author | wenzelm |
Wed, 01 Aug 2007 16:55:40 +0200 | |
changeset 24112 | 6c4e7d17f9b0 |
parent 23765 | 997e5fe47532 |
child 24493 | d4380e9b287b |
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, TU Muenchen and Norbert Voelker, FernUni Hagen |
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|
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Package for defining functions on datatypes by primitive recursion. |
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*) |
7 |
||
8 |
signature PRIMREC_PACKAGE = |
|
9 |
sig |
|
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val quiet_mode: bool ref |
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val unify_consts: theory -> term list -> term list -> term list * term list |
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val add_primrec: string -> ((bstring * string) * Attrib.src list) list |
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-> theory -> thm list * theory |
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val add_primrec_unchecked: string -> ((bstring * string) * Attrib.src list) list |
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-> theory -> thm list * theory |
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val add_primrec_i: string -> ((bstring * term) * attribute list) list |
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-> theory -> thm list * theory |
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val add_primrec_unchecked_i: string -> ((bstring * term) * attribute list) list |
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-> theory -> thm list * theory |
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(* FIXME !? *) |
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val gen_primrec: ((bstring * attribute list) * thm list -> theory -> (bstring * thm list) * theory) |
22 |
-> ((bstring * attribute list) * term -> theory -> (bstring * thm) * theory) |
|
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-> string -> ((bstring * attribute list) * term) list |
|
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-> theory -> thm list * theory; |
|
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end; |
26 |
||
27 |
structure PrimrecPackage : PRIMREC_PACKAGE = |
|
28 |
struct |
|
29 |
||
30 |
open DatatypeAux; |
|
31 |
||
32 |
exception RecError of string; |
|
33 |
||
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fun primrec_err s = error ("Primrec definition error:\n" ^ s); |
|
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fun primrec_eq_err thy s eq = |
36 |
primrec_err (s ^ "\nin\n" ^ quote (Sign.string_of_term thy eq)); |
|
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|
38 |
||
39 |
(* messages *) |
|
40 |
||
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val quiet_mode = ref false; |
|
42 |
fun message s = if ! quiet_mode then () else writeln s; |
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|
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|
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(*the following code ensures that each recursive set always has the |
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same type in all introduction rules*) |
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fun unify_consts thy cs intr_ts = |
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(let |
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val add_term_consts_2 = fold_aterms (fn Const c => insert (op =) c | _ => I); |
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fun varify (t, (i, ts)) = |
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let val t' = map_types (Logic.incr_tvar (i + 1)) (snd (Type.varify [] t)) |
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in (maxidx_of_term t', t'::ts) end; |
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val (i, cs') = foldr varify (~1, []) cs; |
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val (i', intr_ts') = foldr varify (i, []) intr_ts; |
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val rec_consts = fold add_term_consts_2 cs' []; |
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val intr_consts = fold add_term_consts_2 intr_ts' []; |
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fun unify (cname, cT) = |
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let val consts = map snd (filter (fn (c, _) => c = cname) intr_consts) |
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in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end; |
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val (env, _) = fold unify rec_consts (Vartab.empty, i'); |
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val subst = Type.freeze o map_types (Envir.norm_type env) |
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|
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in (map subst cs', map subst intr_ts') |
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end) handle Type.TUNIFY => |
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(warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts)); |
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|
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67 |
|
