# HG changeset patch # User berghofe # Date 1164625851 -3600 # Node ID ea881fbe0489521914341bde24d159673b9fcdde # Parent f3faed8276e62e778697feb4cb09aa246eb9c81f Implemented new "nominal_primrec" command for defining functions on nominal datatypes. diff -r f3faed8276e6 -r ea881fbe0489 src/HOL/Nominal/Nominal.thy --- a/src/HOL/Nominal/Nominal.thy Mon Nov 27 12:09:55 2006 +0100 +++ b/src/HOL/Nominal/Nominal.thy Mon Nov 27 12:10:51 2006 +0100 @@ -7,6 +7,7 @@ ("nominal_package.ML") ("nominal_induct.ML") ("nominal_permeq.ML") + ("nominal_primrec.ML") begin section {* Permutations *} @@ -3009,6 +3010,10 @@ use "nominal_permeq.ML"; use "nominal_package.ML" setup "NominalAtoms.setup" +setup "NominalPackage.setup" + +(** primitive recursive functions on nominal datatypes **) +use "nominal_primrec.ML" (*****************************************) (* setup for induction principles method *) diff -r f3faed8276e6 -r ea881fbe0489 src/HOL/Nominal/nominal_primrec.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Nominal/nominal_primrec.ML Mon Nov 27 12:10:51 2006 +0100 @@ -0,0 +1,445 @@ +(* Title: HOL/Nominal/nominal_primrec.ML + ID: $Id$ + Author: Stefan Berghofer, TU Muenchen and Norbert Voelker, FernUni Hagen + +Package for defining functions on nominal datatypes by primitive recursion. +Taken from HOL/Tools/primrec_package.ML +*) + +signature NOMINAL_PRIMREC = +sig + val quiet_mode: bool ref + val add_primrec: string -> string list option -> string option -> + ((bstring * string) * Attrib.src list) list -> theory -> Proof.state + val add_primrec_unchecked: string -> string list option -> string option -> + ((bstring * string) * Attrib.src list) list -> theory -> Proof.state + val add_primrec_i: string -> term list option -> term option -> + ((bstring * term) * attribute list) list -> theory -> Proof.state + val add_primrec_unchecked_i: string -> term list option -> term option -> + ((bstring * term) * attribute list) list -> theory -> Proof.state +end; + +structure NominalPrimrec : NOMINAL_PRIMREC = +struct + +open DatatypeAux; + +exception RecError of string; + +fun primrec_err s = error ("Nominal primrec definition error:\n" ^ s); +fun primrec_eq_err thy s eq = + primrec_err (s ^ "\nin\n" ^ quote (Sign.string_of_term thy eq)); + + +(* messages *) + +val quiet_mode = ref false; +fun message s = if ! quiet_mode then () else writeln s; + + +(* preprocessing of equations *) + +fun process_eqn thy eq rec_fns = + let + val (lhs, rhs) = + if null (term_vars eq) then + HOLogic.dest_eq (HOLogic.dest_Trueprop (Logic.strip_imp_concl eq)) + handle TERM _ => raise RecError "not a proper equation" + else raise RecError "illegal schematic variable(s)"; + + val (recfun, args) = strip_comb lhs; + val fnameT = dest_Const recfun handle TERM _ => + raise RecError "function is not declared as constant in theory"; + + 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 raise RecError "constructor missing" + else strip_comb (hd middle); + val (cname, T) = dest_Const constr + handle TERM _ => raise RecError "ill-formed constructor"; + val (tname, _) = dest_Type (body_type T) handle TYPE _ => + raise RecError "cannot determine datatype associated with function" + + val (ls, cargs, rs) = + (map dest_Free ls', map dest_Free cargs', map dest_Free rs') + handle TERM _ => raise RecError "illegal argument in pattern"; + val lfrees = ls @ rs @ cargs; + + fun check_vars _ [] = () + | check_vars s vars = raise RecError (s ^ commas_quote (map fst vars)) + in + if length middle > 1 then + raise RecError "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) \\ lfrees); + case AList.lookup (op =) rec_fns fnameT of + NONE => + (fnameT, (tname, rpos, [(cname, (ls, cargs, rs, rhs, eq))]))::rec_fns + | SOME (_, rpos', eqns) => + if AList.defined (op =) eqns cname then + raise RecError "constructor already occurred as