrite_rule ctxt raw_thm; val thm_sym = Thm.symmetric thm; in
thy |> map_pre_post (fn (pre, post) =>
(pre |> simpset_map ctxt (add_del thm_sym),
post |> simpset_map ctxt (add_del thm))) end;
fun add_functrans (name, f) = (map_data o apsnd)
(AList.update (op =) (name, (serial (), f)));
fun del_functrans name = (map_data o apsnd)
(delete_force "function transformer" name);
(* algebra of sandwiches: cterm transformations with pending postprocessors *)
fun matches_transitive eq1 eq2 = Thm.rhs_of eq1 aconvc Thm.lhs_of eq2;
fun trans_comb eq1 eq2 = (*explicit assertions: evaluation conversion stacks are error-prone*) if Thm.is_reflexive eq1 then (\<^assert> (matches_transitive eq1 eq2); eq2) elseif Thm.is_reflexive eq2 then (\<^assert> (matches_transitive eq1 eq2); eq1) else Thm.transitive eq1 eq2;
fun trans_conv_rule conv eq = trans_comb eq (conv (Thm.rhs_of eq));
structure Sandwich : sig type T = Proof.context -> cterm -> (Proof.context -> thm -> thm) * cterm; val chain: T -> T -> T val lift: (Proof.context -> cterm -> (Proof.context -> cterm -> thm) * thm) -> T val conversion: T -> (Proof.context -> term -> conv) -> Proof.context -> conv; val computation: T -> ((term -> term) -> 'a -> 'b) ->
(Proof.context -> term -> 'a) -> Proof.context -> term -> 'b; end = struct
type T = Proof.context -> cterm -> (Proof.context -> thm -> thm) * cterm;
fun chain sandwich2 sandwich1 ctxt =
sandwich1 ctxt
##>> sandwich2 ctxt
#>> (fn (f, g) => fn ctxt => f ctxt o g ctxt);
fun lift conv_sandwhich ctxt ct = let val (postproc_conv, eq) = conv_sandwhich ctxt ct; fun potentail_trans_comb eq1 eq2 = if matches_transitive eq1 eq2 then trans_comb eq1 eq2 else eq2; (*weakened protocol for plain term evaluation*) in (fn ctxt => trans_conv_rule (postproc_conv ctxt) o potentail_trans_comb eq, Thm.rhs_of eq) end;
fun conversion sandwich conv ctxt ct = let val (postproc, ct') = sandwich ctxt ct; val thm = conv ctxt (Thm.term_of ct') ct'; val thm' = postproc ctxt thm; in thm' end;
fun computation sandwich lift_postproc eval ctxt t = let val (postproc, ct') = sandwich ctxt (Thm.cterm_of ctxt t); val result = eval ctxt (Thm.term_of ct'); val result' = lift_postproc
(Thm.term_of o Thm.rhs_of o postproc ctxt o Thm.reflexive o Thm.cterm_of ctxt)
result in result' end;
end;
(* post- and preprocessing *)
fun normalized_tfrees_sandwich ctxt ct = let val t = Thm.term_of ct; val vs_original =
build (fold_term_types (K (fold_atyps (insert (eq_fst op =) o dest_TFree))) t); val vs_normalized = Name.invent_types_global (map snd vs_original); val normalize =
map_type_tfree (TFree o the o AList.lookup (op =) (vs_original ~~ vs_normalized)); val normalization =
map2 (fn (v, sort) => fn (v', _) => (((v', 0), sort), Thm.ctyp_of ctxt (TFree (v, sort))))
vs_original vs_normalized; in if eq_list (eq_fst (op =)) (vs_normalized, vs_original) then (K I, ct) else
(K (Thm.instantiate (TVars.make normalization, Vars.empty) o Thm.varifyT_global),
Thm.cterm_of ctxt (map_types normalize t)) end;
fun no_variables_sandwich ctxt ct = let val all_vars = fold_aterms (fn t as Free _ => insert (op aconvc) (Thm.cterm_of ctxt t)
| t as Var _ => insert (op aconvc) (Thm.cterm_of ctxt t)
| _ => I) (Thm.term_of ct) []; fun apply_beta var thm = Thm.combination thm (Thm.reflexive var)
|> Conv.fconv_rule (Conv.arg_conv (Conv.try_conv (Thm.beta_conversion false)))
|> Conv.fconv_rule (Conv.arg1_conv (Thm.beta_conversion false)); in if null all_vars then (K I, ct) else (K (fold apply_beta all_vars), fold_rev Thm.lambda all_vars ct) end;
fun simplifier_conv_sandwich ctxt = let val thy = Proof_Context.theory_of ctxt; val pre = (#pre o the_thmproc) thy; val post = (#post o the_thmproc) thy; fun pre_conv ctxt' =
Simplifier.rewrite (put_simpset pre ctxt')
#> trans_conv_rule (Axclass.unoverload_conv ctxt')