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(* preprocessing of equations *) |
69 |
||
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fun process_eqn thy 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 |
74 |
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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|
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val (recfun, args) = strip_comb lhs; |
|
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val fnameT = dest_Const recfun handle TERM _ => |
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raise RecError "function is not declared as constant in theory"; |
81 |
||
82 |
val (ls', rest) = take_prefix is_Free args; |
|
83 |
val (middle, rs') = take_suffix is_Free rest; |
|
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val rpos = length ls'; |
|
85 |
||
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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" |
92 |
||
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val (ls, cargs, rs) = |
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(map dest_Free ls', map dest_Free cargs', 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; |
97 |
||
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fun check_vars _ [] = () |
99 |
| check_vars s vars = raise RecError (s ^ commas_quote (map fst vars)) |
|
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in |
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if length middle > 1 then |
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raise RecError "more than one non-variable in pattern" |
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else |
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(check_vars "repeated variable names in pattern: " (duplicates (op =) lfrees); |
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check_vars "extra variables on rhs: " |
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(map dest_Free (term_frees rhs) \\ lfrees); |
|
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case AList.lookup (op =) rec_fns fnameT of |
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NONE => |
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(fnameT, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns |
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| SOME (_, rpos', eqns) => |
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if AList.defined (op =) 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" |
|
115 |
else |
|
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AList.update (op =) (fnameT, (tname, rpos, (cname, (ls, cargs, rs, rhs, eq))::eqns)) |
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rec_fns) |
|
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end |
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handle RecError s => primrec_eq_err thy s eq; |
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|
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fun process_fun thy descr rec_eqns (i, fnameT as (fname, _)) (fnameTs, fnss) = |
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let |
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val (_, (tname, _, constrs)) = List.nth (descr, i); |
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|
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(* substitute "fname ls x rs" by "y ls rs" for (x, (_, y)) in subs *) |
|
126 |
||
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fun subst [] t fs = (t, fs) |
128 |
| subst subs (Abs (a, T, t)) fs = |
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fs |
|
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|> subst subs t |
|
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|-> (fn t' => pair (Abs (a, T, t'))) |
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| subst subs (t as (_ $ _)) fs = |
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let |
|
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val (f, ts) = strip_comb t; |
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in |
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if is_Const f andalso dest_Const f mem map fst rec_eqns then |
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let |
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val fnameT' as (fname', _) = dest_Const f; |
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val (_, rpos, _) = the (AList.lookup (op =) rec_eqns fnameT'); |
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val ls = Library.take (rpos, ts); |
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val rest = Library.drop (rpos, ts); |
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val (x', rs) = (hd rest, tl rest) |
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handle Empty => 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 case AList.lookup (op =) subs x |
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of NONE => |
|
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fs |
|
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|> fold_map (subst subs) ts |
|
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|-> (fn ts' => pair (list_comb (f, ts'))) |
|
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| SOME (i', y) => |
