(* Title: HOL/Tools/primrec_package.ML
ID: $Id$
Author: Stefan Berghofer, TU Muenchen; Norbert Voelker, FernUni Hagen;
Florian Haftmann, TU Muenchen
Package for defining functions on datatypes by primitive recursion.
*)
signature PRIMREC_PACKAGE =
sig
val add_primrec: (Name.binding * typ option * mixfix) list ->
((Name.binding * Attrib.src list) * term) list -> local_theory -> thm list * local_theory
val add_primrec_global: (Name.binding * typ option * mixfix) list ->
((Name.binding * Attrib.src list) * term) list -> theory -> thm list * theory
val add_primrec_overloaded: (string * (string * typ) * bool) list ->
(Name.binding * typ option * mixfix) list ->
((Name.binding * Attrib.src list) * term) list -> theory -> thm list * theory
end;
structure PrimrecPackage : PRIMREC_PACKAGE =
struct
open DatatypeAux;
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);
fun message s = if ! Toplevel.debug then () else writeln s;
(* preprocessing of equations *)
fun process_eqn is_fixed spec rec_fns =
let
val (vs, Ts) = split_list (strip_qnt_vars "all" spec);
val body = strip_qnt_body "all" spec;
val (vs', _) = Name.variants 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: "
(map dest_Free (term_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 ("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 (rename_wrt_term rhs rargs));
val (rhs', (fnames'', fnss'')) = subst (map2 (fn (x, y) => fn z =>
(Free x, (body_index y, Free z))) recs subs) rhs (fnames', fnss')
handle PrimrecError (s, NONE) => primrec_error_eqn s eq
in (fnames'', fnss'',
(list_abs_free (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 ("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 ctxt fixes fs (fname, ls, rec_name, tname) =
let
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 def_name = Thm.def_name (Sign.base_name fname);
val rhs = singleton (Syntax.check_terms ctxt) raw_rhs;
val SOME var = get_first (fn ((b, _), mx) =>
if Name.name_of b = fname then SOME (b, mx) else NONE) fixes;
in (var, ((Name.binding def_name, []), rhs)) 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_error (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);
(* primrec definition *)
local
fun prepare_spec prep_spec ctxt raw_fixes raw_spec =
let
val ((fixes, spec), _) = prep_spec
raw_fixes (map (single o apsnd single) raw_spec) ctxt
in (fixes, map (apsnd the_single) spec) end;
fun prove_spec ctxt names rec_rewrites defs =
let
val rewrites = map mk_meta_eq rec_rewrites @ map (snd o snd) defs;
fun tac _ = EVERY [rewrite_goals_tac rewrites, rtac refl 1];
val _ = message ("Proving equations for primrec function(s) " ^ commas_quote names);
in map (fn (a, t) => (a, [Goal.prove ctxt [] [] t tac])) end;
fun gen_primrec set_group prep_spec raw_fixes raw_spec lthy =
let
val (fixes, spec) = prepare_spec prep_spec lthy raw_fixes raw_spec;
val eqns = fold_rev (process_eqn (fn v => Variable.is_fixed lthy v
orelse exists (fn ((w, _), _) => v = Name.name_of w) fixes) o snd) spec [];
val tnames = distinct (op =) (map (#1 o snd) eqns);
val dts = find_dts (DatatypePackage.get_datatypes (ProofContext.theory_of lthy)) 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, defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []);
val names1 = map snd fnames;
val names2 = map fst eqns;
val _ = if gen_eq_set (op =) (names1, names2) then ()
else primrec_error ("functions " ^ commas_quote names2 ^
"\nare not mutually recursive");
val qualify = NameSpace.qualified
(space_implode "_" (map (Sign.base_name o #1) defs));
val spec' = (map o apfst o apfst o Name.map_name) qualify spec;
val simp_atts = map (Attrib.internal o K)
[Simplifier.simp_add, RecfunCodegen.add NONE];
in
lthy
|> set_group ? LocalTheory.set_group (serial_string ())
|> fold_map (LocalTheory.define Thm.definitionK o make_def lthy fixes fs) defs
|-> (fn defs => `(fn ctxt => prove_spec ctxt names1 rec_rewrites defs spec'))
|-> (fn simps => fold_map (LocalTheory.note Thm.theoremK) simps)
|-> (fn simps' => LocalTheory.note Thm.theoremK
((Name.binding (qualify "simps"), simp_atts), maps snd simps'))
|>> snd
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 lthy eqn)
| NONE => ""));
in
val add_primrec = gen_primrec false Specification.check_specification;
val add_primrec_cmd = gen_primrec true Specification.read_specification;
end;
fun add_primrec_global fixes specs thy =
let
val lthy = TheoryTarget.init NONE thy;
val (simps, lthy') = add_primrec fixes specs lthy;
val simps' = ProofContext.export lthy' lthy simps;
in (simps', ProofContext.theory_of (LocalTheory.exit lthy')) end;
fun add_primrec_overloaded ops fixes specs thy =
let
val lthy = TheoryTarget.overloading ops thy;
val (simps, lthy') = add_primrec fixes specs lthy;
val simps' = ProofContext.export lthy' lthy simps;
in (simps', ProofContext.theory_of (LocalTheory.exit lthy')) end;
(* 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.$$$ ")")) (false, "");
val old_primrec_decl =
opt_unchecked_name -- Scan.repeat1 ((SpecParse.opt_thm_name ":" >> apfst Name.name_of) -- P.prop);
fun pipe_error t = P.!!! (Scan.fail_with (K
(cat_lines ["Equations must be separated by " ^ quote "|", quote t])));
val statement = SpecParse.opt_thm_name ":" -- P.prop --| Scan.ahead
((P.term :-- pipe_error) || Scan.succeed ("",""));
val statements = P.enum1 "|" statement;
val primrec_decl = P.opt_target -- P.fixes --| P.$$$ "where" -- statements;
val _ =
OuterSyntax.command "primrec" "define primitive recursive functions on datatypes" K.thy_decl
((primrec_decl >> (fn ((opt_target, raw_fixes), raw_spec) =>
Toplevel.local_theory opt_target (add_primrec_cmd raw_fixes raw_spec #> snd)))
|| (old_primrec_decl >> (fn ((unchecked, alt_name), eqns) =>
Toplevel.theory (snd o
(if unchecked then OldPrimrecPackage.add_primrec_unchecked else OldPrimrecPackage.add_primrec) alt_name
(map P.triple_swap eqns)))));
end;
end;