(* Title: Pure/Isar/code_unit.ML
Author: Florian Haftmann, TU Muenchen
Basic notions of code generation. Auxiliary.
*)
signature CODE_UNIT =
sig
(*generic non-sense*)
val bad_thm: string -> 'a
val error_thm: ('a -> 'b) -> 'a -> 'b
val warning_thm: ('a -> 'b) -> 'a -> 'b option
val try_thm: ('a -> 'b) -> 'a -> 'b option
(*typ instantiations*)
val typscheme: theory -> string * typ -> (string * sort) list * typ
val inst_thm: theory -> sort Vartab.table -> thm -> thm
val constrain_thm: theory -> sort -> thm -> thm
(*constant aliasses*)
val add_const_alias: thm -> theory -> theory
val triv_classes: theory -> class list
val resubst_alias: theory -> string -> string
(*constants*)
val string_of_typ: theory -> typ -> string
val string_of_const: theory -> string -> string
val no_args: theory -> string -> int
val check_const: theory -> term -> string
val read_bare_const: theory -> string -> string * typ
val read_const: theory -> string -> string
(*constructor sets*)
val constrset_of_consts: theory -> (string * typ) list
-> string * ((string * sort) list * (string * typ list) list)
(*code equations*)
val assert_eqn: theory -> thm -> thm
val mk_eqn: theory -> thm -> thm * bool
val assert_linear: (string -> bool) -> thm * bool -> thm * bool
val const_eqn: thm -> string
val const_typ_eqn: thm -> string * typ
val head_eqn: theory -> thm -> string * ((string * sort) list * typ)
val expand_eta: theory -> int -> thm -> thm
val rewrite_eqn: simpset -> thm -> thm
val rewrite_head: thm list -> thm -> thm
val norm_args: theory -> thm list -> thm list
val norm_varnames: theory -> (string -> string) -> (string -> string) -> thm list -> thm list
(*case certificates*)
val case_cert: thm -> string * (int * string list)
end;
structure Code_Unit: CODE_UNIT =
struct
(* auxiliary *)
exception BAD_THM of string;
fun bad_thm msg = raise BAD_THM msg;
fun error_thm f thm = f thm handle BAD_THM msg => error msg;
fun warning_thm f thm = SOME (f thm) handle BAD_THM msg
=> (warning ("code generator: " ^ msg); NONE);
fun try_thm f thm = SOME (f thm) handle BAD_THM _ => NONE;
fun string_of_typ thy = setmp show_sorts true (Syntax.string_of_typ_global thy);
fun string_of_const thy c = case AxClass.inst_of_param thy c
of SOME (c, tyco) => Sign.extern_const thy c ^ " " ^ enclose "[" "]" (Sign.extern_type thy tyco)
| NONE => Sign.extern_const thy c;
fun no_args thy = length o fst o strip_type o Sign.the_const_type thy;
(* utilities *)
fun typscheme thy (c, ty) =
let
val ty' = Logic.unvarifyT ty;
fun dest (TFree (v, sort)) = (v, sort)
| dest ty = error ("Illegal type parameter in type scheme: " ^ Syntax.string_of_typ_global thy ty);
val vs = map dest (Sign.const_typargs thy (c, ty'));
in (vs, Type.strip_sorts ty') end;
fun inst_thm thy tvars' thm =
let
val tvars = (Term.add_tvars o Thm.prop_of) thm [];
val inter_sort = Sorts.inter_sort (Sign.classes_of thy);
fun mk_inst (tvar as (v, sort)) = case Vartab.lookup tvars' v
of SOME sort' => SOME (pairself (Thm.ctyp_of thy o TVar)
(tvar, (v, inter_sort (sort, sort'))))
| NONE => NONE;
val insts = map_filter mk_inst tvars;
in Thm.instantiate (insts, []) thm end;
fun constrain_thm thy sort thm =
let
val constrain = curry (Sorts.inter_sort (Sign.classes_of thy)) sort
val tvars = (Term.add_tvars o Thm.prop_of) thm [];
fun mk_inst (tvar as (v, sort)) = pairself (Thm.ctyp_of thy o TVar o pair v)
(sort, constrain sort)
val insts = map mk_inst tvars;
in Thm.instantiate (insts, []) thm end;
fun expand_eta thy k thm =
let
val (lhs, rhs) = (Logic.dest_equals o Thm.plain_prop_of) thm;
val (head, args) = strip_comb lhs;
val l = if k = ~1
then (length o fst o strip_abs) rhs
else Int.max (0, k - length args);
val used = Name.make_context (map (fst o fst) (Term.add_vars lhs []));
