(* Title: HOL/Tools/datatype_package.ML
ID: $Id$
Author: Stefan Berghofer
Copyright 1998 TU Muenchen
Package for defining functions on datatypes
by primitive recursion
*)
signature PRIMREC_PACKAGE =
sig
val add_primrec_i : string option -> string list ->
term list -> theory -> theory * thm list
val add_primrec : string option -> string list ->
string list -> theory -> theory * thm list
end;
structure PrimrecPackage : PRIMREC_PACKAGE =
struct
open DatatypeAux;
exception RecError of string;
(* FIXME: move? *)
fun dest_eq (Const ("Trueprop", _) $ (Const ("op =", _) $ lhs $ rhs)) = (lhs, rhs)
| dest_eq t = raise TERM ("dest_eq", [t])
fun dest_Type (Type x) = x
| dest_Type T = raise TYPE ("dest_Type", [T], []);
fun primrec_err s = error ("Primrec definition error:\n" ^ s);
fun primrec_eq_err sign s eq =
primrec_err (s ^ "\nin equation\n" ^ Sign.string_of_term sign eq);
(* preprocessing of equations *)
fun process_eqn sign (eq, rec_fns) =
let
val (lhs, rhs) = if null (term_vars eq) then
dest_eq eq handle _ => raise RecError "not a proper equation"
else raise RecError "illegal schematic variable(s)";
val (recfun, args) = strip_comb lhs;
val (fname, _) = dest_Const recfun handle _ =>
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 _ => raise RecError "ill-formed constructor";
val (tname, _) = dest_Type (body_type T) handle _ =>
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 _ => raise RecError "illegal argument in pattern";
val lfrees = ls @ rs @ cargs;
in
if not (null (duplicates lfrees)) then
raise RecError "repeated variable name in pattern"
else if not ((map dest_Free (term_frees rhs)) subset lfrees) then
raise RecError "extra variables on rhs"
else if length middle > 1 then
raise RecError "more than one non-variable in pattern"
else (case assoc (rec_fns, fname) of
None =>
(fname, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns
| Some (_, rpos', eqns) =>
if is_some (assoc (eqns, cname)) then
raise RecError "constructor already occured as pattern"
else if rpos <> rpos' then
raise RecError "position of recursive argument inconsistent"
else
overwrite (rec_fns, (fname, (tname, rpos,
(cname, (ls, cargs, rs, rhs, eq))::eqns))))
end
handle RecError s => primrec_eq_err sign s eq;
fun process_fun sign descr rec_eqns ((i, fname), (fnames, fnss)) =
let
val (_, (tname, _, constrs)) = nth_elem (i, descr);
(* substitute "fname ls x rs" by "y ls rs" for (x, (_, y)) in subs *)
fun subst [] x = x
| subst subs (fs, Abs (a, T, t)) =
let val (fs', t') = subst subs (fs, t)
in (fs', Abs (a, T, t')) end
| subst subs (fs, t as (_ $ _)) =
let val (f, ts) = strip_comb t;
in
if is_Const f andalso (fst (dest_Const f)) mem (map fst rec_eqns) then
let
val (fname', _) = dest_Const f;
val (_, rpos, _) = the (assoc (rec_eqns, fname'));
val ls = take (rpos, ts);
val rest = drop (rpos, ts);
val (x, rs) = (hd rest, tl rest)
handle _ => raise RecError ("not enough arguments\
\ in recursive application\nof function " ^ fname' ^ " on rhs")
in
(case assoc (subs, x) of
None =>
let
val (fs', ts') = foldl_map (subst subs) (fs, ts)
in (fs', list_comb (f, ts')) end
| Some (i', y) =>
let
val (fs', ts') = foldl_map (subst subs) (fs, ls @ rs);
val fs'' = process_fun sign descr rec_eqns ((i', fname'), fs')
in (fs'', list_comb (y, ts'))
end)
end
else
let
val (fs', f'::ts') = foldl_map (subst subs) (fs, f::ts)
in (fs', list_comb (f', ts')) end
end
| subst _ x = x;
(* translate rec equations into function arguments suitable for rec comb *)
fun trans eqns ((cname, cargs), (fnames', fnss', fns)) =
(case assoc (eqns, cname) of
None => (warning ("no equation for constructor " ^ cname ^
"\nin definition of function " ^ fname);
