src/HOLCF/Tools/fixrec.ML
author huffman
Mon Nov 02 18:39:41 2009 -0800 (2009-11-02)
changeset 33401 fc43fa403a69
parent 33004 715566791eb0
child 33425 7e4f3c66190d
permissions -rw-r--r--
add fixrec support for HOL pair constructor patterns
     1 (*  Title:      HOLCF/Tools/fixrec.ML
     2     Author:     Amber Telfer and Brian Huffman
     3 
     4 Recursive function definition package for HOLCF.
     5 *)
     6 
     7 signature FIXREC =
     8 sig
     9   val add_fixrec: bool -> (binding * typ option * mixfix) list
    10     -> (Attrib.binding * term) list -> local_theory -> local_theory
    11   val add_fixrec_cmd: bool -> (binding * string option * mixfix) list
    12     -> (Attrib.binding * string) list -> local_theory -> local_theory
    13   val add_fixpat: Thm.binding * term list -> theory -> theory
    14   val add_fixpat_cmd: Attrib.binding * string list -> theory -> theory
    15   val add_matchers: (string * string) list -> theory -> theory
    16   val setup: theory -> theory
    17 end;
    18 
    19 structure Fixrec :> FIXREC =
    20 struct
    21 
    22 val def_cont_fix_eq = @{thm def_cont_fix_eq};
    23 val def_cont_fix_ind = @{thm def_cont_fix_ind};
    24 
    25 
    26 fun fixrec_err s = error ("fixrec definition error:\n" ^ s);
    27 fun fixrec_eq_err thy s eq =
    28   fixrec_err (s ^ "\nin\n" ^ quote (Syntax.string_of_term_global thy eq));
    29 
    30 (*************************************************************************)
    31 (***************************** building types ****************************)
    32 (*************************************************************************)
    33 
    34 (* ->> is taken from holcf_logic.ML *)
    35 fun cfunT (T, U) = Type(@{type_name "->"}, [T, U]);
    36 
    37 infixr 6 ->>; val (op ->>) = cfunT;
    38 
    39 fun dest_cfunT (Type(@{type_name "->"}, [T, U])) = (T, U)
    40   | dest_cfunT T = raise TYPE ("dest_cfunT", [T], []);
    41 
    42 fun maybeT T = Type(@{type_name "maybe"}, [T]);
    43 
    44 fun dest_maybeT (Type(@{type_name "maybe"}, [T])) = T
    45   | dest_maybeT T = raise TYPE ("dest_maybeT", [T], []);
    46 
    47 fun tupleT [] = HOLogic.unitT
    48   | tupleT [T] = T
    49   | tupleT (T :: Ts) = HOLogic.mk_prodT (T, tupleT Ts);
    50 
    51 local
    52 
    53 fun binder_cfun (Type(@{type_name "->"},[T, U])) = T :: binder_cfun U
    54   | binder_cfun (Type(@{type_name "fun"},[T, U])) = T :: binder_cfun U
    55   | binder_cfun _   =  [];
    56 
    57 fun body_cfun (Type(@{type_name "->"},[T, U])) = body_cfun U
    58   | body_cfun (Type(@{type_name "fun"},[T, U])) = body_cfun U
    59   | body_cfun T   =  T;
    60 
    61 fun strip_cfun T : typ list * typ =
    62   (binder_cfun T, body_cfun T);
    63 
    64 fun cfunsT (Ts, U) = List.foldr cfunT U Ts;
    65 
    66 in
    67 
    68 fun matchT (T, U) =
    69   body_cfun T ->> cfunsT (binder_cfun T, U) ->> U;
    70 
    71 end
    72 
    73 (*************************************************************************)
    74 (***************************** building terms ****************************)
    75 (*************************************************************************)
    76 
    77 val mk_trp = HOLogic.mk_Trueprop;
    78 
    79 (* splits a cterm into the right and lefthand sides of equality *)
    80 fun dest_eqs t = HOLogic.dest_eq (HOLogic.dest_Trueprop t);
    81 
    82 (* similar to Thm.head_of, but for continuous application *)
    83 fun chead_of (Const(@{const_name Rep_CFun},_)$f$t) = chead_of f
    84   | chead_of u = u;
    85 
    86 fun capply_const (S, T) =
    87   Const(@{const_name Rep_CFun}, (S ->> T) --> (S --> T));
    88 
    89 fun cabs_const (S, T) =
    90   Const(@{const_name Abs_CFun}, (S --> T) --> (S ->> T));
    91 
    92 fun mk_cabs t =
    93   let val T = Term.fastype_of t
    94   in cabs_const (Term.domain_type T, Term.range_type T) $ t end
    95 
    96 fun mk_capply (t, u) =
    97   let val (S, T) =