#> trans_conv_rule (Thm.eta_conversion); fun post_conv ctxt'' =
Axclass.overload_conv ctxt''
#> trans_conv_rule (Simplifier.rewrite (put_simpset post ctxt'')); in
fn ctxt' => timed_conv "preprocessing term" pre_conv ctxt'
#> pair (timed_conv "postprocessing term" post_conv) end;
fun simplifier_sandwich ctxt =
Sandwich.lift (simplifier_conv_sandwich ctxt);
fun print_codeproc ctxt = let val thy = Proof_Context.theory_of ctxt; val pre = (#pre o the_thmproc) thy; val post = (#post o the_thmproc) thy; val functrans = (map fst o #functrans o the_thmproc) thy; in
Pretty.writeln (Pretty.chunks [
Pretty.block [
Pretty.str "preprocessing simpset:",
Pretty.fbrk,
Simplifier.pretty_simpset true (put_simpset pre ctxt)
],
Pretty.block [
Pretty.str "postprocessing simpset:",
Pretty.fbrk,
Simplifier.pretty_simpset true (put_simpset post ctxt)
],
Pretty.block (
Pretty.str "function transformers:"
:: Pretty.fbrk
:: (Pretty.fbreaks o map Pretty.str) functrans
)
]) end;
fun simple_functrans f ctxt eqns = case f ctxt (map fst eqns) of SOME thms' => SOME (map (rpair (forall snd eqns)) thms')
| NONE => NONE;
(** sort algebra and code equation graph types **)
type code_algebra = (sort -> sort) * Sorts.algebra; type code_graph = ((string * sort) list * Code.cert) Graph.T;
fun get_node eqngr const = Graph.get_node eqngr const handle Graph.UNDEF _ => error ("No such constant in code equation graph: " ^ quote const);
fun cert eqngr = snd o get_node eqngr; fun sortargs eqngr = map snd o fst o get_node eqngr; funall eqngr = Graph.keys eqngr;
fun pretty ctxt eqngr = let val thy = Proof_Context.theory_of ctxt; in
AList.make (snd o Graph.get_node eqngr) (Graph.keys eqngr)
|> (map o apfst) (Code.string_of_const thy)
|> sort (string_ord o apply2 fst)
|> (map o apsnd) (Code.pretty_cert thy)
|> filter_out (null o snd)
|> map (fn (s, ps) => (Pretty.block o Pretty.fbreaks) (Pretty.str s :: ps))
|> Pretty.chunks end;
(** simplifier tracing **)
structure Trace_Switch = Generic_Data
( type T = stringlistoption; val empty = SOME []; fun merge (NONE, _) = NONE
| merge (_, NONE) = NONE
| merge (SOME cs1, SOME cs2) = SOME (Library.merge (op =) (cs1, cs2));
);
val trace_none = Trace_Switch.put (SOME []);
val trace_all = Trace_Switch.put NONE;
fun gen_trace_only prep_const raw_cs context = let val cs = map (prep_const (Context.proof_of context)) raw_cs; in Trace_Switch.put (SOME cs) context end;
val trace_only = gen_trace_only (K I); val trace_only_ext = gen_trace_only Code.read_const;
fun switch_trace c ctxt = let val d = Trace_Switch.get (Context.Proof ctxt); val switch = case d of NONE => true | SOME cs => member (op =) cs c; val _ = if switch then tracing ("Preprocessing function equations for "
^ Code.string_of_const (Proof_Context.theory_of ctxt) c) else (); in Config.put simp_trace switch ctxt end;
(** the Waisenhaus algorithm **)
(* auxiliary *)
fun is_proper_class thy = can (Axclass.get_info thy);
fun complete_proper_sort thy =
Sign.complete_sort thy #> filter (is_proper_class thy);
fun inst_params thy tyco = map (fn (c, _) => Axclass.param_of_inst thy (c, tyco))
o maps (#params o Axclass.get_info thy);
(* data structures *)
datatypeconst = Funofstring | Inst of class * string;
fun const_ord (Fun c1, Fun c2) = fast_string_ord (c1, c2)
| const_ord (Inst class_tyco1, Inst class_tyco2) =
prod_ord fast_string_ord fast_string_ord (class_tyco1, class_tyco2)
| const_ord (Fun _, Inst _) = LESS
| const_ord (Inst _, Fun _) = GREATER;
datatype styp = Tyco ofstring * styp list | Var of var | Free;
fun styp_of c_lhs (Type (tyco, tys)) = Tyco (tyco, map (styp_of c_lhs) tys)
| styp_of c_lhs (TFree (v, _)) = case c_lhs of SOME (c, lhs) => Var (Fun c, find_index (fn (v', _) => v = v') lhs)
| NONE => Free;
type vardeps_data = ((string * styp list) list * class list) Vargraph.T
