(* Title: Tools/nbe.ML
ID: $Id$
Authors: Klaus Aehlig, LMU Muenchen; Tobias Nipkow, Florian Haftmann, TU Muenchen
Normalization by evaluation, based on generic code generator.
*)
signature NBE =
sig
val norm_conv: cterm -> thm
val norm_term: theory -> term -> term
datatype Univ =
Const of int * Univ list (*named (uninterpreted) constants*)
| Free of string * Univ list (*free (uninterpreted) variables*)
| DFree of string * int (*free (uninterpreted) dictionary parameters*)
| BVar of int * Univ list
| Abs of (int * (Univ list -> Univ)) * Univ list;
val apps: Univ -> Univ list -> Univ (*explicit applications*)
val abss: int -> (Univ list -> Univ) -> Univ
(*abstractions as closures*)
val univs_ref: (unit -> Univ list -> Univ list) option ref
val trace: bool ref
val setup: theory -> theory
end;
structure Nbe: NBE =
struct
(* generic non-sense *)
val trace = ref false;
fun tracing f x = if !trace then (Output.tracing (f x); x) else x;
(** the semantical universe **)
(*
Functions are given by their semantical function value. To avoid
trouble with the ML-type system, these functions have the most
generic type, that is "Univ list -> Univ". The calling convention is
that the arguments come as a list, the last argument first. In
other words, a function call that usually would look like
f x_1 x_2 ... x_n or f(x_1,x_2, ..., x_n)
would be in our convention called as
f [x_n,..,x_2,x_1]
Moreover, to handle functions that are still waiting for some
arguments we have additionally a list of arguments collected to far
and the number of arguments we're still waiting for.
*)
datatype Univ =
Const of int * Univ list (*named (uninterpreted) constants*)
| Free of string * Univ list (*free variables*)
| DFree of string * int (*free (uninterpreted) dictionary parameters*)
| BVar of int * Univ list (*bound variables, named*)
| Abs of (int * (Univ list -> Univ)) * Univ list
(*abstractions as closures*);
(* constructor functions *)
fun abss n f = Abs ((n, f), []);
fun apps (Abs ((n, f), xs)) ys = let val k = n - length ys in
case int_ord (k, 0)
of EQUAL => f (ys @ xs)
| LESS => let val (zs, ws) = chop (~ k) ys in apps (f (ws @ xs)) zs end
| GREATER => Abs ((k, f), ys @ xs) (*note: reverse convention also for apps!*)
end
| apps (Const (name, xs)) ys = Const (name, ys @ xs)
| apps (Free (name, xs)) ys = Free (name, ys @ xs)
| apps (BVar (n, xs)) ys = BVar (n, ys @ xs);
(** assembling and compiling ML code from terms **)
(* abstract ML syntax *)
infix 9 `$` `$$`;
fun e1 `$` e2 = "(" ^ e1 ^ " " ^ e2 ^ ")";
fun e `$$` [] = e
| e `$$` es = "(" ^ e ^ " " ^ space_implode " " es ^ ")";
fun ml_abs v e = "(fn " ^ v ^ " => " ^ e ^ ")";
fun ml_cases t cs =
"(case " ^ t ^ " of " ^ space_implode " | " (map (fn (p, t) => p ^ " => " ^ t) cs) ^ ")";
fun ml_Let d e = "let\n" ^ d ^ " in " ^ e ^ " end";
fun ml_as v t = "(" ^ v ^ " as " ^ t ^ ")";
fun ml_list es = "[" ^ commas es ^ "]";
fun ml_fundefs ([(name, [([], e)])]) =
"val " ^ name ^ " = " ^ e ^ "\n"
| ml_fundefs (eqs :: eqss) =
let
fun fundef (name, eqs) =
let
fun eqn (es, e) = name ^ " " ^ space_implode " " es ^ " = " ^ e