    98     case Term.fastype_of t of
    99         Type(@{type_name "->"}, [S, T]) => (S, T)
   100       | _ => raise TERM ("mk_capply " ^ ML_Syntax.print_list ML_Syntax.print_term [t, u], [t, u]);
   101   in capply_const (S, T) $ t $ u end;
   102 
   103 infix 0 ==;  val (op ==) = Logic.mk_equals;
   104 infix 1 ===; val (op ===) = HOLogic.mk_eq;
   105 infix 9 `  ; val (op `) = mk_capply;
   106 
   107 (* builds the expression (LAM v. rhs) *)
   108 fun big_lambda v rhs =
   109   cabs_const (Term.fastype_of v, Term.fastype_of rhs) $ Term.lambda v rhs;
   110 
   111 (* builds the expression (LAM v1 v2 .. vn. rhs) *)
   112 fun big_lambdas [] rhs = rhs
   113   | big_lambdas (v::vs) rhs = big_lambda v (big_lambdas vs rhs);
   114 
   115 fun mk_return t =
   116   let val T = Term.fastype_of t
   117   in Const(@{const_name Fixrec.return}, T ->> maybeT T) ` t end;
   118 
   119 fun mk_bind (t, u) =
   120   let val (T, mU) = dest_cfunT (Term.fastype_of u);
   121       val bindT = maybeT T ->> (T ->> mU) ->> mU;
   122   in Const(@{const_name Fixrec.bind}, bindT) ` t ` u end;
   123 
   124 fun mk_mplus (t, u) =
   125   let val mT = Term.fastype_of t
   126   in Const(@{const_name Fixrec.mplus}, mT ->> mT ->> mT) ` t ` u end;
   127 
   128 fun mk_run t =
   129   let val mT = Term.fastype_of t
   130       val T = dest_maybeT mT
   131   in Const(@{const_name Fixrec.run}, mT ->> T) ` t end;
   132 
   133 fun mk_fix t =
   134   let val (T, _) = dest_cfunT (Term.fastype_of t)
   135   in Const(@{const_name fix}, (T ->> T) ->> T) ` t end;
   136 
   137 fun mk_cont t =
   138   let val T = Term.fastype_of t
   139   in Const(@{const_name cont}, T --> HOLogic.boolT) $ t end;
   140 
   141 val mk_fst = HOLogic.mk_fst
   142 val mk_snd = HOLogic.mk_snd
   143 
   144 (* builds the expression (v1,v2,..,vn) *)
   145 fun mk_tuple [] = HOLogic.unit
   146 |   mk_tuple (t::[]) = t
   147 |   mk_tuple (t::ts) = HOLogic.mk_prod (t, mk_tuple ts);
   148 
   149 (* builds the expression (%(v1,v2,..,vn). rhs) *)
   150 fun lambda_tuple [] rhs = Term.lambda (Free("unit", HOLogic.unitT)) rhs
   151   | lambda_tuple (v::[]) rhs = Term.lambda v rhs
   152   | lambda_tuple (v::vs) rhs =
   153       HOLogic.mk_split (Term.lambda v (lambda_tuple vs rhs));
   154 
   155 
   156 (*************************************************************************)
   157 (************* fixed-point definitions and unfolding theorems ************)
   158 (*************************************************************************)
   159 
   160 fun add_fixdefs
   161   (fixes : ((binding * typ) * mixfix) list)
   162   (spec : (Attrib.binding * term) list)
   163   (lthy : local_theory) =
   164   let
   165     val thy = ProofContext.theory_of lthy;
   166     val names = map (Binding.name_of o fst o fst) fixes;
   167     val all_names = space_implode "_" names;
   168     val (lhss, rhss) = ListPair.unzip (map (dest_eqs o snd) spec);
   169     val functional = lambda_tuple lhss (mk_tuple rhss);
   170     val fixpoint = mk_fix (mk_cabs functional);
   171     
   172     val cont_thm =
   173       Goal.prove lthy [] [] (mk_trp (mk_cont functional))
   174         (K (simp_tac (simpset_of lthy) 1));
   175 
   176     fun one_def (l as Free(n,_)) r =
   177           let val b = Long_Name.base_name n
   178           in ((Binding.name (b^"_def"), []), r) end
   179       | one_def _ _ = fixrec_err "fixdefs: lhs not of correct form";
   180     fun defs [] _ = []
   181       | defs (l::[]) r = [one_def l r]
   182       | defs (l::ls) r = one_def l (mk_fst r) :: defs ls (mk_snd r);
   183     val fixdefs = defs lhss fixpoint;
   184     val define_all = fold_map (LocalTheory.define Thm.definitionK);
   185     val (fixdef_thms : (term * (string * thm)) list, lthy') = lthy
   186       |> define_all (map (apfst fst) fixes ~~ fixdefs);
   187     fun pair_equalI (thm1, thm2) = @{thm Pair_equalI} OF [thm1, thm2];
   188     val tuple_fixdef_thm = foldr1 pair_equalI (map (snd o snd) fixdef_thms);