* (((string * sort) list * Code.cert) Symtab.table
* (class * string) list);
val empty_vardeps_data : vardeps_data =
(Vargraph.empty, (Symtab.empty, []));
(* retrieving equations and instances from the background context *)
fun obtain_eqns ctxt eqngr c = casetry (Graph.get_node eqngr) c of SOME (lhs, cert) => ((lhs, []), cert)
| NONE => let val thy = Proof_Context.theory_of ctxt; val functrans = (map (fn (_, (_, f)) => f ctxt)
o #functrans o the_thmproc) thy; val cert = Code.get_cert (switch_trace c ctxt) functrans c; val (lhs, rhss) =
Code.typargs_deps_of_cert thy cert; in ((lhs, rhss), cert) end;
fun obtain_instance ctxt arities (inst as (class, tyco)) = case AList.lookup (op =) arities inst of SOME classess => (classess, ([], []))
| NONE => let val thy = Proof_Context.theory_of ctxt; val all_classes = complete_proper_sort thy [class]; val super_classes = remove (op =) class all_classes; val classess = map (complete_proper_sort thy)
(Proof_Context.arity_sorts ctxt tyco [class]); val inst_params = inst_params thy tyco all_classes; in (classess, (super_classes, inst_params)) end;
(* computing instantiations *)
fun add_classes ctxt arities eqngr c_k new_classes vardeps_data = let val (styps, old_classes) = Vargraph.get_node (fst vardeps_data) c_k; val diff_classes = new_classes |> subtract (op =) old_classes; inif null diff_classes then vardeps_data elselet val c_ks = Vargraph.immediate_succs (fst vardeps_data) c_k |> insert (op =) c_k; in
vardeps_data
|> (apfst o Vargraph.map_node c_k o apsnd) (append diff_classes)
|> fold (fn styp => fold (ensure_typmatch_inst ctxt arities eqngr styp) new_classes) styps
|> fold (fn c_k => add_classes ctxt arities eqngr c_k diff_classes) c_ks endend and add_styp ctxt arities eqngr c_k new_tyco_styps vardeps_data = let val (old_tyco_stypss, classes) = Vargraph.get_node (fst vardeps_data) c_k; inif member (op =) old_tyco_stypss new_tyco_styps then vardeps_data else
vardeps_data
|> (apfst o Vargraph.map_node c_k o apfst) (cons new_tyco_styps)
|> fold (ensure_typmatch_inst ctxt arities eqngr new_tyco_styps) classes end and add_dep ctxt arities eqngr c_k c_k' vardeps_data = let val (_, classes) = Vargraph.get_node (fst vardeps_data) c_k; in
vardeps_data
|> add_classes ctxt arities eqngr c_k' classes
|> apfst (Vargraph.add_edge (c_k, c_k')) end and ensure_typmatch_inst ctxt arities eqngr (tyco, styps) class vardeps_data = if can (Proof_Context.arity_sorts ctxt tyco) [class] then vardeps_data
|> ensure_inst ctxt arities eqngr (class, tyco)
|> fold_index (fn (k, styp) =>
ensure_typmatch ctxt arities eqngr styp (Inst (class, tyco), k)) styps else vardeps_data (*permissive!*) and ensure_inst ctxt arities eqngr (inst as (class, tyco)) (vardeps_data as (_, (_, insts))) = if member (op =) insts inst then vardeps_data elselet val (classess, (super_classes, inst_params)) =
obtain_instance ctxt arities inst; in
vardeps_data
|> (apsnd o apsnd) (insert (op =) inst)
|> fold_index (fn (k, _) =>
apfst (Vargraph.new_node ((Inst (class, tyco), k), ([] ,[])))) classess
|> fold (fn super_class => ensure_inst ctxt arities eqngr (super_class, tyco)) super_classes
|> fold (ensure_fun ctxt arities eqngr) inst_params
|> fold_index (fn (k, classes) =>
add_classes ctxt arities eqngr (Inst (class, tyco), k) classes
#> fold (fn super_class =>
add_dep ctxt arities eqngr (Inst (super_class, tyco), k)
(Inst (class, tyco), k)) super_classes
#> fold (fn inst_param =>
add_dep ctxt arities eqngr (Fun inst_param, k)
(Inst (class, tyco), k)
) inst_params
) classess end and ensure_typmatch ctxt arities eqngr (Tyco tyco_styps) c_k vardeps_data =
vardeps_data
|> add_styp ctxt arities eqngr c_k tyco_styps
| ensure_typmatch ctxt arities eqngr (Var c_k') c_k vardeps_data =
vardeps_data
|> add_dep ctxt arities eqngr c_k c_k'
