--- a/src/HOL/Tools/Datatype/primrec.ML Mon Sep 01 16:17:46 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,311 +0,0 @@
-(* Title: HOL/Tools/Datatype/primrec.ML
- Author: Norbert Voelker, FernUni Hagen
- Author: Stefan Berghofer, TU Muenchen
- Author: Florian Haftmann, TU Muenchen
-
-Primitive recursive functions on datatypes.
-*)
-
-signature PRIMREC =
-sig
- val add_primrec: (binding * typ option * mixfix) list ->
- (Attrib.binding * term) list -> local_theory -> (term list * thm list) * local_theory
- val add_primrec_cmd: (binding * string option * mixfix) list ->
- (Attrib.binding * string) list -> local_theory -> (term list * thm list) * local_theory
- val add_primrec_global: (binding * typ option * mixfix) list ->
- (Attrib.binding * term) list -> theory -> (term list * thm list) * theory
- val add_primrec_overloaded: (string * (string * typ) * bool) list ->
- (binding * typ option * mixfix) list ->
- (Attrib.binding * term) list -> theory -> (term list * thm list) * theory
- val add_primrec_simple: ((binding * typ) * mixfix) list -> term list ->
- local_theory -> (string * (term list * thm list)) * local_theory
-end;
-
-structure Primrec : 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 (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, (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 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, tname) :: defs));
-
-
-(* make definition *)
-
-fun make_def ctxt fixes fs (fname, ls, rec_name, tname) =
- 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.conceal (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 : 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 (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, rtac 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 add_primrec_simple fixes ts lthy =
- let
- val ((prefix, (_, defs)), prove) = distill lthy fixes ts;
- in
- lthy
- |> fold_map Local_Theory.define defs
- |-> (fn defs => `(fn lthy => (prefix, (map fst defs, prove lthy defs))))
- end;
-
-local
-
-fun gen_primrec prep_spec 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 :: attrs)) spec;
- fun simp_attr_binding prefix =
- (Binding.qualify true prefix (Binding.name "simps"), @{attributes [simp, nitpick_simp]});
- in
- lthy
- |> add_primrec_simple 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 add_primrec = gen_primrec Specification.check_spec;
-val add_primrec_cmd = gen_primrec Specification.read_spec;
-
-end;
-
-fun add_primrec_global fixes specs thy =
- let
- val lthy = Named_Target.theory_init thy;
- val ((ts, simps), lthy') = add_primrec fixes specs lthy;
- val simps' = Proof_Context.export lthy' lthy simps;
- in ((ts, simps'), Local_Theory.exit_global lthy') end;
-
-fun add_primrec_overloaded ops fixes specs thy =
- let
- val lthy = Overloading.overloading ops thy;
- val ((ts, simps), lthy') = add_primrec fixes specs lthy;
- val simps' = Proof_Context.export lthy' lthy simps;
- in ((ts, simps'), Local_Theory.exit_global lthy') end;
-
-end;