|
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fs |
|
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|> fold_map (subst subs) (xs @ ls @ rs) |
|
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||> process_fun thy descr rec_eqns (i', fnameT') |
|
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|-> (fn ts' => pair (list_comb (y, ts'))) |
|
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end |
157 |
else |
|
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fs |
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|> fold_map (subst subs) (f :: ts) |
|
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|-> (fn (f'::ts') => pair (list_comb (f', ts'))) |
|
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end |
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| subst _ t fs = (t, fs); |
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|
164 |
(* translate rec equations into function arguments suitable for rec comb *) |
|
165 |
||
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fun trans eqns (cname, cargs) (fnameTs', fnss', fns) = |
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(case AList.lookup (op =) 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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(fnameTs', fnss', (Const ("HOL.undefined", dummyT))::fns)) |
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| SOME (ls, cargs', rs, rhs, eq) => |
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let |
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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 (rhs', (fnameTs'', fnss'')) = |
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(subst (map (fn ((x, y), z) => |
179 |
(Free x, (body_index y, Free z))) |
|
21064 | 180 |
(recs ~~ subs)) rhs (fnameTs', fnss')) |
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handle RecError s => primrec_eq_err thy s eq |
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in (fnameTs'', fnss'', |
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(list_abs_free (cargs' @ subs @ ls @ rs, rhs'))::fns) |
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end) |
185 |
||
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in (case AList.lookup (op =) fnameTs i of |
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NONE => |
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188 |
if exists (equal fnameT o snd) fnameTs then |
6427 | 189 |
raise RecError ("inconsistent functions for datatype " ^ quote tname) |
5178 | 190 |
else |
191 |
let |
|
17184 | 192 |
val (_, _, eqns) = the (AList.lookup (op =) rec_eqns fnameT); |
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val (fnameTs', fnss', fns) = fold_rev (trans eqns) constrs |
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((i, fnameT)::fnameTs, fnss, []) |
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in |
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(fnameTs', (i, (fname, #1 (snd (hd eqns)), fns))::fnss') |
5178 | 197 |
end |
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198 |
| SOME fnameT' => |
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199 |
if fnameT = fnameT' then (fnameTs, fnss) |
6427 | 200 |
else raise RecError ("inconsistent functions for datatype " ^ quote tname)) |
5178 | 201 |
end; |
202 |
||
6359 | 203 |
|
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(* prepare functions needed for definitions *) |
205 |
||
21064 | 206 |
fun get_fns fns ((i : int, (tname, _, constrs)), rec_name) (fs, defs) = |
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case AList.lookup (op =) fns i of |
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NONE => |
5178 | 209 |
let |
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val dummy_fns = map (fn (_, cargs) => Const ("HOL.undefined", |
15570 | 211 |
replicate ((length cargs) + (length (List.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) |
5178 | 214 |
in |
215 |
(dummy_fns @ fs, defs) |
|
216 |
end |
|
21064 | 217 |
| SOME (fname, ls, fs') => (fs' @ fs, (fname, ls, rec_name, tname) :: defs); |
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|
6359 | 219 |
|
5178 | 220 |
(* make definition *) |
221 |
||
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fun make_def thy fs (fname, ls, rec_name, tname) = |
5178 | 223 |
let |
21064 | 224 |
val rhs = fold_rev (fn T => fn t => Abs ("", T, t)) |
225 |
((map snd ls) @ [dummyT]) |
|
20176 | 226 |
(list_comb (Const (rec_name, dummyT), |
227 |
fs @ map Bound (0 ::(length ls downto 1)))) |
|
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val def_name = Sign.base_name fname ^ "_" ^ Sign.base_name tname ^ "_def"; |
229 |
val def_prop = |
|
230 |
singleton (ProofContext.infer_types (ProofContext.init thy)) |
|
22728 | 231 |
(Logic.mk_equals (Const (fname, dummyT), rhs)); |
22692 | 232 |
in (def_name, def_prop) end; |
5178 | 233 |
|
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|
5178 | 235 |
(* find datatypes which contain all datatypes in tnames' *) |
236 |
||
237 |
fun find_dts (dt_info : datatype_info Symtab.table) _ [] = [] |
|
238 |
| find_dts dt_info tnames' (tname::tnames) = |
|
17412 | 239 |