   189     val P = Var (("P", 0), map Term.fastype_of lhss ---> HOLogic.boolT);
   190     val predicate = lambda_tuple lhss (list_comb (P, lhss));
   191     val tuple_induct_thm = (def_cont_fix_ind OF [tuple_fixdef_thm, cont_thm])
   192       |> Drule.instantiate' [] [SOME (Thm.cterm_of thy predicate)]
   193       |> LocalDefs.unfold lthy @{thms split_paired_all split_conv split_strict};
   194     val tuple_unfold_thm = (def_cont_fix_eq OF [tuple_fixdef_thm, cont_thm])
   195       |> LocalDefs.unfold lthy' @{thms split_conv};
   196     fun unfolds [] thm = []
   197       | unfolds (n::[]) thm = [(n^"_unfold", thm)]
   198       | unfolds (n::ns) thm = let
   199           val thmL = thm RS @{thm Pair_eqD1};
   200           val thmR = thm RS @{thm Pair_eqD2};
   201         in (n^"_unfold", thmL) :: unfolds ns thmR end;
   202     val unfold_thms = unfolds names tuple_unfold_thm;
   203     fun mk_note (n, thm) = ((Binding.name n, []), [thm]);
   204     val (thmss, lthy'') = lthy'
   205       |> fold_map (LocalTheory.note Thm.generatedK o mk_note)
   206         ((all_names ^ "_induct", tuple_induct_thm) :: unfold_thms);
   207   in
   208     (lthy'', names, fixdef_thms, map snd unfold_thms)
   209   end;
   210 
   211 (*************************************************************************)
   212 (*********** monadic notation and pattern matching compilation ***********)
   213 (*************************************************************************)
   214 
   215 structure FixrecMatchData = TheoryDataFun (
   216   type T = string Symtab.table;
   217   val empty = Symtab.empty;
   218   val copy = I;
   219   val extend = I;
   220   fun merge _ tabs : T = Symtab.merge (K true) tabs;
   221 );
   222 
   223 (* associate match functions with pattern constants *)
   224 fun add_matchers ms = FixrecMatchData.map (fold Symtab.update ms);
   225 
   226 fun taken_names (t : term) : bstring list =
   227   let
   228     fun taken (Const(a,_), bs) = insert (op =) (Long_Name.base_name a) bs
   229       | taken (Free(a,_) , bs) = insert (op =) a bs
   230       | taken (f $ u     , bs) = taken (f, taken (u, bs))
   231       | taken (Abs(a,_,t), bs) = taken (t, insert (op =) a bs)
   232       | taken (_         , bs) = bs;
   233   in
   234     taken (t, [])
   235   end;
   236 
   237 (* builds a monadic term for matching a constructor pattern *)
   238 fun pre_build match_name pat rhs vs taken =
   239   case pat of
   240     Const(@{const_name Rep_CFun},_)$f$(v as Free(n,T)) =>
   241       pre_build match_name f rhs (v::vs) taken
   242   | Const(@{const_name Rep_CFun},_)$f$x =>
   243       let val (rhs', v, taken') = pre_build match_name x rhs [] taken;
   244       in pre_build match_name f rhs' (v::vs) taken' end
   245   | f$(v as Free(n,T)) =>
   246       pre_build match_name f rhs (v::vs) taken
   247   | f$x =>
   248       let val (rhs', v, taken') = pre_build match_name x rhs [] taken;
   249       in pre_build match_name f rhs' (v::vs) taken' end
   250   | Const(c,T) =>
   251       let
   252         val n = Name.variant taken "v";
   253         fun result_type (Type(@{type_name "->"},[_,T])) (x::xs) = result_type T xs
   254           | result_type (Type (@{type_name "fun"},[_,T])) (x::xs) = result_type T xs
   255           | result_type T _ = T;
   256         val v = Free(n, result_type T vs);
   257         val m = Const(match_name c, matchT (T, fastype_of rhs));
   258         val k = big_lambdas vs rhs;
   259       in
   260         (m`v`k, v, n::taken)
   261       end
   262   | Free(n,_) => fixrec_err ("expected constructor, found free variable " ^ quote n)
   263   | _ => fixrec_err "pre_build: invalid pattern";
   264 
   265 (* builds a monadic term for matching a function definition pattern *)
   266 (* returns (name, arity, matcher) *)
   267 fun building match_name pat rhs vs taken =
   268   case pat of
   269     Const(@{const_name Rep_CFun}, _)$f$(v as Free(n,T)) =>