pattern" + else if rpos <> rpos' then + raise RecError "position of recursive argument inconsistent" + else + AList.update (op =) (fnameT, (tname, rpos, (cname, (ls, cargs, rs, rhs, eq))::eqns)) + rec_fns) + end + handle RecError s => primrec_eq_err thy s eq; + +val param_err = "Parameters must be the same for all recursive functions"; + +fun process_fun thy descr rec_eqns (i, fnameT as (fname, _)) (fnameTs, fnss) = + let + val (_, (tname, _, constrs)) = List.nth (descr, i); + + (* substitute "fname ls x rs" by "y" 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_Const f andalso dest_Const f mem map fst rec_eqns then + let + val fnameT' as (fname', _) = dest_Const f; + val (_, rpos, eqns) = the (AList.lookup (op =) rec_eqns fnameT'); + val ls = Library.take (rpos, ts); + val rest = Library.drop (rpos, ts); + val (x', rs) = (hd rest, tl rest) + handle Empty => raise RecError ("not enough arguments\ + \ in recursive application\nof function " ^ quote fname' ^ " on rhs"); + val _ = (case eqns of + (_, (ls', _, rs', _, _)) :: _ => + if ls = map Free ls' andalso rs = map Free rs' then () + else raise RecError param_err + | _ => ()); + 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 + ||> process_fun thy descr rec_eqns (i', fnameT') + |-> (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) (fnameTs', fnss', fns) = + (case AList.lookup (op =) eqns cname of + NONE => (warning ("No equation for constructor " ^ quote cname ^ + "\nin definition of function " ^ quote fname); + (fnameTs', fnss', (Const ("arbitrary", 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', (fnameTs'', fnss'')) = + (subst (map (fn ((x, y), z) => + (Free x, (body_index y, Free z))) + (recs ~~ subs)) rhs (fnameTs', fnss')) + handle RecError s => primrec_eq_err thy s eq + in (fnameTs'', fnss'', + (list_abs_free (cargs' @ subs, rhs'))::fns) + end) + + in (case AList.lookup (op =) fnameTs i of + NONE => + if exists (equal fnameT o snd) fnameTs then + raise RecError ("inconsistent functions for datatype " ^ quote tname) + else + let + val SOME (_, _, eqns as (_, (ls, _, rs, _, _)) :: _) = + AList.lookup (op =) rec_eqns fnameT; + val (fnameTs', fnss', fns) = fold_rev (trans eqns) constrs + ((i, fnameT)::fnameTs, fnss, []) + in + (fnameTs', (i, (fname, ls, rs, fns))::fnss') + end + | SOME fnameT' => + if fnameT = fnameT' then (fnameTs, fnss) + else raise RecError ("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 ("arbitrary", + 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, rs, fs') => (fs' @ fs, (fname, ls, rs, rec_name, tname) :: defs); + + +(* make definition *) + +fun make_def thy fs (fname, ls, rs, rec_name, tname) = + let + val used = map fst (fold Term.add_frees fs []); + val x = (Name.variant used "x", dummyT); + val frees = ls @ x :: rs; + val rhs = list_abs_free (frees, + list_comb (Const (rec_name, dummyT), fs @ [Free x])) + val defpair = (Sign.base_name fname ^ "_" ^ Sign.base_name tname ^ "_def", + Logic.mk_equals (Const (fname, dummyT), rhs)); + val defpair' as (_, _ $ _ $ t) = Theory.inferT_axm thy defpair + in (defpair', subst_bounds (rev (map Free frees), strip_abs_body t)) end; + + +(* find datatypes which contain all datatypes in tnames' *) + +fun find_dts (dt_info : NominalPackage.nominal_datatype_info Symtab.table) _ [] = [] + | find_dts dt_info tnames' (tname::tnames) = + (case Symtab.lookup dt_info tname of + NONE => primrec_err (quote tname ^ " is not a nominal 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); + +fun common_prefix eq ([], _) = [] + | common_prefix eq (_, []) = [] + | common_prefix eq (x :: xs, y :: ys) = + if eq (x, y) then x :: common_prefix eq (xs, ys) else []; + +local + +fun gen_primrec_i note def alt_name invs fctxt eqns_atts thy = + let + val (eqns, atts) = split_list eqns_atts; + val dt_info = NominalPackage.get_nominal_datatypes thy; + val rec_eqns = fold_rev (process_eqn thy o snd) eqns []; + val lsrs :: lsrss = maps (fn (_, (_, _, eqns)) => + map (fn (_, (ls, _, rs, _, _)) => ls @ rs) eqns) rec_eqns + val _ = + (if forall (curry eq_set lsrs) lsrss andalso forall + (fn (_, (_, _, (_, (ls, _, rs, _, _)) :: eqns)) => + forall (fn (_, (ls', _, rs', _, _)) => + ls = ls' andalso rs = rs') eqns + | _ => true) rec_eqns + then () else raise RecError param_err); + val tnames = distinct (op =) (map (#1 o snd) rec_eqns); + val dts = find_dts dt_info tnames tnames; + val main_fns = + map (fn (tname, {index, ...