(case Symtab.lookup dt_info tname of |
15531 | 240 |
NONE => primrec_err (quote tname ^ " is not a datatype") |
241 |
| SOME dt => |
|
5178 | 242 |
if tnames' subset (map (#1 o snd) (#descr dt)) then |
243 |
(tname, dt)::(find_dts dt_info tnames' tnames) |
|
244 |
else find_dts dt_info tnames' tnames); |
|
245 |
||
8432 | 246 |
fun prepare_induct ({descr, induction, ...}: datatype_info) rec_eqns = |
247 |
let |
|
248 |
fun constrs_of (_, (_, _, cs)) = |
|
249 |
map (fn (cname:string, (_, cargs, _, _, _)) => (cname, map fst cargs)) cs; |
|
17184 | 250 |
val params_of = these o AList.lookup (op =) (List.concat (map constrs_of rec_eqns)); |
8432 | 251 |
in |
252 |
induction |
|
15570 | 253 |
|> RuleCases.rename_params (map params_of (List.concat (map (map #1 o #3 o #2) descr))) |
10525 | 254 |
|> RuleCases.save induction |
8432 | 255 |
end; |
256 |
||
20841 | 257 |
local |
258 |
||
259 |
fun gen_primrec_i note def alt_name eqns_atts thy = |
|
5178 | 260 |
let |
20841 | 261 |
val (eqns, atts) = split_list eqns_atts; |
5178 | 262 |
val dt_info = DatatypePackage.get_datatypes thy; |
21064 | 263 |
val rec_eqns = fold_rev (process_eqn thy o snd) eqns [] ; |
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|
264 |
val tnames = distinct (op =) (map (#1 o snd) rec_eqns); |
5178 | 265 |
val dts = find_dts dt_info tnames tnames; |
22692 | 266 |
val main_fns = |
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diff
changeset
|
267 |
map (fn (tname, {index, ...}) => |
22692 | 268 |
(index, |
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changeset
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269 |
(fst o the o find_first (fn f => (#1 o snd) f = tname)) rec_eqns)) |
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|
270 |
dts; |
22692 | 271 |
val {descr, rec_names, rec_rewrites, ...} = |
18362
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removed thms 'swap' and 'nth_map' from ML toplevel
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|
272 |
if null dts then |
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273 |
primrec_err ("datatypes " ^ commas_quote tnames ^ "\nare not mutually recursive") |
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removed thms 'swap' and 'nth_map' from ML toplevel
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diff
changeset
|
274 |
else snd (hd dts); |
20176 | 275 |
val (fnameTs, fnss) = |
21064 | 276 |
fold_rev (process_fun thy descr rec_eqns) main_fns ([], []); |
277 |
val (fs, defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []); |
|
20176 | 278 |
val defs' = map (make_def thy fs) defs; |
16765
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Some changes to allow mutually recursive, overloaded functions with same name.
berghofe
parents:
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279 |
val nameTs1 = map snd fnameTs; |
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280 |
val nameTs2 = map fst rec_eqns; |
20841 | 281 |
val _ = if gen_eq_set (op =) (nameTs1, nameTs2) then () |
282 |
else primrec_err ("functions " ^ commas_quote (map fst nameTs2) ^ |
|
283 |
"\nare not mutually recursive"); |
|
8432 | 284 |
val primrec_name = |
285 |
if alt_name = "" then (space_implode "_" (map (Sign.base_name o #1) defs)) else alt_name; |
|
20841 | 286 |
val (defs_thms', thy') = |
287 |
thy |
|
288 |
|> Theory.add_path primrec_name |
|
289 |
|> fold_map def (map (fn (name, t) => ((name, []), t)) defs'); |
|
290 |
val rewrites = (map mk_meta_eq rec_rewrites) @ map snd defs_thms'; |
|
16765
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Some changes to allow mutually recursive, overloaded functions with same name.
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291 |
val _ = message ("Proving equations for primrec function(s) " ^ |
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Some changes to allow mutually recursive, overloaded functions with same name.
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changeset
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292 |
commas_quote (map fst nameTs1) ^ " ..."); |
20046 | 293 |
val simps = map (fn (_, t) => Goal.prove_global thy' [] [] t |
294 |
(fn _ => EVERY [rewrite_goals_tac rewrites, rtac refl 1])) eqns; |
|
20841 | 295 |
val (simps', thy'') = |
296 |
thy' |
|
297 |
|> fold_map note ((map fst eqns ~~ atts) ~~ map single simps); |
|
298 |
val simps'' = maps snd simps'; |
|
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Added new theory data slot for primrec equations.
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299 |
in |
20176 | 300 |
thy'' |
20841 | 301 |
|> note (("simps", [Simplifier.simp_add, RecfunCodegen.add NONE]), simps'') |
302 |
|> snd |
|
303 |
|> note (("induct", []), [prepare_induct (#2 (hd dts)) rec_eqns]) |
|
304 |
|> snd |
|
20176 | 305 |
|> Theory.parent_path |
20841 | 306 |
|> pair simps'' |
8480
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Added new theory data slot for primrec equations.
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changeset
|
307 |
end; |
6359 | 308 |
|
20841 | 309 |
fun gen_primrec note def alt_name eqns thy = |
7016
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- Now also supports arbitrarily branching datatypes.
