print constants in 'primrec', 'primcorec(ursive)', 'corec(ursive)', like in 'definition' and 'fun(ction)'
(* Title: HOL/Tools/Old_Datatype/old_primrec.ML
Author: Norbert Voelker, FernUni Hagen
Author: Stefan Berghofer, TU Muenchen
Author: Florian Haftmann, TU Muenchen
Primitive recursive functions on datatypes.
*)
signature OLD_PRIMREC =
sig
val primrec: bool -> (binding * typ option * mixfix) list ->
Specification.multi_specs -> local_theory -> (term list * thm list) * local_theory
val primrec_cmd: bool -> (binding * string option * mixfix) list ->
Specification.multi_specs_cmd -> local_theory -> (term list * thm list) * local_theory
val primrec_global: bool -> (binding * typ option * mixfix) list ->
Specification.multi_specs -> theory -> (term list * thm list) * theory
val primrec_overloaded: bool -> (string * (string * typ) * bool) list ->
(binding * typ option * mixfix) list ->
Specification.multi_specs -> theory -> (term list * thm list) * theory
val primrec_simple: bool -> ((binding * typ) * mixfix) list -> term list ->
local_theory -> (string * (term list * thm list)) * local_theory
end;
structure Old_Primrec : OLD_PRIMREC =
struct
exception PrimrecError of string * term option;
fun primrec_error msg = raise PrimrecError (msg, NONE);
fun primrec_error_eqn msg eqn = raise PrimrecError (msg, SOME eqn);
(* preprocessing of equations *)
fun process_eqn is_fixed spec rec_fns =
let
val (vs, Ts) = split_list (strip_qnt_vars @{const_name Pure.all} spec);
val body = strip_qnt_body @{const_name Pure.all} spec;
val (vs', _) = fold_map Name.variant vs (Name.make_context (fold_aterms
(fn Free (v, _) => insert (op =) v | _ => I) body []));
val eqn = curry subst_bounds (map2 (curry Free) vs' Ts |> rev) body;
val (lhs, rhs) = HOLogic.dest_eq (HOLogic.dest_Trueprop eqn)
handle TERM _ => primrec_error "not a proper equation";
val (recfun, args) = strip_comb lhs;
val fname =
(case recfun of
Free (v, _) =>
if is_fixed v then v
else primrec_error "illegal head of function equation"
| _ => primrec_error "illegal head of function equation");
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 primrec_error "constructor missing"
else strip_comb (hd middle);
val (cname, T) = dest_Const constr
handle TERM _ => primrec_error "ill-formed constructor";
val (tname, _) = dest_Type (body_type T) handle TYPE _ =>
primrec_error "cannot determine datatype associated with function"
val (ls, cargs, rs) =
(map dest_Free ls', map dest_Free cargs', map dest_Free rs')
handle TERM _ => primrec_error "illegal argument in pattern";
val lfrees = ls @ rs @ cargs;
fun check_vars _ [] = ()
| check_vars s vars = primrec_error (s ^ commas_quote (map fst vars)) eqn;
in
if length middle > 1 then
primrec_error "more than one non-variable in pattern"
else
(check_vars "repeated variable names in pattern: " (duplicates (op =) lfrees);
check_vars "extra variables on rhs: "
(Term.add_frees rhs [] |> subtract (op =) lfrees
|> filter_out (is_fixed o fst));
(case AList.lookup (op =) rec_fns fname of
NONE =>
(fname, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eqn))])) :: rec_fns
| SOME (_, rpos', eqns) =>
if AList.defined (op =) eqns cname then
primrec_error "constructor already occurred as pattern"
else if rpos <> rpos' then
primrec_error "position of recursive argument inconsistent"
else
AList.update (op =)
(fname, (tname, rpos, (cname, (ls, cargs, rs, rhs, eqn)) :: eqns))
rec_fns))
end handle PrimrecError (msg, NONE) => primrec_error_eqn msg spec;
fun process_fun descr eqns (i, fname) (fnames, fnss) =
let
val (_, (tname, _, constrs)) = 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_Free f
andalso member (fn ((v, _), (w, _)) => v = w) eqns (dest_Free f) then
let
val (fname', _) = dest_Free f;
val (_, rpos, _) = the (AList.lookup (op =) eqns fname');
val (ls, rs) = chop rpos ts
val (x', rs') =
(case rs of
x' :: rs => (x', rs)
| [] => primrec_error ("not enough arguments in recursive application\n" ^
"of 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 descr eqns (i', fname')
|-> (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) (fnames', fnss', fns) =
(case AList.lookup (op =) eqns cname of
NONE => (warning ("No equation for constructor " ^ quote cname ^
"\nin definition of function " ^ quote fname);
(fnames', fnss', (Const (@{const_name undefined}, dummyT)) :: fns))
| SOME (ls, cargs', rs, rhs, eq) =>
let
val recs = filter (Old_Datatype_Aux.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', (fnames'', fnss'')) = subst (map2 (fn (x, y) => fn z =>
(Free x, (Old_Datatype_Aux.body_index y, Free z))) recs subs) rhs (fnames', fnss')
handle PrimrecError (s, NONE) => primrec_error_eqn s eq
in
(fnames'', fnss'', fold_rev absfree (cargs' @ subs @ ls @ rs) rhs' :: fns)
end)
in
(case AList.lookup (op =) fnames i of