}) => + (index, + (fst o the o find_first (fn f => (#1 o snd) f = tname)) rec_eqns)) + dts; + val {descr, rec_names, rec_rewrites, ...} = + if null dts then + primrec_err ("datatypes " ^ commas_quote tnames ^ "\nare not mutually recursive") + else snd (hd dts); + val (fnameTs, fnss) = + fold_rev (process_fun thy descr rec_eqns) main_fns ([], []); + val (fs, defs) = fold_rev (get_fns fnss) (descr ~~ rec_names) ([], []); + val defs' = map (make_def thy fs) defs; + val nameTs1 = map snd fnameTs; + val nameTs2 = map fst rec_eqns; + val _ = if gen_eq_set (op =) (nameTs1, nameTs2) then () + else primrec_err ("functions " ^ commas_quote (map fst nameTs2) ^ + "\nare not mutually recursive"); + val primrec_name = + if alt_name = "" then (space_implode "_" (map (Sign.base_name o #1) defs)) else alt_name; + val (defs_thms', thy') = + thy + |> Theory.add_path primrec_name + |> fold_map def (map (fn ((name, t), _) => ((name, []), t)) defs'); + val cert = cterm_of thy'; + + fun mk_idx eq = + let + val Const c = head_of (fst (HOLogic.dest_eq (HOLogic.dest_Trueprop + (Logic.strip_imp_concl eq)))); + val SOME i = AList.lookup op = (map swap fnameTs) c; + val SOME (_, _, constrs) = AList.lookup op = descr i; + val SOME (_, _, eqns) = AList.lookup op = rec_eqns c; + val SOME (cname, (_, cargs, _, _, _)) = find_first + (fn (_, (_, _, _, _, eq')) => eq = eq') eqns + in (i, find_index (fn (cname', _) => cname = cname') constrs, cargs) end; + + val rec_rewritess = + unflat (map (fn (_, (_, _, constrs)) => constrs) descr) rec_rewrites; + val fvars = rec_rewrites |> hd |> concl_of |> HOLogic.dest_Trueprop |> + HOLogic.dest_eq |> fst |> strip_comb |> snd |> take_prefix is_Var |> fst; + val (pvars, ctxtvars) = List.partition + (equal HOLogic.boolT o body_type o snd) + (fold Term.add_vars (map Logic.strip_assums_concl + (prems_of (hd rec_rewrites))) [] \\ map dest_Var fvars); + val cfs = defs' |> hd |> snd |> strip_comb |> snd |> + curry (List.take o swap) (length fvars) |> map cert; + val invs' = (case invs of + NONE => map (fn (i, _) => + let + val SOME (_, T) = AList.lookup op = fnameTs i + val (Ts, U) = strip_type T + in + Abs ("x", List.drop (Ts, length lsrs + 1) ---> U, HOLogic.true_const) + end) descr + | SOME invs' => invs'); + val inst = (map cert fvars ~~ cfs) @ + (map (cert o Var) pvars ~~ map cert invs') @ + (case ctxtvars of + [ctxtvar] => [(cert (Var ctxtvar), cert (the_default HOLogic.unit fctxt))] + | _ => []); + val rec_rewrites' = map (fn (_, eq) => + let + val (i, j, cargs) = mk_idx eq + val th = nth (nth rec_rewritess i) j; + val cargs' = th |> concl_of |> HOLogic.dest_Trueprop |> + HOLogic.dest_eq |> fst |> strip_comb |> snd |> split_last |> snd |> + strip_comb |> snd + in (cargs, Logic.strip_imp_prems eq, + Drule.cterm_instantiate (inst @ + (map (cterm_of thy') cargs' ~~ map (cterm_of thy' o Free) cargs)) th) + end) eqns; + + val prems = foldr1 (common_prefix op aconv) (map (prems_of o #3) rec_rewrites'); + val cprems = map cert prems; + val asms = map Thm.assume cprems; + val premss = map (fn (cargs, eprems, eqn) => + map (fn t => list_all_free (cargs, Logic.list_implies (eprems, t))) + (List.drop (prems_of eqn, length prems))) rec_rewrites'; + val cpremss = map (map cert) premss; + val asmss = map (map Thm.assume) cpremss; + + fun