author | berghofe |
Mon, 20 Sep 1999 12:01:41 +0200 | |
changeset 7544 | dee529666dcd |
parent 7152 | 44d46a112127 |
child 7722 | 8add8fdce3f1 |
permissions | -rw-r--r-- |
5719 | 1 |
(* Title: HOL/Tools/primrec_package.ML |
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ID: $Id$ |
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Author: Stefan Berghofer and Norbert Voelker |
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Copyright 1998 TU Muenchen |
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Package for defining functions on datatypes by primitive recursion. |
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*) |
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signature PRIMREC_PACKAGE = |
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sig |
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val quiet_mode: bool ref |
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val add_primrec: string -> ((bstring * string) * Args.src list) list |
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-> theory -> theory * thm list |
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val add_primrec_i: string -> ((bstring * term) * theory attribute list) list |
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-> theory -> theory * thm list |
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end; |
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structure PrimrecPackage : PRIMREC_PACKAGE = |
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struct |
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open DatatypeAux; |
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||
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exception RecError of string; |
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fun primrec_err s = error ("Primrec definition error:\n" ^ s); |
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fun primrec_eq_err sign s eq = |
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primrec_err (s ^ "\nin\n" ^ quote (Sign.string_of_term sign eq)); |
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(* messages *) |
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val quiet_mode = ref false; |
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fun message s = if ! quiet_mode then () else writeln s; |
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(* preprocessing of equations *) |
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fun process_eqn sign (eq, rec_fns) = |
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let |
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val (lhs, rhs) = |
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if null (term_vars eq) then |
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HOLogic.dest_eq (HOLogic.dest_Trueprop eq) |
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handle TERM _ => raise RecError "not a proper equation" |
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else raise RecError "illegal schematic variable(s)"; |
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val (recfun, args) = strip_comb lhs; |
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val (fname, _) = dest_Const recfun handle TERM _ => |
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raise RecError "function is not declared as constant in theory"; |
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val (ls', rest) = take_prefix is_Free args; |
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val (middle, rs') = take_suffix is_Free rest; |
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val rpos = length ls'; |
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val (constr, cargs') = if null middle then raise RecError "constructor missing" |
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else strip_comb (hd middle); |
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val (cname, T) = dest_Const constr |
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handle TERM _ => raise RecError "ill-formed constructor"; |
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val (tname, _) = dest_Type (body_type T) handle TYPE _ => |
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raise RecError "cannot determine datatype associated with function" |
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val (ls, cargs, rs) = (map dest_Free ls', |
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map dest_Free cargs', |
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map dest_Free rs') |
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handle TERM _ => raise RecError "illegal argument in pattern"; |
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val lfrees = ls @ rs @ cargs; |
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in |
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if not (null (duplicates lfrees)) then |
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raise RecError "repeated variable name in pattern" |
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else if not ((map dest_Free (term_frees rhs)) subset lfrees) then |
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raise RecError "extra variables on rhs" |
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else if length middle > 1 then |
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raise RecError "more than one non-variable in pattern" |
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else (case assoc (rec_fns, fname) of |
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None => |
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(fname, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns |
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| Some (_, rpos', eqns) => |
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if is_some (assoc (eqns, cname)) then |
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raise RecError "constructor already occurred as pattern" |
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else if rpos <> rpos' then |
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raise RecError "position of recursive argument inconsistent" |
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else |
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overwrite (rec_fns, |
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(fname, |
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(tname, rpos, |
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(cname, (ls, cargs, rs, rhs, eq))::eqns)))) |
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end |
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handle RecError s => primrec_eq_err sign s eq; |
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fun process_fun sign descr rec_eqns ((i, fname), (fnames, fnss)) = |
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let |
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val (_, (tname, _, constrs)) = nth_elem (i, descr); |
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(* substitute "fname ls x rs" by "y ls rs" for (x, (_, y)) in subs *) |
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fun subst [] x = x |
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| subst subs (fs, Abs (a, T, t)) = |
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let val (fs', t') = subst subs (fs, t) |
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in (fs', Abs (a, T, t')) end |
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| subst subs (fs, t as (_ $ _)) = |
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let val (f, ts) = strip_comb t; |
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in |
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if is_Const f andalso (fst (dest_Const f)) mem (map fst rec_eqns) then |