in space_implode "\n | " (map eqn eqs) end;
in
(prefix "fun " o fundef) eqs :: map (prefix "and " o fundef) eqss
|> cat_lines
|> suffix "\n"
end;
(* nbe specific syntax and sandbox communication *)
val univs_ref = ref (NONE : (unit -> Univ list -> Univ list) option);
local
val prefix = "Nbe.";
val name_ref = prefix ^ "univs_ref";
val name_const = prefix ^ "Const";
val name_abss = prefix ^ "abss";
val name_apps = prefix ^ "apps";
in
val univs_cookie = (name_ref, univs_ref);
fun nbe_fun 0 "" = "nbe_value"
| nbe_fun i c = "c_" ^ translate_string (fn "." => "_" | c => c) c ^ "_" ^ string_of_int i;
fun nbe_dict v n = "d_" ^ v ^ "_" ^ string_of_int n;
fun nbe_bound v = "v_" ^ v;
fun nbe_default v = "w_" ^ v;
(*note: these three are the "turning spots" where proper argument order is established!*)
fun nbe_apps t [] = t
| nbe_apps t ts = name_apps `$$` [t, ml_list (rev ts)];
fun nbe_apps_local i c ts = nbe_fun i c `$` ml_list (rev ts);
fun nbe_apps_constr idx_of c ts =
let
val c' = if !trace then string_of_int (idx_of c) ^ " (*" ^ c ^ "*)"
else string_of_int (idx_of c);
in name_const `$` ("(" ^ c' ^ ", " ^ ml_list (rev ts) ^ ")") end;
fun nbe_abss 0 f = f `$` ml_list []
| nbe_abss n f = name_abss `$$` [string_of_int n, f];
end;
open Basic_Code_Thingol;
(* code generation *)
fun assemble_eqnss idx_of deps eqnss =
let
fun prep_eqns (c, (vs, eqns)) =
let
val dicts = maps (fn (v, sort) => map_index (nbe_dict v o fst) sort) vs;
val num_args = length dicts + ((length o fst o hd) eqns);
in (c, (num_args, (dicts, eqns))) end;
val eqnss' = map prep_eqns eqnss;
fun assemble_constapp c dss ts =
let
val ts' = (maps o map) assemble_idict dss @ ts;
in case AList.lookup (op =) eqnss' c
of SOME (num_args, _) => if num_args <= length ts'
then let val (ts1, ts2) = chop num_args ts'
in nbe_apps (nbe_apps_local 0 c ts1) ts2
end else nbe_apps (nbe_abss num_args (nbe_fun 0 c)) ts'
| NONE => if member (op =) deps c
then nbe_apps (nbe_fun 0 c) ts'
else nbe_apps_constr idx_of c ts'
end
and assemble_idict (DictConst (inst, dss)) =
assemble_constapp inst dss []
| assemble_idict (DictVar (supers, (v, (n, _)))) =
fold_rev (fn super => assemble_constapp super [] o single) supers (nbe_dict v n);
fun assemble_iterm match_cont constapp =
let
fun of_iterm t =
let
val (t', ts) = Code_Thingol.unfold_app t
in of_iapp t' (fold_rev (cons o of_iterm) ts []) end
and of_iapp (IConst (c, (dss, _))) ts = constapp c dss ts
| of_iapp (IVar v) ts = nbe_apps (nbe_bound v) ts
| of_iapp ((v, _) `|-> t) ts =
nbe_apps (nbe_abss 1 (ml_abs (ml_list [nbe_bound v]) (of_iterm t))) ts
| of_iapp (ICase (((t, _), cs), t0)) ts =
nbe_apps (ml_cases (of_iterm t) (map (pairself of_iterm) cs
@ [("_", case match_cont of SOME s => s | NONE => of_iterm t0)])) ts
in of_iterm end;
fun assemble_eqn c dicts default_args (i, (args, rhs)) =
let
val is_eval = (c = "");
val default_rhs = nbe_apps_local (i+1) c (dicts @ default_args);
val match_cont = if is_eval then NONE else SOME default_rhs;
val assemble_arg = assemble_iterm NONE
(fn c => fn _ => fn ts => nbe_apps_constr idx_of c ts);
val assemble_rhs = assemble_iterm match_cont assemble_constapp;
