(* Title: HOL/Tools/old_primrec.ML
Author: Norbert Voelker, FernUni Hagen
Author: Stefan Berghofer, TU Muenchen
Package for defining functions on datatypes by primitive recursion.
*)
signature OLD_PRIMREC =
sig
val unify_consts: theory -> term list -> term list -> term list * term list
val add_primrec: string -> ((bstring * string) * Attrib.src list) list
-> theory -> thm list * theory
val add_primrec_unchecked: string -> ((bstring * string) * Attrib.src list) list
-> theory -> thm list * theory
val add_primrec_i: string -> ((bstring * term) * attribute list) list
-> theory -> thm list * theory
val add_primrec_unchecked_i: string -> ((bstring * term) * attribute list) list
-> theory -> thm list * theory
end;
structure OldPrimrec : OLD_PRIMREC =
struct
open DatatypeAux;
exception RecError of string;
fun primrec_err s = error ("Primrec definition error:\n" ^ s);
fun primrec_eq_err thy s eq =
primrec_err (s ^ "\nin\n" ^ quote (Syntax.string_of_term_global thy eq));
(*the following code ensures that each recursive set always has the
same type in all introduction rules*)
fun unify_consts thy cs intr_ts =
(let
fun varify (t, (i, ts)) =
let val t' = map_types (Logic.incr_tvar (i + 1)) (snd (Type.varify [] t))
in (maxidx_of_term t', t'::ts) end;
val (i, cs') = List.foldr varify (~1, []) cs;
val (i', intr_ts') = List.foldr varify (i, []) intr_ts;
val rec_consts = fold Term.add_consts cs' [];
val intr_consts = fold Term.add_consts intr_ts' [];
fun unify (cname, cT) =
let val consts = map snd (filter (fn (c, _) => c = cname) intr_consts)
in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end;
val (env, _) = fold unify rec_consts (Vartab.empty, i');
val subst = Type.freeze o map_types (Envir.norm_type env)
in (map subst cs', map subst intr_ts')
end) handle Type.TUNIFY =>
(warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
(* preprocessing of equations *)
fun process_eqn thy eq rec_fns =
let
val (lhs, rhs) =
if null (Term.add_vars eq []) then
HOLogic.dest_eq (HOLogic.dest_Trueprop eq)
handle TERM _ => raise RecError "not a proper equation"
else raise RecError "illegal schematic variable(s)";
val (recfun, args) = strip_comb lhs;
val fnameT = dest_Const recfun handle TERM _ =>
raise RecError "function is not declared as constant in theory";
val (ls', rest) = take_prefix is_Free args;
val (middle, rs') = take_suffix is_Free rest;
val rpos = length ls';
val (constr, cargs') = if null middle then raise RecError "constructor missing"
else strip_comb (hd middle);
val (cname, T) = dest_Const constr
handle TERM _ => raise RecError "ill-formed constructor";
val (tname, _) = dest_Type (body_type T) handle TYPE _ =>
raise RecError "cannot determine datatype associated with function"
val (ls, cargs, rs) =
(map dest_Free ls', map dest_Free cargs', map dest_Free rs')
handle TERM _ => raise RecError "illegal argument in pattern";
val lfrees = ls @ rs @ cargs;
fun check_vars _ [] = ()
| check_vars s vars = raise RecError (s ^ commas_quote (map fst vars))
in
if length middle > 1 then
raise RecError "more than one non-variable in pattern"
else
(check_vars "repeated variable names in pattern: " (duplicates (op =) lfrees);
check_vars "extra variables on rhs: "
(map dest_Free (OldTerm.term_frees rhs) \\ lfrees);
case AList.lookup (op =) rec_fns fnameT of
NONE =>
(fnameT, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns
| SOME (_, rpos', eqns) =>
if AList.defined (op =) eqns cname then
raise RecError "constructor already occurred as pattern"
else if rpos <> rpos' then
raise RecError "position of recursive argument inconsistent"
else
AList.update (op =) (fnameT, (tname, rpos, (cname, (ls, cargs, rs, rhs, eq))::eqns))
rec_fns)
end
handle RecError s => primrec_eq_err thy s eq;
fun process_fun thy descr rec_eqns (i, fnameT as (fname, _)) (fnameTs, fnss) =
let
val (_, (tname, _, constrs)) = List.nth (descr, i);
(* substitute "fname ls x rs" by "y ls rs" for (x, (_, y)) in subs *)
fun subst [] t fs = (t, fs)