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let |
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val (fname', _) = dest_Const f; |
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val (_, rpos, _) = the (assoc (rec_eqns, fname')); |
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val ls = take (rpos, ts); |
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val rest = drop (rpos, ts); |
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val (x', rs) = (hd rest, tl rest) |
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handle LIST _ => raise RecError ("not enough arguments\ |
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\ in recursive application\nof function " ^ quote fname' ^ " on rhs"); |
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val (x, xs) = strip_comb x' |
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in |
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(case assoc (subs, x) of |
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None => |
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let |
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val (fs', ts') = foldl_map (subst subs) (fs, ts) |
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in (fs', list_comb (f, ts')) end |
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| Some (i', y) => |
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let |
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val (fs', ts') = foldl_map (subst subs) (fs, xs @ ls @ rs); |
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val fs'' = process_fun sign descr rec_eqns ((i', fname'), fs') |
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in (fs'', list_comb (y, ts')) |
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end) |
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end |
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else |
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let |
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val (fs', f'::ts') = foldl_map (subst subs) (fs, f::ts) |
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in (fs', list_comb (f', ts')) end |
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end |
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| subst _ x = x; |
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(* translate rec equations into function arguments suitable for rec comb *) |
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fun trans eqns ((cname, cargs), (fnames', fnss', fns)) = |
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(case assoc (eqns, cname) of |
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None => (warning ("no equation for constructor " ^ quote cname ^ |
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"\nin definition of function " ^ quote fname); |
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(fnames', fnss', (Const ("arbitrary", dummyT))::fns)) |
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| Some (ls, cargs', rs, rhs, eq) => |
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let |
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fun rec_index (DtRec k) = k |
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| rec_index (DtType ("fun", [_, DtRec k])) = k; |
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val recs = filter (is_rec_type o snd) (cargs' ~~ cargs); |
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val rargs = map fst recs; |
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val subs = map (rpair dummyT o fst) |
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(rev (rename_wrt_term rhs rargs)); |
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val ((fnames'', fnss''), rhs') = |
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(subst (map (fn ((x, y), z) => |
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(Free x, (rec_index y, Free z))) |
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(recs ~~ subs)) |
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((fnames', fnss'), rhs)) |
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handle RecError s => primrec_eq_err sign s eq |
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in (fnames'', fnss'', |
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(list_abs_free (cargs' @ subs @ ls @ rs, rhs'))::fns) |
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end) |
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in (case assoc (fnames, i) of |
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None => |
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if exists (equal fname o snd) fnames then |
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raise RecError ("inconsistent functions for datatype " ^ quote tname) |
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else |
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let |
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val (_, _, eqns) = the (assoc (rec_eqns, fname)); |
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val (fnames', fnss', fns) = foldr (trans eqns) |
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(constrs, ((i, fname)::fnames, fnss, [])) |
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in |
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(fnames', (i, (fname, #1 (snd (hd eqns)), fns))::fnss') |
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end |
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| Some fname' => |
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if fname = fname' then (fnames, fnss) |
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else raise RecError ("inconsistent functions for datatype " ^ quote tname)) |
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end; |
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(* prepare functions needed for definitions *) |
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fun get_fns fns (((i, (tname, _, constrs)), rec_name), (fs, defs)) = |
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case assoc (fns, i) of |
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None => |
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let |
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val dummy_fns = map (fn (_, cargs) => Const ("arbitrary", |
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replicate ((length cargs) + (length (filter is_rec_type cargs))) |
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dummyT ---> HOLogic.unitT)) constrs; |
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val _ = warning ("No function definition for datatype " ^ quote tname) |
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in |
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(dummy_fns @ fs, defs) |
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end |
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| Some (fname, ls, fs') => (fs' @ fs, (fname, ls, rec_name, tname)::defs); |
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(* make definition *) |
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fun make_def sign fs (fname, ls, rec_name, tname) = |
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let |
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val rhs = foldr (fn (T, t) => Abs ("", T, t)) |
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((map snd ls) @ [dummyT], |
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list_comb (Const (rec_name, dummyT), |
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fs @ map Bound (0 ::(length ls downto 1)))); |
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val defpair = (Sign.base_name fname ^ "_" ^ Sign.base_name tname ^ "_def", |
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Logic.mk_equals (Const (fname, dummyT), rhs)) |