val eqns = if is_eval then
[([ml_list (rev (dicts @ map assemble_arg args))], assemble_rhs rhs)]
else
[([ml_list (rev (dicts @ map2 ml_as default_args
(map assemble_arg args)))], assemble_rhs rhs),
([ml_list (rev (dicts @ default_args))], default_rhs)]
in (nbe_fun i c, eqns) end;
fun assemble_eqns (c, (num_args, (dicts, eqns))) =
let
val default_args = map nbe_default
(Name.invent_list [] "a" (num_args - length dicts));
val eqns' = map_index (assemble_eqn c dicts default_args) eqns
@ (if c = "" then [] else [(nbe_fun (length eqns) c,
[([ml_list (rev (dicts @ default_args))],
nbe_apps_constr idx_of c (dicts @ default_args))])]);
in (eqns', nbe_abss num_args (nbe_fun 0 c)) end;
val (fun_vars, fun_vals) = map_split assemble_eqns eqnss';
val deps_vars = ml_list (map (nbe_fun 0) deps);
in ml_abs deps_vars (ml_Let (ml_fundefs (flat fun_vars)) (ml_list fun_vals)) end;
(* code compilation *)
fun compile_eqnss _ gr raw_deps [] = []
| compile_eqnss ctxt gr raw_deps eqnss =
let
val (deps, deps_vals) = split_list (map_filter
(fn dep => Option.map (fn univ => (dep, univ)) (fst ((Graph.get_node gr dep)))) raw_deps);
val idx_of = raw_deps
|> map (fn dep => (dep, snd (Graph.get_node gr dep)))
|> AList.lookup (op =)
|> (fn f => the o f);
val s = assemble_eqnss idx_of deps eqnss;
val cs = map fst eqnss;
in
s
|> tracing (fn s => "\n--- code to be evaluated:\n" ^ s)
|> ML_Context.evaluate ctxt
(Output.tracing o enclose "\n---compiler echo:\n" "\n---\n",
Output.tracing o enclose "\n--- compiler echo (with error):\n" "\n---\n")
(!trace) univs_cookie
|> (fn f => f deps_vals)
|> (fn univs => cs ~~ univs)
end;
(* preparing function equations *)
fun eqns_of_stmt (_, Code_Thingol.Fun (_, [])) =
[]
| eqns_of_stmt (const, Code_Thingol.Fun ((vs, _), eqns)) =
[(const, (vs, map fst eqns))]
| eqns_of_stmt (_, Code_Thingol.Datatypecons _) =
[]
| eqns_of_stmt (_, Code_Thingol.Datatype _) =
[]
| eqns_of_stmt (class, Code_Thingol.Class (v, (superclasses, classops))) =
let
val names = map snd superclasses @ map fst classops;
val params = Name.invent_list [] "d" (length names);
fun mk (k, name) =
(name, ([(v, [])],
[([IConst (class, ([], [])) `$$ map IVar params], IVar (nth params k))]));
in map_index mk names end
| eqns_of_stmt (_, Code_Thingol.Classrel _) =
[]
| eqns_of_stmt (_, Code_Thingol.Classparam _) =
[]
| eqns_of_stmt (inst, Code_Thingol.Classinst ((class, (_, arities)), (superinsts, instops))) =
[(inst, (arities, [([], IConst (class, ([], [])) `$$
map (fn (_, (_, (inst, dicts))) => IConst (inst, (dicts, []))) superinsts
@ map (IConst o snd o fst) instops)]))];
fun compile_stmts ctxt stmts_deps =
let
val names = map (fst o fst) stmts_deps;
val names_deps = map (fn ((name, _), deps) => (name, deps)) stmts_deps;
val eqnss = maps (eqns_of_stmt o fst) stmts_deps;
val refl_deps = names_deps
|> maps snd
|> distinct (op =)
|> fold (insert (op =)) names;
fun new_node name (gr, (maxidx, idx_tab)) = if can (Graph.get_node gr) name
then (gr, (maxidx, idx_tab))
else (Graph.new_node (name, (NONE, maxidx)) gr,
(maxidx + 1, Inttab.update_new (maxidx, name) idx_tab));