| subst subs (Abs (a, T, t)) fs =
fs
|> subst subs t
|-> (fn t' => pair (Abs (a, T, t')))
| subst subs (t as (_ $ _)) fs =
let
val (f, ts) = strip_comb t;
in
if is_Const f andalso dest_Const f mem map fst rec_eqns then
let
val fnameT' as (fname', _) = dest_Const f;
val (_, rpos, _) = the (AList.lookup (op =) rec_eqns fnameT');
val ls = Library.take (rpos, ts);
val rest = Library.drop (rpos, ts);
val (x', rs) = (hd rest, tl rest)
handle Empty => raise RecError ("not enough arguments\
\ in recursive application\nof function " ^ quote fname' ^ " on rhs");
val (x, xs) = strip_comb x'
in case AList.lookup (op =) subs x
of NONE =>
fs
|> fold_map (subst subs) ts
|-> (fn ts' => pair (list_comb (f, ts')))
| SOME (i', y) =>
fs
|> fold_map (subst subs) (xs @ ls @ rs)
||> process_fun thy descr rec_eqns (i', fnameT')
|-> (fn ts' => pair (list_comb (y, ts')))
end
else
fs
|> fold_map (subst subs) (f :: ts)
|-> (fn (f'::ts') => pair (list_comb (f', ts')))
end
| subst _ t fs = (t, fs);
(* translate rec equations into function arguments suitable for rec comb *)
fun trans eqns (cname, cargs) (fnameTs', fnss', fns) =
(case AList.lookup (op =) eqns cname of
NONE => (warning ("No equation for constructor " ^ quote cname ^
"\nin definition of function " ^ quote fname);
(fnameTs', fnss', (Const ("HOL.undefined", dummyT))::fns))
| SOME (ls, cargs', rs, rhs, eq) =>
let
val recs = filter (is_rec_type o snd) (cargs' ~~ cargs);
val rargs = map fst recs;
val subs = map (rpair dummyT o fst)
(rev (Term.rename_wrt_term rhs rargs));
val (rhs', (fnameTs'', fnss'')) =
(subst (map (fn ((x, y), z) =>
(Free x, (body_index y, Free z)))
(recs ~~ subs)) rhs (fnameTs', fnss'))
handle RecError s => primrec_eq_err thy s eq
in (fnameTs'', fnss'',
(list_abs_free (cargs' @ subs @ ls @ rs, rhs'))::fns)
end)
in (case AList.lookup (op =) fnameTs i of
NONE =>
if exists (equal fnameT o snd) fnameTs then
raise RecError ("inconsistent functions for datatype " ^ quote tname)
else
let
val (_, _, eqns) = the (AList.lookup (op =) rec_eqns fnameT);
val (fnameTs', fnss', fns) = fold_rev (trans eqns) constrs
((i, fnameT)::fnameTs, fnss, [])
in
(fnameTs', (i, (fname, #1 (snd (hd eqns)), fns))::fnss')
end
| SOME fnameT' =>
if fnameT = fnameT' then (fnameTs, fnss)
else raise RecError ("inconsistent functions for datatype " ^ quote tname))
end;
(* prepare functions needed for definitions *)
fun get_fns fns ((i : int, (tname, _, constrs)), rec_name) (fs, defs) =
case AList.lookup (op =) fns i of
NONE =>
let
val dummy_fns = map (fn (_, cargs) => Const ("HOL.undefined",
replicate ((length cargs) + (length (List.filter is_rec_type cargs)))
dummyT ---> HOLogic.unitT)) constrs;
val _ = warning ("No function definition for datatype " ^ quote tname)
in
(dummy_fns @ fs, defs)
end
| SOME (fname, ls, fs') => (fs' @ fs, (fname, ls, rec_name, tname) :: defs);
(* make definition *)
fun make_def thy fs (fname, ls, rec_name, tname) =
let
val rhs = fold_rev (fn T => fn t => Abs ("", T, t))
((map snd ls) @ [dummyT])
(list_comb (Const (rec_name, dummyT),
fs @ map Bound (0 ::(length ls downto 1))))
val def_name = Long_Name.base_name fname ^ "_" ^ Long_Name.base_name tname ^ "_def";
val def_prop =
singleton (Syntax.check_terms (ProofContext.init thy))
(Logic.mk_equals (Const (fname, dummyT), rhs));
in (def_name, def_prop) end;
(* find datatypes which contain all datatypes in tnames' *)
fun find_dts (dt_info : info Symtab.table) _ [] = []
| find_dts dt_info tnames' (tname::tnames) =
(case Symtab.lookup dt_info tname of
NONE => primrec_err (quote tname ^ " is not a datatype")
| SOME dt =>
if tnames' subset (map (#1 o snd) (#descr dt)) then
(tname, dt)::(find_dts dt_info tnames' tnames)
else find_dts dt_info tnames' tnames);
fun prepare_induct ({descr, induction, ...}: info) rec_eqns =
let
fun constrs_of (_, (_, _, cs)) =
map (fn (cname:string, (_, cargs, _, _, _)) => (cname, map fst cargs)) cs;
val params_of = these o AList.lookup (op =) (List.concat (map constrs_of rec_eqns));