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in Theory.inferT_axm sign defpair end; |
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(* find datatypes which contain all datatypes in tnames' *) |
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fun find_dts (dt_info : datatype_info Symtab.table) _ [] = [] |
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| find_dts dt_info tnames' (tname::tnames) = |
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(case Symtab.lookup (dt_info, tname) of |
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None => primrec_err (quote tname ^ " is not a datatype") |
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| Some dt => |
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if tnames' subset (map (#1 o snd) (#descr dt)) then |
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(tname, dt)::(find_dts dt_info tnames' tnames) |
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else find_dts dt_info tnames' tnames); |
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fun add_primrec_i alt_name eqns_atts thy = |
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let |
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val (eqns, atts) = split_list eqns_atts; |
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val sg = Theory.sign_of thy; |
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val dt_info = DatatypePackage.get_datatypes thy; |
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val rec_eqns = foldr (process_eqn sg) (map snd eqns, []); |
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val tnames = distinct (map (#1 o snd) rec_eqns); |
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val dts = find_dts dt_info tnames tnames; |
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val main_fns = |
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map (fn (tname, {index, ...}) => |
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(index, |
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fst (the (find_first (fn f => #1 (snd f) = tname) rec_eqns)))) |
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dts; |
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val {descr, rec_names, rec_rewrites, ...} = |
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if null dts then |
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primrec_err ("datatypes " ^ commas_quote tnames ^ |
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"\nare not mutually recursive") |
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else snd (hd dts); |
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val (fnames, fnss) = foldr (process_fun sg descr rec_eqns) |
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(main_fns, ([], [])); |
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val (fs, defs) = foldr (get_fns fnss) (descr ~~ rec_names, ([], [])); |
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val defs' = map (make_def sg fs) defs; |
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val names1 = map snd fnames; |
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val names2 = map fst rec_eqns; |
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val thy' = thy |> |
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Theory.add_path (if alt_name = "" then (space_implode "_" |
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(map (Sign.base_name o #1) defs)) else alt_name) |> |
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(if eq_set (names1, names2) then Theory.add_defs_i defs' |
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else primrec_err ("functions " ^ commas_quote names2 ^ |
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"\nare not mutually recursive")); |
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changeset
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247 |
val rewrites = o_def :: (map mk_meta_eq rec_rewrites) @ (map (get_axiom thy' o fst) defs'); |
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val _ = message ("Proving equations for primrec function(s) " ^ commas_quote names1 ^ " ..."); |
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val char_thms = map (fn (_, t) => prove_goalw_cterm rewrites (cterm_of (Theory.sign_of thy') t) |
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(fn _ => [rtac refl 1])) eqns; |
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val simps = char_thms; |
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val thy'' = |
253 |
thy' |
|
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|> PureThy.add_thmss [(("simps", simps), [Simplifier.simp_add_global])] |
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|> PureThy.add_thms ((map fst eqns ~~ simps) ~~ atts) |
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|> Theory.parent_path; |
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257 |
in (thy'', char_thms) end; |
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fun add_primrec alt_name eqns thy = |
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261 |
let |
7544
dee529666dcd
Fixed bug in add_primrec which caused non-informative error message.
berghofe
parents:
7152
diff
changeset
|
262 |
val sign = Theory.sign_of thy; |
7016
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- Now also supports arbitrarily branching datatypes.
berghofe
parents:
6729
diff
changeset
|
263 |
val ((names, strings), srcss) = apfst split_list (split_list eqns); |
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|
264 |
val atts = map (map (Attrib.global_attribute thy)) srcss; |
7544
dee529666dcd
Fixed bug in add_primrec which caused non-informative error message.
berghofe
parents:
7152
diff
changeset
|
265 |
val eqn_ts = map (readtm sign propT) strings; |
7016
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- Now also supports arbitrarily branching datatypes.
berghofe
parents:
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diff
changeset
|
266 |
val rec_ts = map (fn eq => head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop eq))) |
7544
dee529666dcd
Fixed bug in add_primrec which caused non-informative error message.
berghofe
parents:
7152
diff
changeset
|
267 |
handle TERM _ => primrec_eq_err sign "not a proper equation" eq) eqn_ts; |
7016
df54b5365477
- Now also supports arbitrarily branching datatypes.
berghofe
parents:
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changeset
|
268 |
val (_, eqn_ts') = InductivePackage.unify_consts (sign_of thy) rec_ts eqn_ts |
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|
269 |
in |
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- Now also supports arbitrarily branching datatypes.
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|
270 |
add_primrec_i alt_name (names ~~ eqn_ts' ~~ atts) thy |
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- Now also supports arbitrarily branching datatypes.
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parents:
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|
271 |
end; |
6359 | 272 |
|
5178 | 273 |
|
6359 | 274 |
(* outer syntax *) |
275 |
||
6723 | 276 |
local structure P = OuterParse and K = OuterSyntax.Keyword in |
6359 | 277 |
|
278 |
val primrec_decl = |
|
6723 | 279 |
Scan.optional (P.$$$ "(" |-- P.name --| P.$$$ ")") "" -- |
7152 | 280 |
Scan.repeat1 (P.opt_thm_name ":" -- P.prop --| P.marg_comment); |
6359 | 281 |
|
282 |
val primrecP = |
|
6723 | 283 |
OuterSyntax.command "primrec" "define primitive recursive functions on datatypes" K.thy_decl |
6359 | 284 |
(primrec_decl >> (fn (alt_name, eqns) => |
6723 | 285 |
Toplevel.theory (#1 o add_primrec alt_name (map P.triple_swap eqns)))); |
6359 | 286 |
|
287 |
val _ = OuterSyntax.add_parsers [primrecP]; |
|
5178 | 288 |
|
289 |
end; |
|
6384 | 290 |
|
291 |
||
292 |
end; |