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310 |
let |
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- Now also supports arbitrarily branching datatypes.
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diff
changeset
|
311 |
val ((names, strings), srcss) = apfst split_list (split_list eqns); |
18728 | 312 |
val atts = map (map (Attrib.attribute thy)) srcss; |
20176 | 313 |
val eqn_ts = map (fn s => term_of (Thm.read_cterm thy (s, propT)) |
18678 | 314 |
handle ERROR msg => cat_error msg ("The error(s) above occurred for " ^ s)) strings; |
7016
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changeset
|
315 |
val rec_ts = map (fn eq => head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop eq))) |
20176 | 316 |
handle TERM _ => primrec_eq_err thy "not a proper equation" eq) eqn_ts; |
23765
997e5fe47532
Function unify_consts moved from OldInductivePackage to PrimrecPackage.
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parents:
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diff
changeset
|
317 |
val (_, eqn_ts') = unify_consts thy rec_ts eqn_ts |
7016
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- Now also supports arbitrarily branching datatypes.
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parents:
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diff
changeset
|
318 |
in |
20841 | 319 |
gen_primrec_i note def alt_name (names ~~ eqn_ts' ~~ atts) thy |
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changeset
|
320 |
end; |
6359 | 321 |
|
20841 | 322 |
fun thy_note ((name, atts), thms) = |
323 |
PureThy.add_thmss [((name, thms), atts)] #-> (fn [thms] => pair (name, thms)); |
|
324 |
fun thy_def false ((name, atts), t) = |
|
325 |
PureThy.add_defs_i false [((name, t), atts)] #-> (fn [thm] => pair (name, thm)) |
|
326 |
| thy_def true ((name, atts), t) = |
|
327 |
PureThy.add_defs_unchecked_i false [((name, t), atts)] #-> (fn [thm] => pair (name, thm)); |
|
328 |
||
329 |
in |
|
330 |
||
331 |
val add_primrec = gen_primrec thy_note (thy_def false); |
|
332 |
val add_primrec_unchecked = gen_primrec thy_note (thy_def true); |
|
333 |
val add_primrec_i = gen_primrec_i thy_note (thy_def false); |
|
334 |
val add_primrec_unchecked_i = gen_primrec_i thy_note (thy_def true); |
|
335 |
fun gen_primrec note def alt_name specs = |
|
336 |
gen_primrec_i note def alt_name (map (fn ((name, t), atts) => ((name, atts), t)) specs); |
|
337 |
||
22692 | 338 |
end; |
19688 | 339 |
|
5178 | 340 |
|
6359 | 341 |
(* outer syntax *) |
342 |
||
17057 | 343 |
local structure P = OuterParse and K = OuterKeyword in |
6359 | 344 |
|
19688 | 345 |
val opt_unchecked_name = |
346 |
Scan.optional (P.$$$ "(" |-- P.!!! |
|
347 |
(((P.$$$ "unchecked" >> K true) -- Scan.optional P.name "" || |
|
348 |
P.name >> pair false) --| P.$$$ ")")) (false, ""); |
|
349 |
||
6359 | 350 |
val primrec_decl = |
22101 | 351 |
opt_unchecked_name -- Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop); |
6359 | 352 |
|
353 |
val primrecP = |
|
6723 | 354 |
OuterSyntax.command "primrec" "define primitive recursive functions on datatypes" K.thy_decl |
19688 | 355 |
(primrec_decl >> (fn ((unchecked, alt_name), eqns) => |
20176 | 356 |
Toplevel.theory (snd o |
19688 | 357 |
(if unchecked then add_primrec_unchecked else add_primrec) alt_name |
358 |
(map P.triple_swap eqns)))); |
|
6359 | 359 |
|
360 |
val _ = OuterSyntax.add_parsers [primrecP]; |
|
5178 | 361 |
|
362 |
end; |
|
6384 | 363 |
|
364 |
end; |