in
induction
|> RuleCases.rename_params (map params_of (List.concat (map (map #1 o #3 o #2) descr)))
|> RuleCases.save induction
end;
local
fun gen_primrec_i note def alt_name eqns_atts thy =
let
val (eqns, atts) = split_list eqns_atts;
val dt_info = Datatype.get_all thy;
val rec_eqns = fold_rev (process_eqn thy o snd) eqns [] ;
val tnames = distinct (op =) (map (#1 o snd) rec_eqns);
val dts = find_dts dt_info tnames tnames;
val main_fns =
map (fn (tname, {index, ...}) =>
(index,
(fst o the o find_first (fn f => (#1 o snd) f = tname)) rec_eqns))
dts;
val {descr, rec_names, rec_rewrites, ...} =
if null dts then
primrec_err ("datatypes " ^ commas_quote tnames ^ "\nare not mutually recursive")
else snd (hd dts);
val (fnameTs, fnss) =
fold_rev (process_fun thy descr rec_eqns) main_fns ([], []);
val (fs, defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []);
val defs' = map (make_def thy fs) defs;
val nameTs1 = map snd fnameTs;
val nameTs2 = map fst rec_eqns;
val _ = if gen_eq_set (op =) (nameTs1, nameTs2) then ()
else primrec_err ("functions " ^ commas_quote (map fst nameTs2) ^
"\nare not mutually recursive");
val primrec_name =
if alt_name = "" then (space_implode "_" (map (Long_Name.base_name o #1) defs)) else alt_name;
val (defs_thms', thy') =
thy
|> Sign.add_path primrec_name
|> fold_map def (map (fn (name, t) => ((name, []), t)) defs');
val rewrites = (map mk_meta_eq rec_rewrites) @ map snd defs_thms';
val simps = map (fn (_, t) => Goal.prove_global thy' [] [] t
(fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) eqns;
val (simps', thy'') =
thy'
|> fold_map note ((map fst eqns ~~ atts) ~~ map single simps);
val simps'' = maps snd simps';
in
thy''
|> note (("simps", [Simplifier.simp_add, Nitpick_Const_Simp_Thms.add,
Code.add_default_eqn_attribute]), simps'')
|> snd
|> note (("induct", []), [prepare_induct (#2 (hd dts)) rec_eqns])
|> snd
|> Sign.parent_path
|> pair simps''
end;
fun gen_primrec note def alt_name eqns thy =
let
val ((names, strings), srcss) = apfst split_list (split_list eqns);
val atts = map (map (Attrib.attribute thy)) srcss;
val eqn_ts = map (fn s => Syntax.read_prop_global thy s
handle ERROR msg => cat_error msg ("The error(s) above occurred for " ^ s)) strings;
val rec_ts = map (fn eq => head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop eq)))
handle TERM _ => primrec_eq_err thy "not a proper equation" eq) eqn_ts;
val (_, eqn_ts') = unify_consts thy rec_ts eqn_ts
in
gen_primrec_i note def alt_name (names ~~ eqn_ts' ~~ atts) thy
end;
fun thy_note ((name, atts), thms) =
PureThy.add_thmss [((Binding.name name, thms), atts)] #-> (fn [thms] => pair (name, thms));
fun thy_def false ((name, atts), t) =
PureThy.add_defs false [((Binding.name name, t), atts)] #-> (fn [thm] => pair (name, thm))
| thy_def true ((name, atts), t) =
PureThy.add_defs_unchecked false [((Binding.name name, t), atts)] #-> (fn [thm] => pair (name, thm));
in
val add_primrec = gen_primrec thy_note (thy_def false);
val add_primrec_unchecked = gen_primrec thy_note (thy_def true);
val add_primrec_i = gen_primrec_i thy_note (thy_def false);
val add_primrec_unchecked_i = gen_primrec_i thy_note (thy_def true);
fun gen_primrec note def alt_name specs =
gen_primrec_i note def alt_name (map (fn ((name, t), atts) => ((name, atts), t)) specs);
end;
(* see primrec.ML (* outer syntax *)
local structure P = OuterParse and K = OuterKeyword in
val opt_unchecked_name =
Scan.optional (P.$$$ "(" |-- P.!!!
(((P.$$$ "unchecked" >> K true) -- Scan.optional P.name "" ||
P.name >> pair false) --| P.$$$ ")")) (false, "");
val primrec_decl =
opt_unchecked_name -- Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop);
val _ =
OuterSyntax.command "primrec" "define primitive recursive functions on datatypes" K.thy_decl
(primrec_decl >> (fn ((unchecked, alt_name), eqns) =>
Toplevel.theory (snd o
(if unchecked then add_primrec_unchecked else add_primrec) alt_name
(map P.triple_swap eqns))));
end;*)
end;