(* 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) list option) -> theory -> theory
val del_functrans: string -> theory -> theory
val simple_functrans: (Proof.context -> thm list -> thm list option)
-> Proof.context -> (thm * bool) list -> (thm * bool) list option
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
val all: code_graph -> string list
val pretty: Proof.context -> code_graph -> Pretty.T
val obtain: bool -> theory -> string list -> term list -> code_algebra * 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: string list }
-> ({ 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: string list }
-> ({ algebra: code_algebra, eqngr: code_graph } -> Proof.context -> term -> 'a)
-> Proof.context -> term -> 'b
end
structure Code_Preproc : CODE_PREPROC =
struct
(** preprocessor administration **)
(* theory data *)
datatype thmproc = Thmproc of {
pre: simpset,
post: simpset,
functrans: (string * (serial * (Proof.context -> (thm * bool) list -> (thm * bool) list option))) 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 extend = I;
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)
else if 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 -> (thm -> thm) * cterm;
val chain: T -> T -> T
val lift: (Proof.context -> cterm -> (cterm -> thm) * thm) -> T
val conversion: T -> (Proof.context -> term -> conv) -> Proof.context -> conv;
val evaluation: T -> ((term -> term) -> 'a -> 'b) ->
(Proof.context -> term -> 'a) -> Proof.context -> term -> 'b;
end = struct
type T = Proof.context -> cterm -> (thm -> thm) * cterm;
fun chain sandwich2 sandwich1 ctxt =
sandwich1 ctxt
##>> sandwich2 ctxt
#>> (op o);
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 (trans_conv_rule postproc_conv o potentail_trans_comb eq, Thm.rhs_of eq) end;
fun conversion sandwich conv ctxt ct =
let
val (postproc, ct') = sandwich ctxt ct;
in postproc (conv ctxt (term_of ct') ct') end;
fun evaluation sandwich lift_postproc eval ctxt t =
let
val cert = Thm.cterm_of (Proof_Context.theory_of ctxt);
val (postproc, ct') = sandwich ctxt (cert t);
in
term_of ct'
|> eval ctxt
|> lift_postproc (term_of o Thm.rhs_of o postproc o Thm.reflexive o cert)
end;
end;
(* post- and preprocessing *)
fun normalized_tfrees_sandwich ctxt ct =
let
val cert = cterm_of (Proof_Context.theory_of ctxt);
val t = term_of ct;
val vs_original = fold_term_types (K (fold_atyps (insert (eq_fst op =)
o dest_TFree))) t [];
val vs_normalized = Name.invent_names Name.context Name.aT (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), TFree (v, sort))) vs_original vs_normalized;
in
if eq_list (eq_fst (op =)) (vs_normalized, vs_original)
then (I, ct)
else (Thm.certify_instantiate (normalization, []) o Thm.varifyT_global, cert (map_types normalize t))
end;
fun no_variables_sandwich ctxt ct =
let
val thy = Proof_Context.theory_of ctxt;
val cert = Thm.cterm_of thy;
val all_vars = fold_aterms (fn t as Free _ => insert (op aconvc) (cert t)
| t as Var _ => insert (op aconvc) (cert 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 (I, ct)
else (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 (Proof_Context.theory_of ctxt'))
fun post_conv ctxt' =
Axclass.overload_conv (Proof_Context.theory_of ctxt')
#> trans_conv_rule (Simplifier.rewrite (put_simpset post ctxt'))
in fn ctxt' => pre_conv ctxt' #> pair (post_conv ctxt') end;
fun simplifier_sandwich ctxt = Sandwich.lift (simplifier_conv_sandwich ctxt);
fun value_sandwich ctxt =
normalized_tfrees_sandwich
|> Sandwich.chain no_variables_sandwich
|> Sandwich.chain (simplifier_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_chunks [
Pretty.block [
Pretty.str "preprocessing simpset:",
Pretty.fbrk,
Simplifier.pretty_simpset (put_simpset pre ctxt)
],
Pretty.block [
Pretty.str "postprocessing simpset:",
Pretty.fbrk,
Simplifier.pretty_simpset (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;
fun all 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 pairself fst)
|> map (fn (s, cert) => (Pretty.block o Pretty.fbreaks) (Pretty.str s :: Code.pretty_cert thy cert))
|> Pretty.chunks
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 *)
datatype const = Fun of string | 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;
type var = const * int;
structure Vargraph =
Graph(type key = var val ord = prod_ord const_ord int_ord);
datatype styp = Tyco of string * 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 =
case try (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 thy { functrans = functrans, ss = simpset_of ctxt } c; (*FIXME*)
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)
(Sign.arity_sorts thy 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;
in if null diff_classes then vardeps_data
else let
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
end end
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;
in if 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 (Sign.arity_sorts (Proof_Context.theory_of 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
else let
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
else let
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 dicts_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)
else let
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.pretty_global 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 (dicts_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 **)
fun obtain ignore_cache thy consts ts = apsnd snd
(Wellsorted.change_yield (if ignore_cache then NONE else SOME thy)
(extend_arities_eqngr (Proof_Context.init_global thy) consts ts));
fun dynamic_evaluator eval ctxt t =
let
val consts = fold_aterms
(fn Const (c, _) => insert (op =) c | _ => I) t [];
val (algebra, eqngr) = obtain false (Proof_Context.theory_of ctxt) consts [t];
in eval algebra eqngr t end;
fun dynamic_conv ctxt conv =
Sandwich.conversion (value_sandwich ctxt) (dynamic_evaluator conv) ctxt;
fun dynamic_value ctxt lift_postproc evaluator =
Sandwich.evaluation (value_sandwich ctxt) lift_postproc (dynamic_evaluator evaluator) ctxt;
fun static_conv { ctxt, consts } conv =
let
val (algebra, eqngr) = obtain true (Proof_Context.theory_of ctxt) consts [];
in Sandwich.conversion (value_sandwich ctxt) (conv { algebra = algebra, eqngr = eqngr }) end;
fun static_value { ctxt, lift_postproc, consts } evaluator =
let
val (algebra, eqngr) = obtain true (Proof_Context.theory_of ctxt) consts [];
in Sandwich.evaluation (value_sandwich ctxt) lift_postproc (evaluator { algebra = algebra, eqngr = eqngr }) end;
(** setup **)
val _ =
let
fun mk_attribute f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I);
fun add_del_attribute_parser process =
Attrib.add_del (mk_attribute (process Simplifier.add_simp))
(mk_attribute (process Simplifier.del_simp));
in
Context.>> (Context.map_theory
(Attrib.setup @{binding code_unfold} (add_del_attribute_parser process_unfold)
"preprocessing equations for code generator"
#> Attrib.setup @{binding code_post} (add_del_attribute_parser process_post)
"postprocessing equations for code generator"
#> Attrib.setup @{binding code_abbrev} (add_del_attribute_parser process_abbrev)
"post- and preprocessing equations for code generator"))
end;
val _ =
Outer_Syntax.improper_command @{command_spec "print_codeproc"} "print code preprocessor setup"
(Scan.succeed (Toplevel.unknown_context o Toplevel.keep (print_codeproc o Toplevel.context_of)));
end; (*struct*)