fun compile gr = eqnss
|> compile_eqnss ctxt gr refl_deps
|> rpair gr;
in
fold new_node refl_deps
#> apfst (fold (fn (name, deps) => fold (curry Graph.add_edge name) deps) names_deps
#> compile
#-> fold (fn (name, univ) => (Graph.map_node name o apfst) (K (SOME univ))))
end;
fun ensure_stmts ctxt program =
let
fun add_stmts names (gr, (maxidx, idx_tab)) = if exists ((can o Graph.get_node) gr) names
then (gr, (maxidx, idx_tab))
else (gr, (maxidx, idx_tab))
|> compile_stmts ctxt (map (fn name => ((name, Graph.get_node program name),
Graph.imm_succs program name)) names);
in fold_rev add_stmts (Graph.strong_conn program) end;
(** evaluation **)
(* term evaluation *)
fun eval_term ctxt gr deps ((vs, ty) : typscheme, t) =
let
val frees = Code_Thingol.fold_unbound_varnames (insert (op =)) t []
val frees' = map (fn v => Free (v, [])) frees;
val dict_frees = maps (fn (v, sort) => map_index (curry DFree v o fst) sort) vs;
in
("", (vs, [(map IVar frees, t)]))
|> singleton (compile_eqnss ctxt gr deps)
|> snd
|> (fn t => apps t (rev (dict_frees @ frees')))
end;
(* reification *)
fun term_of_univ thy idx_tab t =
let
fun take_until f [] = []
| take_until f (x::xs) = if f x then [] else x :: take_until f xs;
fun is_dict (Const (idx, _)) =
let
val c = the (Inttab.lookup idx_tab idx);
in
(is_some o Code_Name.class_rev thy) c
orelse (is_some o Code_Name.classrel_rev thy) c
orelse (is_some o Code_Name.instance_rev thy) c
end
| is_dict (DFree _) = true
| is_dict _ = false;
fun of_apps bounds (t, ts) =
fold_map (of_univ bounds) ts
#>> (fn ts' => list_comb (t, rev ts'))
and of_univ bounds (Const (idx, ts)) typidx =
let
val ts' = take_until is_dict ts;
val c = (the o Code_Name.const_rev thy o the o Inttab.lookup idx_tab) idx;
val (_, T) = Code.default_typ thy c;
val T' = map_type_tvar (fn ((v, i), S) => TypeInfer.param (typidx + i) (v, [])) T;
val typidx' = typidx + maxidx_of_typ T' + 1;
in of_apps bounds (Term.Const (c, T'), ts') typidx' end
| of_univ bounds (Free (name, ts)) typidx =
of_apps bounds (Term.Free (name, dummyT), ts) typidx
| of_univ bounds (BVar (n, ts)) typidx =
of_apps bounds (Bound (bounds - n - 1), ts) typidx
| of_univ bounds (t as Abs _) typidx =
typidx
|> of_univ (bounds + 1) (apps t [BVar (bounds, [])])
|-> (fn t' => pair (Term.Abs ("u", dummyT, t')))
in of_univ 0 t 0 |> fst end;
(* function store *)
structure Nbe_Functions = CodeDataFun
(
type T = (Univ option * int) Graph.T * (int * string Inttab.table);
val empty = (Graph.empty, (0, Inttab.empty));
fun purge thy cs (gr, (maxidx, idx_tab)) =
let
val cs_exisiting =
map_filter (Code_Name.const_rev thy) (Graph.keys gr);
val dels = (Graph.all_preds gr
o map (Code_Name.const thy)
o filter (member (op =) cs_exisiting)
) cs;
in (Graph.del_nodes dels gr, (maxidx, idx_tab)) end;
);
(* compilation, evaluation and reification *)
fun compile_eval thy program vs_ty_t deps =
let
val ctxt = ProofContext.init thy;
val (gr, (_, idx_tab)) = Nbe_Functions.change thy (ensure_stmts ctxt program);
in
vs_ty_t
|> eval_term ctxt gr deps
|> term_of_univ thy idx_tab
end;
(* evaluation with type reconstruction *)