NONE =>
if exists (fn (_, v) => fname = v) fnames then
primrec_error ("inconsistent functions for datatype " ^ quote tname)
else
let
val (_, _, eqns) = the (AList.lookup (op =) eqns fname);
val (fnames', fnss', fns) = fold_rev (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 primrec_error ("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 (@{const_name undefined},
replicate (length cargs + length (filter Old_Datatype_Aux.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) :: defs));
(* make definition *)
fun make_def ctxt fixes fs (fname, ls, rec_name) =
let
val SOME (var, varT) = get_first (fn ((b, T), mx) =>
if Binding.name_of b = fname then SOME ((b, mx), T) else NONE) fixes;
val def_name = Thm.def_name (Long_Name.base_name fname);
val raw_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 rhs = singleton (Syntax.check_terms ctxt) (Type.constraint varT raw_rhs);
in (var, ((Binding.concealed (Binding.name def_name), []), rhs)) end;
(* find datatypes which contain all datatypes in tnames' *)
fun find_dts _ _ [] = []
| find_dts dt_info tnames' (tname :: tnames) =
(case Symtab.lookup dt_info tname of
NONE => primrec_error (quote tname ^ " is not a datatype")
| SOME (dt : Old_Datatype_Aux.info) =>
if subset (op =) (tnames', map (#1 o snd) (#descr dt)) then
(tname, dt) :: (find_dts dt_info tnames' tnames)
else find_dts dt_info tnames' tnames);
(* distill primitive definition(s) from primrec specification *)
fun distill ctxt fixes eqs =
let
val eqns = fold_rev (process_eqn (fn v => Variable.is_fixed ctxt v
orelse exists (fn ((w, _), _) => v = Binding.name_of w) fixes)) eqs [];
val tnames = distinct (op =) (map (#1 o snd) eqns);
val dts = find_dts (Old_Datatype_Data.get_all (Proof_Context.theory_of ctxt)) tnames tnames;
val main_fns = map (fn (tname, {index, ...}) =>
(index, (fst o the o find_first (fn (_, x) => #1 x = tname)) eqns)) dts;
val {descr, rec_names, rec_rewrites, ...} =
if null dts then primrec_error
("datatypes " ^ commas_quote tnames ^ "\nare not mutually recursive")
else snd (hd dts);
val (fnames, fnss) = fold_rev (process_fun descr eqns) main_fns ([], []);
val (fs, raw_defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []);
val defs = map (make_def ctxt fixes fs) raw_defs;
val names = map snd fnames;
val names_eqns = map fst eqns;
val _ =
if eq_set (op =) (names, names_eqns) then ()
else primrec_error ("functions " ^ commas_quote names_eqns ^
"\nare not mutually recursive");
val rec_rewrites' = map mk_meta_eq rec_rewrites;
val prefix = space_implode "_" (map (Long_Name.base_name o #1) raw_defs);
fun prove ctxt defs =
let
val frees = fold (Variable.add_free_names ctxt) eqs [];
val rewrites = rec_rewrites' @ map (snd o snd) defs;
in
map (fn eq => Goal.prove ctxt frees [] eq
(fn {context = ctxt', ...} =>
EVERY [rewrite_goals_tac ctxt' rewrites, resolve_tac ctxt' [refl] 1])) eqs
end;
in ((prefix, (fs, defs)), prove) end
handle PrimrecError (msg, some_eqn) =>
error ("Primrec definition error:\n" ^ msg ^
(case some_eqn of
SOME eqn => "\nin\n" ^ quote (Syntax.string_of_term ctxt eqn)
| NONE => ""));
(* primrec definition *)
fun primrec_simple int fixes ts lthy =
let
val ((prefix, (_, defs)), prove) = distill lthy fixes ts;
in
lthy
|> fold_map Local_Theory.define defs
|> tap (uncurry (BNF_FP_Rec_Sugar_Util.print_def_consts int))
|-> (fn defs => `(fn lthy => (prefix, (map fst defs, prove lthy defs))))
end;
local
fun gen_primrec prep_spec int raw_fixes raw_spec lthy =
let
val (fixes, spec) = fst (prep_spec raw_fixes raw_spec lthy);
fun attr_bindings prefix = map (fn ((b, attrs), _) =>
(Binding.qualify false prefix b, Code.add_default_eqn_attrib Code.Equation :: attrs)) spec;
fun simp_attr_binding prefix =
(Binding.qualify true prefix (Binding.name "simps"), @{attributes [simp, nitpick_simp]});
in
lthy
|> primrec_simple int fixes (map snd spec)
|-> (fn (prefix, (ts, simps)) =>
Spec_Rules.add Spec_Rules.Equational (ts, simps)
#> fold_map Local_Theory.note (attr_bindings prefix ~~ map single simps)
#-> (fn simps' => Local_Theory.note (simp_attr_binding prefix, maps snd simps')
#>> (fn (_, simps'') => (ts, simps''))))
end;
in
val primrec = gen_primrec Specification.check_multi_specs;
val primrec_cmd = gen_primrec Specification.read_multi_specs;
end;
fun primrec_global int fixes specs thy =
let
val lthy = Named_Target.theory_init thy;
val ((ts, simps), lthy') = primrec int fixes specs lthy;
val simps' = Proof_Context.export lthy' lthy simps;
in ((ts, simps'), Local_Theory.exit_global lthy') end;
fun primrec_overloaded int ops fixes specs thy =
let
val lthy = Overloading.overloading ops thy;
val ((ts, simps), lthy') = primrec int fixes specs lthy;
val simps' = Proof_Context.export lthy' lthy simps;
in ((ts, simps'), Local_Theory.exit_global lthy') end;
end;