| ensure_typmatch ctxt arities eqngr Free c_k vardeps_data =
vardeps_data and ensure_rhs ctxt arities eqngr (c', styps) vardeps_data =
vardeps_data
|> ensure_fun ctxt arities eqngr c'
|> fold_index (fn (k, styp) =>
ensure_typmatch ctxt arities eqngr styp (Fun c', k)) styps and ensure_fun ctxt arities eqngr c (vardeps_data as (_, (eqntab, _))) = if Symtab.defined eqntab c then vardeps_data elselet val ((lhs, rhss), eqns) = obtain_eqns ctxt eqngr c; val rhss' = (map o apsnd o map) (styp_of (SOME (c, lhs))) rhss; in
vardeps_data
|> (apsnd o apfst) (Symtab.update_new (c, (lhs, eqns)))
|> fold_index (fn (k, _) =>
apfst (Vargraph.new_node ((Fun c, k), ([] ,[])))) lhs
|> fold_index (fn (k, (_, sort)) => add_classes ctxt arities eqngr (Fun c, k)
(complete_proper_sort (Proof_Context.theory_of ctxt) sort)) lhs
|> fold (ensure_rhs ctxt arities eqngr) rhss' end;
(* applying instantiations *)
fun dictss_of ctxt (proj_sort, algebra) (T, sort) = let val thy = Proof_Context.theory_of ctxt; fun class_relation _ (x, _) _ = x; fun type_constructor (tyco, _) xs class =
inst_params thy tyco (Sorts.complete_sort algebra [class])
@ (maps o maps) fst xs; fun type_variable (TFree (_, sort)) = map (pair []) (proj_sort sort); in
flat (Sorts.of_sort_derivation algebra
{ class_relation = K class_relation, type_constructor = type_constructor,
type_variable = type_variable } (T, proj_sort sort) handle Sorts.CLASS_ERROR _ => [] (*permissive!*)) end;
fun add_arity ctxt vardeps (class, tyco) =
AList.default (op =) ((class, tyco),
map_range (fn k => (snd o Vargraph.get_node vardeps) (Inst (class, tyco), k))
(Sign.arity_number (Proof_Context.theory_of ctxt) tyco));
fun add_cert ctxt vardeps (c, (proto_lhs, proto_cert)) (rhss, eqngr) = if can (Graph.get_node eqngr) c then (rhss, eqngr) elselet val thy = Proof_Context.theory_of ctxt; val lhs = map_index (fn (k, (v, _)) =>
(v, snd (Vargraph.get_node vardeps (Fun c, k)))) proto_lhs; val cert = proto_cert
|> Code.constrain_cert thy (map (Sign.minimize_sort thy o snd) lhs)
|> Code.conclude_cert; val (vs, rhss') = Code.typargs_deps_of_cert thy cert; val eqngr' = Graph.new_node (c, (vs, cert)) eqngr; in (map (pair c) rhss' @ rhss, eqngr') end;
fun extend_arities_eqngr raw_ctxt cs ts (arities, (eqngr : code_graph)) = let val thy = Proof_Context.theory_of raw_ctxt; val {pre, ...} = the_thmproc thy; val ctxt = put_simpset pre raw_ctxt; val cs_rhss = (fold o fold_aterms) (fn Const (c_ty as (c, _)) =>
insert (op =) (c, (map (styp_of NONE) o Sign.const_typargs thy) c_ty) | _ => I) ts []; val (vardeps, (eqntab, insts)) = empty_vardeps_data
|> fold (ensure_fun ctxt arities eqngr) cs
|> fold (ensure_rhs ctxt arities eqngr) cs_rhss; val arities' = fold (add_arity ctxt vardeps) insts arities; val algebra = Sorts.subalgebra (Context.Theory thy) (is_proper_class thy)
(AList.lookup (op =) arities') (Sign.classes_of thy); val (rhss, eqngr') = Symtab.fold (add_cert ctxt vardeps) eqntab ([], eqngr); fun deps_of (c, rhs) = c :: maps (dictss_of ctxt algebra)
(rhs ~~ sortargs eqngr' c); val eqngr'' = fold (fn (c, rhs) => fold
(curry Graph.add_edge c) (deps_of rhs)) rhss eqngr'; in (algebra, (arities', eqngr'')) end;
(** store for preprocessed arities and code equations **)
structure Wellsorted = Code_Data
( type T = ((string * class) * sort list) list * code_graph; val empty = ([], Graph.empty);
);
(** retrieval and evaluation interfaces **)
(* naming conventions * evaluator "eval" is either * conversion "conv" * value computation "comp" * "evaluation" is a lifting of an evaluator
*)
Die Informationen auf dieser Webseite wurden
nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit,
noch Qualität der bereit gestellten Informationen zugesichert.
Bemerkung:
Die farbliche Syntaxdarstellung ist noch experimentell.