(fnames', fnss', (Const ("arbitrary", 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 (rename_wrt_term rhs rargs));
val ((fnames'', fnss''), rhs') = (subst (map (fn ((x, y), z) =>
(Free x, (dest_DtRec y, Free z))) (recs ~~ subs)) ((fnames', fnss'), rhs))
handle RecError s => primrec_eq_err sign s eq
in (fnames'', fnss'', (list_abs_free (cargs' @ subs @ ls @ rs, rhs'))::fns)
end)
in (case assoc (fnames, i) of
None =>
if exists (equal fname o snd) fnames then
raise RecError ("inconsistent functions for datatype " ^ tname)
else
let
val (_, _, eqns) = the (assoc (rec_eqns, fname));
val (fnames', fnss', fns) = foldr (trans eqns)
(constrs, ((i, fname)::fnames, fnss, []))
in
(fnames', (i, (fname, #1 (snd (hd eqns)), fns))::fnss')
end
| Some fname' =>
if fname = fname' then (fnames, fnss)
else raise RecError ("inconsistent functions for datatype " ^ tname))
end;
(* prepare functions needed for definitions *)
fun get_fns fns (((i, (tname, _, constrs)), rec_name), (fs, defs)) =
case assoc (fns, i) of
None =>
let
val dummy_fns = map (fn (_, cargs) => Const ("arbitrary",
replicate ((length cargs) + (length (filter is_rec_type cargs)))
dummyT ---> HOLogic.unitT)) constrs;
val _ = warning ("no function definition for datatype " ^ tname)
in
(dummy_fns @ fs, defs)
end
| Some (fname, ls, fs') => (fs' @ fs, (fname, ls, rec_name, tname)::defs);
(* make definition *)
fun make_def sign fs (fname, ls, rec_name, tname) =
let
val rhs = foldr (fn (T, t) => Abs ("", T, t)) ((map snd ls) @ [dummyT],
list_comb (Const (rec_name, dummyT),
fs @ map Bound (0 ::(length ls downto 1))));
val defpair = (Sign.base_name fname ^ "_" ^ Sign.base_name tname ^ "_def",
Logic.mk_equals (Const (fname, dummyT), rhs))
in
inferT_axm sign defpair
end;
(* find datatypes which contain all datatypes in tnames' *)
fun find_dts (dt_info : datatype_info Symtab.table) _ [] = []
| find_dts dt_info tnames' (tname::tnames) =
(case Symtab.lookup (dt_info, tname) of
None => primrec_err (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 add_primrec_i alt_name eqn_names eqns thy =
let
val sg = sign_of thy;
val dt_info = DatatypePackage.get_datatypes thy;
val rec_eqns = foldr (process_eqn sg) (eqns, []);
val tnames = distinct (map (#1 o snd) rec_eqns);
val dts = find_dts dt_info tnames tnames;
val main_fns = map (fn (tname, {index, ...}) =>
(index, fst (the (find_first (fn f => #1 (snd f) = tname) rec_eqns)))) dts;
val {descr, rec_names, rec_rewrites, ...} = if null dts then
primrec_err ("datatypes " ^ commas tnames ^ "\nare not mutually recursive")
else snd (hd dts);
val (fnames, fnss) = foldr (process_fun sg descr rec_eqns) (main_fns, ([], []));
val (fs, defs) = foldr (get_fns fnss) (descr ~~ rec_names, ([], []));
val defs' = map (make_def sg fs) defs;
val names1 = map snd fnames;
val names2 = map fst rec_eqns;
val thy' = thy |>
Theory.add_path (if_none alt_name (space_implode "_"
(map (Sign.base_name o #1) defs))) |>
(if eq_set (names1, names2) then Theory.add_defs_i defs'
else primrec_err ("functions " ^ commas names2 ^
"\nare not mutually recursive"));
val rewrites = (map meta_eq rec_rewrites) @ (map (get_axiom thy' o fst) defs');
val _ = writeln ("Proving equations for primrec function(s)\n" ^
commas names1 ^ " ...");
val char_thms = map (fn t => prove_goalw_cterm rewrites (cterm_of (sign_of thy') t)
(fn _ => [rtac refl 1])) eqns;
val tsimps = map Attribute.tthm_of char_thms;
val thy'' = thy' |>
PureThy.add_tthmss [(("simps", tsimps), [Simplifier.simp_add_global])] |>
(if null eqn_names then I
else PureThy.add_tthms (map (rpair []) (eqn_names ~~ tsimps))) |>
Theory.parent_path;
in
(thy'', char_thms)
end;
fun add_primrec alt_name eqn_names eqns thy =
add_primrec_i alt_name eqn_names (map (readtm (sign_of thy) propT) eqns) thy;
end;