   270       building match_name f rhs (v::vs) taken
   271   | Const(@{const_name Rep_CFun}, _)$f$x =>
   272       let val (rhs', v, taken') = pre_build match_name x rhs [] taken;
   273       in building match_name f rhs' (v::vs) taken' end
   274   | Free(_,_) => ((pat, length vs), big_lambdas vs rhs)
   275   | Const(_,_) => ((pat, length vs), big_lambdas vs rhs)
   276   | _ => fixrec_err ("function is not declared as constant in theory: "
   277                     ^ ML_Syntax.print_term pat);
   278 
   279 fun strip_alls t =
   280   if Logic.is_all t then strip_alls (snd (Logic.dest_all t)) else t;
   281 
   282 fun match_eq match_name eq =
   283   let
   284     val (lhs,rhs) = dest_eqs (Logic.strip_imp_concl (strip_alls eq));
   285   in
   286     building match_name lhs (mk_return rhs) [] (taken_names eq)
   287   end;
   288 
   289 (* returns the sum (using +++) of the terms in ms *)
   290 (* also applies "run" to the result! *)
   291 fun fatbar arity ms =
   292   let
   293     fun LAM_Ts 0 t = ([], Term.fastype_of t)
   294       | LAM_Ts n (_ $ Abs(_,T,t)) =
   295           let val (Ts, U) = LAM_Ts (n-1) t in (T::Ts, U) end
   296       | LAM_Ts _ _ = fixrec_err "fatbar: internal error, not enough LAMs";
   297     fun unLAM 0 t = t
   298       | unLAM n (_$Abs(_,_,t)) = unLAM (n-1) t
   299       | unLAM _ _ = fixrec_err "fatbar: internal error, not enough LAMs";
   300     fun reLAM ([], U) t = t
   301       | reLAM (T::Ts, U) t = reLAM (Ts, T ->> U) (cabs_const(T,U)$Abs("",T,t));
   302     val msum = foldr1 mk_mplus (map (unLAM arity) ms);
   303     val (Ts, U) = LAM_Ts arity (hd ms)
   304   in
   305     reLAM (rev Ts, dest_maybeT U) (mk_run msum)
   306   end;
   307 
   308 (* this is the pattern-matching compiler function *)
   309 fun compile_pats match_name eqs =
   310   let
   311     val (((n::names),(a::arities)),mats) =
   312       apfst ListPair.unzip (ListPair.unzip (map (match_eq match_name) eqs));
   313     val cname = if forall (fn x => n=x) names then n
   314           else fixrec_err "all equations in block must define the same function";
   315     val arity = if forall (fn x => a=x) arities then a
   316           else fixrec_err "all equations in block must have the same arity";
   317     val rhs = fatbar arity mats;
   318   in
   319     mk_trp (cname === rhs)
   320   end;
   321 
   322 (*************************************************************************)
   323 (********************** Proving associated theorems **********************)
   324 (*************************************************************************)
   325 
   326 (* proves a block of pattern matching equations as theorems, using unfold *)
   327 fun make_simps ctxt (unfold_thm, eqns : (Attrib.binding * term) list) =
   328   let
   329     val tacs =
   330       [rtac (unfold_thm RS @{thm ssubst_lhs}) 1,
   331        asm_simp_tac (simpset_of ctxt) 1];
   332     fun prove_term t = Goal.prove ctxt [] [] t (K (EVERY tacs));
   333     fun prove_eqn (bind, eqn_t) = (bind, prove_term eqn_t);
   334   in
   335     map prove_eqn eqns
   336   end;
   337 
   338 (*************************************************************************)
   339 (************************* Main fixrec function **************************)
   340 (*************************************************************************)
   341 
   342 local
   343 (* code adapted from HOL/Tools/primrec.ML *)
   344 
   345 fun gen_fixrec
   346   (set_group : bool)
   347   prep_spec
   348   (strict : bool)
   349   raw_fixes
   350   raw_spec
   351   (lthy : local_theory) =
   352   let
   353     val (fixes : ((binding * typ) * mixfix) list,
   354          spec : (Attrib.binding * term) list) =
   355           fst (prep_spec raw_fixes raw_spec lthy);
   356     val chead_of_spec =
   357       chead_of o fst o dest_eqs o Logic.strip_imp_concl o strip_alls o snd;
   358     fun name_of (Free (n, _)) = n