fun get_name _ 0 = pair []
| get_name (Abs (v, ty, t)) k =
Name.variants [v]
##>> get_name t (k - 1)
#>> (fn ([v'], vs') => (v', ty) :: vs')
| get_name t k =
let
val (tys, _) = (strip_type o fastype_of) t
in case tys
of [] => raise TERM ("expand_eta", [t])
| ty :: _ =>
Name.variants [""]
#-> (fn [v] => get_name (t $ Var ((v, 0), ty)) (k - 1)
#>> (fn vs' => (v, ty) :: vs'))
end;
val (vs, _) = get_name rhs l used;
fun expand (v, ty) thm = Drule.fun_cong_rule thm
(Thm.cterm_of thy (Var ((v, 0), ty)));
in
thm
|> fold expand vs
|> Conv.fconv_rule Drule.beta_eta_conversion
end;
fun eqn_conv conv =
let
fun lhs_conv ct = if can Thm.dest_comb ct
then (Conv.combination_conv lhs_conv conv) ct
else Conv.all_conv ct;
in Conv.combination_conv (Conv.arg_conv lhs_conv) conv end;
fun head_conv conv =
let
fun lhs_conv ct = if can Thm.dest_comb ct
then (Conv.fun_conv lhs_conv) ct
else conv ct;
in Conv.fun_conv (Conv.arg_conv lhs_conv) end;
val rewrite_eqn = Conv.fconv_rule o eqn_conv o Simplifier.rewrite;
val rewrite_head = Conv.fconv_rule o head_conv o MetaSimplifier.rewrite false;
fun norm_args thy thms =
let
val num_args_of = length o snd o strip_comb o fst o Logic.dest_equals;
val k = fold (curry Int.max o num_args_of o Thm.prop_of) thms 0;
in
thms
|> map (expand_eta thy k)
|> map (Conv.fconv_rule Drule.beta_eta_conversion)
end;
fun canonical_tvars thy purify_tvar thm =
let
val ctyp = Thm.ctyp_of thy;
fun tvars_subst_for thm = (fold_types o fold_atyps)
(fn TVar (v_i as (v, _), sort) => let
val v' = purify_tvar v
in if v = v' then I
else insert (op =) (v_i, (v', sort)) end
| _ => I) (prop_of thm) [];
fun mk_inst (v_i, (v', sort)) (maxidx, acc) =
let
val ty = TVar (v_i, sort)
in
(maxidx + 1, (ctyp ty, ctyp (TVar ((v', maxidx), sort))) :: acc)
end;
val maxidx = Thm.maxidx_of thm + 1;
val (_, inst) = fold mk_inst (tvars_subst_for thm) (maxidx + 1, []);
in Thm.instantiate (inst, []) thm end;
fun canonical_vars thy purify_var thm =
let
val cterm = Thm.cterm_of thy;
fun vars_subst_for thm = fold_aterms
(fn Var (v_i as (v, _), ty) => let
val v' = purify_var v
in if v = v' then I
else insert (op =) (v_i, (v', ty)) end
| _ => I) (prop_of thm) [];
fun mk_inst (v_i as (v, i), (v', ty)) (maxidx, acc) =
let
val t = Var (v_i, ty)
in
(maxidx + 1, (cterm t, cterm (Var ((v', maxidx), ty))) :: acc)
end;
val maxidx = Thm.maxidx_of thm + 1;
val (_, inst) = fold mk_inst (vars_subst_for thm) (maxidx + 1, []);
in Thm.instantiate ([], inst) thm end;
fun canonical_absvars purify_var thm =
let
val t = Thm.plain_prop_of thm;
val t' = Term.map_abs_vars purify_var t;
in Thm.rename_boundvars t t' thm end;
fun norm_varnames thy purify_tvar purify_var thms =
let
fun burrow_thms f [] = []
| burrow_thms f thms =
thms
|> Conjunction.intr_balanced
|> f
|> Conjunction.elim_balanced (length thms)
in
thms
|> burrow_thms (canonical_tvars thy purify_tvar)
|> map (canonical_vars thy purify_var)
|> map (canonical_absvars purify_var)
|> map Drule.zero_var_indexes
end;
(* const aliasses *)
structure ConstAlias = TheoryDataFun
(
type T = ((string * string) * thm) list * class list;
val empty = ([], []);
val copy = I;
val extend = I;
fun merge _ ((alias1, classes1), (alias2, classes2)) : T =
(Library.merge (eq_snd Thm.eq_thm_prop) (alias1, alias2),
Library.merge (op =) (classes1, classes2));
);
fun add_const_alias thm thy =
let
val lhs_rhs = case try Logic.dest_equals (Thm.prop_of thm)
of SOME lhs_rhs => lhs_rhs
| _ => error ("Not an equation: " ^ Display.string_of_thm thm);
val c_c' = case try (pairself (AxClass.unoverload_const thy o dest_Const)) lhs_rhs
of SOME c_c' => c_c'
| _ => error ("Not an equation with two constants: " ^ Display.string_of_thm thm);