fun eval thy t program vs_ty_t deps =
let
fun subst_const f = map_aterms (fn t as Term.Const (c, ty) => Term.Const (f c, ty)
| t => t);
val subst_triv_consts = subst_const (Code_Unit.resubst_alias thy);
val ty = type_of t;
val type_free = AList.lookup (op =)
(map (fn (s, T) => (s, Term.Free (s, T))) (Term.add_frees t []));
val type_frees = Term.map_aterms
(fn (t as Term.Free (s, _)) => the_default t (type_free s) | t => t);
fun type_infer t =
singleton (TypeInfer.infer_types (Syntax.pp_global thy) (Sign.tsig_of thy) I
(try (Type.strip_sorts o Sign.the_const_type thy)) (K NONE) Name.context 0)
(TypeInfer.constrain ty t);
fun check_tvars t = if null (Term.term_tvars t) then t else
error ("Illegal schematic type variables in normalized term: "
^ setmp show_types true (Syntax.string_of_term_global thy) t);
val string_of_term = setmp show_types true (Syntax.string_of_term_global thy);
in
compile_eval thy program vs_ty_t deps
|> tracing (fn t => "Normalized:\n" ^ string_of_term t)
|> subst_triv_consts
|> type_frees
|> tracing (fn t => "Vars typed:\n" ^ string_of_term t)
|> type_infer
|> tracing (fn t => "Types inferred:\n" ^ string_of_term t)
|> check_tvars
|> tracing (fn t => "---\n")
end;
(* evaluation oracle *)
val (_, norm_oracle) = Context.>>> (Context.map_theory_result
(Thm.add_oracle ("norm", fn (thy, t, program, vs_ty_t, deps) =>
Thm.cterm_of thy (Logic.mk_equals (t, eval thy t program vs_ty_t deps)))));
fun add_triv_classes thy =
let
val inters = curry (Sorts.inter_sort (Sign.classes_of thy))
(Code_Unit.triv_classes thy);
fun map_sorts f = (map_types o map_atyps)
(fn TVar (v, sort) => TVar (v, f sort)
| TFree (v, sort) => TFree (v, f sort));
in map_sorts inters end;
fun norm_conv ct =
let
val thy = Thm.theory_of_cterm ct;
fun evaluator' t program vs_ty_t deps = norm_oracle (thy, t, program, vs_ty_t, deps);
fun evaluator t = (add_triv_classes thy t, evaluator' t);
in Code_Thingol.eval_conv thy evaluator ct end;
fun norm_term thy t =
let
fun evaluator' t program vs_ty_t deps = eval thy t program vs_ty_t deps;
fun evaluator t = (add_triv_classes thy t, evaluator' t);
in (Code.postprocess_term thy o Code_Thingol.eval_term thy evaluator) t end;
(* evaluation command *)
fun norm_print_term ctxt modes t =
let
val thy = ProofContext.theory_of ctxt;
val t' = norm_term thy t;
val ty' = Term.type_of t';
val ctxt' = Variable.auto_fixes t ctxt;
val p = PrintMode.with_modes modes (fn () =>
Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk,
Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) ();
in Pretty.writeln p end;
(** Isar setup **)
fun norm_print_term_cmd (modes, s) state =
let val ctxt = Toplevel.context_of state
in norm_print_term ctxt modes (Syntax.read_term ctxt s) end;
val setup =
Value.add_evaluator ("nbe", norm_term o ProofContext.theory_of);
local structure P = OuterParse and K = OuterKeyword in
val opt_modes = Scan.optional (P.$$$ "(" |-- P.!!! (Scan.repeat1 P.xname --| P.$$$ ")")) [];
val _ =
OuterSyntax.improper_command "normal_form" "normalize term by evaluation" K.diag
(opt_modes -- P.term >> (Toplevel.keep o norm_print_term_cmd));
end;
end;