mk_eqn ((cargs, eprems, eqn), asms') = + let + val ceprems = map cert eprems; + val asms'' = map Thm.assume ceprems; + val ccargs = map (cert o Free) cargs; + val asms''' = map (fn th => implies_elim_list + (forall_elim_list ccargs th) asms'') asms' + in + implies_elim_list eqn (asms @ asms''') |> + implies_intr_list ceprems |> + forall_intr_list ccargs + end; + + val rule_prems = cprems @ flat cpremss; + val rule = implies_intr_list rule_prems + (foldr1 (uncurry Conjunction.intr) (map mk_eqn (rec_rewrites' ~~ asmss))); + + val goals = map (fn ((cargs, _, _), (_, eqn)) => + (list_all_free (cargs, eqn), [])) (rec_rewrites' ~~ eqns); + + in + thy' |> + ProofContext.init |> + Proof.theorem_i NONE + (fn thss => ProofContext.theory (fn thy => + let + val simps = flat thss; + val (simps', thy') = + fold_map note ((map fst eqns ~~ atts) ~~ map single simps) thy; + val simps'' = maps snd simps' + in + thy' + |> note (("simps", [Simplifier.simp_add]), simps'') + |> snd + |> Theory.parent_path + end)) + [goals] |> + Proof.apply (Method.Basic (fn ctxt => Method.RAW_METHOD (fn ths => + rewrite_goals_tac (map snd defs_thms') THEN + compose_tac (false, rule, length rule_prems) 1))) |> + Seq.hd + end; + +fun gen_primrec note def alt_name invs fctxt eqns thy = + let + fun readt T s = term_of (Thm.read_cterm thy (s, T)); + val ((names, strings), srcss) = apfst split_list (split_list eqns); + val atts = map (map (Attrib.attribute thy)) srcss; + val eqn_ts = map (fn s => readt propT s + handle ERROR msg => cat_error msg ("The error(s) above occurred for " ^ s)) strings; + val rec_ts = map (fn eq => head_of (fst (HOLogic.dest_eq + (HOLogic.dest_Trueprop (Logic.strip_imp_concl eq)))) + handle TERM _ => primrec_eq_err thy "not a proper equation" eq) eqn_ts; + val (_, eqn_ts') = OldInductivePackage.unify_consts thy rec_ts eqn_ts + in + gen_primrec_i note def alt_name + (Option.map (map (readt TypeInfer.logicT)) invs) + (Option.map (readt TypeInfer.logicT) fctxt) + (names ~~ eqn_ts' ~~ atts) thy + end; + +fun thy_note ((name, atts), thms) = + PureThy.add_thmss [((name, thms), atts)] #-> (fn [thms] => pair (name, thms)); +fun thy_def false ((name, atts), t) = + PureThy.add_defs_i false [((name, t), atts)] #-> (fn [thm] => pair (name, thm)) + | thy_def true ((name, atts), t) = + PureThy.add_defs_unchecked_i false [((name, t), atts)] #-> (fn [thm] => pair (name, thm)); + +in + +val add_primrec = gen_primrec thy_note (thy_def false); +val add_primrec_unchecked = gen_primrec thy_note (thy_def true); +val add_primrec_i = gen_primrec_i thy_note (thy_def false); +val add_primrec_unchecked_i = gen_primrec_i thy_note (thy_def true); + +end; (*local*) + + +(* outer syntax *) + +local structure P = OuterParse and K = OuterKeyword in + +val parser1 = P.$$$ "freshness_context" |-- P.$$$ ":" |-- (P.term >> SOME); +val parser2 = + P.$$$ "invariant" |-- P.$$$ ":" |-- + (Scan.repeat1 P.term >> SOME) -- Scan.optional parser1 NONE || + (parser1 >> pair NONE); +val parser3 = + P.name -- Scan.optional parser2 (NONE, NONE) || + (parser2 >> pair ""); +val parser4 = + (P.$$$ "unchecked" >> K true) -- Scan.optional parser3 ("", (NONE, NONE)) || + (parser3 >> pair false); +val options = + Scan.optional (P.$$$ "(" |-- P.!!! + (parser4 --| P.$$$ ")")) (false, ("", (NONE, NONE))); + +val primrec_decl = + options -- Scan.repeat1 (P.opt_thm_name ":" -- P.prop); + +val primrecP = + OuterSyntax.command "nominal_primrec" "define primitive recursive functions on nominal datatypes" K.thy_goal + (primrec_decl >> (fn ((unchecked, (alt_name, (invs, fctxt))), eqns) => + Toplevel.theory_to_proof + ((if unchecked then add_primrec_unchecked else add_primrec) alt_name invs fctxt + (map P.triple_swap eqns)))); + +val _ = OuterSyntax.add_parsers [primrecP]; +val _ = OuterSyntax.add_keywords ["invariant", "freshness_context"]; + +end; + + +end; +