   359       | name_of t = fixrec_err ("unknown term");
   360     val all_names = map (name_of o chead_of_spec) spec;
   361     val names = distinct (op =) all_names;
   362     fun block_of_name n =
   363       map_filter
   364         (fn (m,eq) => if m = n then SOME eq else NONE)
   365         (all_names ~~ spec);
   366     val blocks = map block_of_name names;
   367 
   368     val matcher_tab = FixrecMatchData.get (ProofContext.theory_of lthy);
   369     fun match_name c =
   370       case Symtab.lookup matcher_tab c of SOME m => m
   371         | NONE => fixrec_err ("unknown pattern constructor: " ^ c);
   372 
   373     val matches = map (compile_pats match_name) (map (map snd) blocks);
   374     val spec' = map (pair Attrib.empty_binding) matches;
   375     val (lthy', cnames, fixdef_thms, unfold_thms) =
   376       add_fixdefs fixes spec' lthy;
   377   in
   378     if strict then let (* only prove simp rules if strict = true *)
   379       val simps : (Attrib.binding * thm) list list =
   380         map (make_simps lthy') (unfold_thms ~~ blocks);
   381       fun mk_bind n : Attrib.binding =
   382        (Binding.name (n ^ "_simps"),
   383          [Attrib.internal (K Simplifier.simp_add)]);
   384       val simps1 : (Attrib.binding * thm list) list =
   385         map (fn (n,xs) => (mk_bind n, map snd xs)) (names ~~ simps);
   386       val simps2 : (Attrib.binding * thm list) list =
   387         map (apsnd (fn thm => [thm])) (flat simps);
   388       val (_, lthy'') = lthy'
   389         |> fold_map (LocalTheory.note Thm.generatedK) (simps1 @ simps2);
   390     in
   391       lthy''
   392     end
   393     else lthy'
   394   end;
   395 
   396 in
   397 
   398 val add_fixrec = gen_fixrec false Specification.check_spec;
   399 val add_fixrec_cmd = gen_fixrec true Specification.read_spec;
   400 
   401 end; (* local *)
   402 
   403 (*************************************************************************)
   404 (******************************** Fixpat *********************************)
   405 (*************************************************************************)
   406 
   407 fun fix_pat thy t = 
   408   let
   409     val T = fastype_of t;
   410     val eq = mk_trp (HOLogic.eq_const T $ t $ Var (("x",0),T));
   411     val cname = case chead_of t of Const(c,_) => c | _ =>
   412               fixrec_err "function is not declared as constant in theory";
   413     val unfold_thm = PureThy.get_thm thy (cname^"_unfold");
   414     val simp = Goal.prove_global thy [] [] eq
   415           (fn _ => EVERY [stac unfold_thm 1, simp_tac (global_simpset_of thy) 1]);
   416   in simp end;
   417 
   418 fun gen_add_fixpat prep_term prep_attrib ((name, srcs), strings) thy =
   419   let
   420     val atts = map (prep_attrib thy) srcs;
   421     val ts = map (prep_term thy) strings;
   422     val simps = map (fix_pat thy) ts;
   423   in
   424     (snd o PureThy.add_thmss [((name, simps), atts)]) thy
   425   end;
   426 
   427 val add_fixpat = gen_add_fixpat Sign.cert_term (K I);
   428 val add_fixpat_cmd = gen_add_fixpat Syntax.read_term_global Attrib.attribute;
   429 
   430 
   431 (*************************************************************************)
   432 (******************************** Parsers ********************************)
   433 (*************************************************************************)
   434 
   435 local structure P = OuterParse and K = OuterKeyword in
   436 
   437 val _ = OuterSyntax.local_theory "fixrec" "define recursive functions (HOLCF)" K.thy_decl
   438   ((P.opt_keyword "permissive" >> not) -- P.fixes -- SpecParse.where_alt_specs
   439     >> (fn ((strict, fixes), specs) => add_fixrec_cmd strict fixes specs));
   440 
   441 val _ = OuterSyntax.command "fixpat" "define rewrites for fixrec functions" K.thy_decl
   442   (SpecParse.specs >> (Toplevel.theory o add_fixpat_cmd));
   443   
   444 end;
   445 
   446 val setup = FixrecMatchData.init;
   447 
   448 end;