val some_class = the_list (AxClass.class_of_param thy (snd c_c'));
in thy |>
ConstAlias.map (fn (alias, classes) =>
((c_c', thm) :: alias, fold (insert (op =)) some_class classes))
end;
fun resubst_alias thy =
let
val alias = fst (ConstAlias.get thy);
val subst_inst_param = Option.map fst o AxClass.inst_of_param thy;
fun subst_alias c =
get_first (fn ((c', c''), _) => if c = c'' then SOME c' else NONE) alias;
in
perhaps subst_inst_param
#> perhaps subst_alias
end;
val triv_classes = snd o ConstAlias.get;
(* reading constants as terms *)
fun check_bare_const thy t = case try dest_Const t
of SOME c_ty => c_ty
| NONE => error ("Not a constant: " ^ Syntax.string_of_term_global thy t);
fun check_const thy = AxClass.unoverload_const thy o check_bare_const thy;
fun read_bare_const thy = check_bare_const thy o Syntax.read_term_global thy;
fun read_const thy = AxClass.unoverload_const thy o read_bare_const thy;
(* constructor sets *)
fun constrset_of_consts thy cs =
let
val _ = map (fn (c, _) => if (is_some o AxClass.class_of_param thy) c
then error ("Is a class parameter: " ^ string_of_const thy c) else ()) cs;
fun no_constr (c, ty) = error ("Not a datatype constructor: " ^ string_of_const thy c
^ " :: " ^ string_of_typ thy ty);
fun last_typ c_ty ty =
let
val frees = OldTerm.typ_tfrees ty;
val (tyco, vs) = ((apsnd o map) (dest_TFree) o dest_Type o snd o strip_type) ty
handle TYPE _ => no_constr c_ty
val _ = if has_duplicates (eq_fst (op =)) vs then no_constr c_ty else ();
val _ = if length frees <> length vs then no_constr c_ty else ();
in (tyco, vs) end;
fun ty_sorts (c, ty) =
let
val ty_decl = (Logic.unvarifyT o Sign.the_const_type thy) c;
val (tyco, _) = last_typ (c, ty) ty_decl;
val (_, vs) = last_typ (c, ty) ty;
in ((tyco, map snd vs), (c, (map fst vs, ty))) end;
fun add ((tyco', sorts'), c) ((tyco, sorts), cs) =
let
val _ = if tyco' <> tyco
then error "Different type constructors in constructor set"
else ();
val sorts'' = map2 (curry (Sorts.inter_sort (Sign.classes_of thy))) sorts' sorts
in ((tyco, sorts), c :: cs) end;
fun inst vs' (c, (vs, ty)) =
let
val the_v = the o AList.lookup (op =) (vs ~~ vs');
val ty' = map_atyps (fn TFree (v, _) => TFree (the_v v)) ty;
in (c, (fst o strip_type) ty') end;
val c' :: cs' = map ty_sorts cs;
val ((tyco, sorts), cs'') = fold add cs' (apsnd single c');
val vs = Name.names Name.context Name.aT sorts;
val cs''' = map (inst vs) cs'';
in (tyco, (vs, rev cs''')) end;
(* code equations *)
fun assert_eqn thy thm =
let
val (lhs, rhs) = (Logic.dest_equals o Thm.plain_prop_of) thm
handle TERM _ => bad_thm ("Not an equation: " ^ Display.string_of_thm thm)
| THM _ => bad_thm ("Not an equation: " ^ Display.string_of_thm thm);
fun vars_of t = fold_aterms
(fn Var (v, _) => insert (op =) v
| Free _ => bad_thm ("Illegal free variable in rewrite theorem\n"
^ Display.string_of_thm thm)
| _ => I) t [];
fun tvars_of t = fold_term_types
(fn _ => fold_atyps (fn TVar (v, _) => insert (op =) v
| TFree _ => bad_thm
("Illegal free type variable in rewrite theorem\n" ^ Display.string_of_thm thm))) t [];
val lhs_vs = vars_of lhs;
val rhs_vs = vars_of rhs;
val lhs_tvs = tvars_of lhs;
val rhs_tvs = tvars_of lhs;
val _ = if null (subtract (op =) lhs_vs rhs_vs)
then ()
else bad_thm ("Free variables on right hand side of rewrite theorem\n"
^ Display.string_of_thm thm);
val _ = if null (subtract (op =) lhs_tvs rhs_tvs)
then ()
else bad_thm ("Free type variables on right hand side of rewrite theorem\n"
^ Display.string_of_thm thm) val (head, args) = (strip_comb o fst o Logic.dest_equals o Thm.plain_prop_of) thm;
val (c, ty) = case head of Const c_ty => c_ty | _ =>
bad_thm ("Equation not headed by constant\n" ^ Display.string_of_thm thm);
fun check _ (Abs _) = bad_thm
("Abstraction on left hand side of equation\n"
^ Display.string_of_thm thm)
| check 0 (Var _) = ()
| check _ (Var _) = bad_thm
("Variable with application on left hand side of code equation\n"
^ Display.string_of_thm thm)
| check n (t1 $ t2) = (check (n+1) t1; check 0 t2)
| check n (Const (_, ty)) = if n <> (length o fst o strip_type) ty
then bad_thm
("Partially applied constant on left hand side of equation\n"
^ Display.string_of_thm thm)
else ();
val _ = map (check 0) args;
val ty_decl = Sign.the_const_type thy c;
val _ = if Sign.typ_equiv thy (Type.strip_sorts ty_decl, Type.strip_sorts ty)
then () else bad_thm ("Type\n" ^ string_of_typ thy ty
^ "\nof code equation\n"
^ Display.string_of_thm thm
^ "\nis incompatible with declared function type\n"
^ string_of_typ thy ty_decl)
in thm end;
fun add_linear thm =
let
val (_, args) = (strip_comb o fst o Logic.dest_equals o Thm.plain_prop_of) thm;
val linear = not (has_duplicates (op =)
((fold o fold_aterms) (fn Var (v, _) => cons v | _ => I) args []))
in (thm, linear) end;
fun assert_pat is_cons thm =
let
val args = (snd o strip_comb o fst o Logic.dest_equals o Thm.plain_prop_of) thm;
val _ = (map o map_aterms) (fn t as Const (c, _) => if is_cons c then t
else bad_thm ("Not a constructor on left hand side of equation: "
^ quote c ^ ",\n in equation\n" ^ Display.string_of_thm thm)
| t => t) args;
in thm end;
fun assert_linear is_cons (thm, false) = (thm, false)
| assert_linear is_cons (thm, true) = if snd (add_linear (assert_pat is_cons thm)) then (thm, true)
else bad_thm
("Duplicate variables on left hand side of code equation:\n"
^ Display.string_of_thm thm);
fun mk_eqn thy = add_linear o assert_eqn thy o AxClass.unoverload thy
o LocalDefs.meta_rewrite_rule (ProofContext.init thy);
val const_typ_eqn = dest_Const o fst o strip_comb o fst o Logic.dest_equals o Thm.plain_prop_of;
val const_eqn = fst o const_typ_eqn;
fun head_eqn thy thm = let val (c, ty) = const_typ_eqn thm in (c, typscheme thy (c, ty)) end;
(* case cerificates *)
fun case_certificate thm =
let
val ((head, raw_case_expr), cases) = (apfst Logic.dest_equals
o apsnd Logic.dest_conjunctions o Logic.dest_implies o Thm.prop_of) thm;
val _ = case head of Free _ => true
| Var _ => true
| _ => raise TERM ("case_cert", []);
val ([(case_var, _)], case_expr) = Term.strip_abs_eta 1 raw_case_expr;
val (Const (case_const, _), raw_params) = strip_comb case_expr;
val n = find_index (fn Free (v, _) => v = case_var | _ => false) raw_params;
val _ = if n = ~1 then raise TERM ("case_cert", []) else ();
val params = map (fst o dest_Var) (nth_drop n raw_params);
fun dest_case t =
let
val (head' $ t_co, rhs) = Logic.dest_equals t;
val _ = if head' = head then () else raise TERM ("case_cert", []);
val (Const (co, _), args) = strip_comb t_co;
val (Var (param, _), args') = strip_comb rhs;
val _ = if args' = args then () else raise TERM ("case_cert", []);
in (param, co) end;
fun analyze_cases cases =
let
val co_list = fold (AList.update (op =) o dest_case) cases [];
in map (the o AList.lookup (op =) co_list) params end;
fun analyze_let t =
let
val (head' $ arg, Var (param', _) $ arg') = Logic.dest_equals t;
val _ = if head' = head then () else raise TERM ("case_cert", []);
val _ = if arg' = arg then () else raise TERM ("case_cert", []);
val _ = if [param'] = params then () else raise TERM ("case_cert", []);
in [] end;
fun analyze (cases as [let_case]) =
(analyze_cases cases handle Bind => analyze_let let_case)
| analyze cases = analyze_cases cases;
in (case_const, (n, analyze cases)) end;
fun case_cert thm = case_certificate thm
handle Bind => error "bad case certificate"
| TERM _ => error "bad case certificate";
end;