(*  Title:      HOLCF/Tools/fixrec_package.ML

    ID:         $Id$

    Author:     Amber Telfer and Brian Huffman

Recursive function definition package for HOLCF.

*)

signature FIXREC_PACKAGE =

sig

  val legacy_infer_term: theory -> term -> term

  val legacy_infer_prop: theory -> term -> term

  val add_fixrec: bool -> ((string * Attrib.src list) * string) list list -> theory -> theory

  val add_fixrec_i: bool -> ((string * attribute list) * term) list list -> theory -> theory

  val add_fixpat: (string * Attrib.src list) * string list -> theory -> theory

  val add_fixpat_i: (string * attribute list) * term list -> theory -> theory

end;

structure FixrecPackage: FIXREC_PACKAGE =

struct

(* legacy type inference *)

fun legacy_infer_term thy t =

  singleton (Syntax.check_terms (ProofContext.init thy)) (Sign.intern_term thy t);

fun legacy_infer_prop thy t = legacy_infer_term thy (TypeInfer.constrain propT t);

val fix_eq2 = thm "fix_eq2";

val def_fix_ind = thm "def_fix_ind";

fun fixrec_err s = error ("fixrec definition error:\n" ^ s);

fun fixrec_eq_err thy s eq =

  fixrec_err (s ^ "\nin\n" ^ quote (Sign.string_of_term thy eq));

(* ->> is taken from holcf_logic.ML *)

(* TODO: fix dependencies so we can import HOLCFLogic here *)

infixr 6 ->>;

fun S ->> T = Type ("Cfun.->",[S,T]);

(* extern_name is taken from domain/library.ML *)

fun extern_name con = case Symbol.explode con of 

		   ("o"::"p"::" "::rest) => implode rest

		   | _ => con;

val mk_trp = HOLogic.mk_Trueprop;

(* splits a cterm into the right and lefthand sides of equality *)

fun dest_eqs t = HOLogic.dest_eq (HOLogic.dest_Trueprop t);

(* similar to Thm.head_of, but for continuous application *)

fun chead_of (Const("Cfun.Rep_CFun",_)$f$t) = chead_of f

  | chead_of u = u;

(* these are helpful functions copied from HOLCF/domain/library.ML *)

fun %: s = Free(s,dummyT);

fun %%: s = Const(s,dummyT);

infix 0 ==;  fun S ==  T = %%:"==" $ S $ T;

infix 1 ===; fun S === T = %%:"op =" $ S $ T;

infix 9 `  ; fun f ` x = %%:"Cfun.Rep_CFun" $ f $ x;

(* builds the expression (LAM v. rhs) *)

fun big_lambda v rhs = %%:"Cfun.Abs_CFun"$(Term.lambda v rhs);

(* builds the expression (LAM v1 v2 .. vn. rhs) *)

fun big_lambdas [] rhs = rhs

  | big_lambdas (v::vs) rhs = big_lambda v (big_lambdas vs rhs);

(* builds the expression (LAM <v1,v2,..,vn>. rhs) *)

fun lambda_ctuple [] rhs = big_lambda (%:"unit") rhs

  | lambda_ctuple (v::[]) rhs = big_lambda v rhs

  | lambda_ctuple (v::vs) rhs =

      %%:"Cprod.csplit"`(big_lambda v (lambda_ctuple vs rhs));

(* builds the expression <v1,v2,..,vn> *)

fun mk_ctuple [] = %%:"UU"

|   mk_ctuple (t::[]) = t

|   mk_ctuple (t::ts) = %%:"Cprod.cpair"`t`(mk_ctuple ts);

(*************************************************************************)

(************* fixed-point definitions and unfolding theorems ************)

(*************************************************************************)

fun add_fixdefs eqs thy =

  let

    val (lhss,rhss) = ListPair.unzip (map dest_eqs eqs);

    val fixpoint = %%:"Fix.fix"`lambda_ctuple lhss (mk_ctuple rhss);

    fun one_def (l as Const(n,T)) r =

          let val b = Sign.base_name n in (b, (b^"_def", l == r)) end

      | one_def _ _ = fixrec_err "fixdefs: lhs not of correct form";

    fun defs [] _ = []

      | defs (l::[]) r = [one_def l r]

      | defs (l::ls) r = one_def l (%%:"Cprod.cfst"`r) :: defs ls (%%:"Cprod.csnd"`r);

    val (names, pre_fixdefs) = ListPair.unzip (defs lhss fixpoint);

    val fixdefs = map (apsnd (legacy_infer_prop thy)) pre_fixdefs;

    val (fixdef_thms, thy') =

      PureThy.add_defs_i false (map Thm.no_attributes fixdefs) thy;

    val ctuple_fixdef_thm = foldr1 (fn (x,y) => cpair_equalI OF [x,y]) fixdef_thms;

    val ctuple_unfold = legacy_infer_term thy' (mk_trp (mk_ctuple lhss === mk_ctuple rhss));

    val ctuple_unfold_thm = Goal.prove_global thy' [] [] ctuple_unfold

          (fn _ => EVERY [rtac (ctuple_fixdef_thm RS fix_eq2 RS trans) 1,

                    simp_tac (simpset_of thy') 1]);

    val ctuple_induct_thm =

          (space_implode "_" names ^ "_induct", ctuple_fixdef_thm RS def_fix_ind);

    fun unfolds [] thm = []

      | unfolds (n::[]) thm = [(n^"_unfold", thm)]

      | unfolds (n::ns) thm = let

          val thmL = thm RS cpair_eqD1;

          val thmR = thm RS cpair_eqD2;

        in (n^"_unfold", thmL) :: unfolds ns thmR end;

    val unfold_thms = unfolds names ctuple_unfold_thm;

    val thms = ctuple_induct_thm :: unfold_thms;

    val (_, thy'') = PureThy.add_thms (map Thm.no_attributes thms) thy';

  in

    (thy'', names, fixdef_thms, map snd unfold_thms)

  end;

(*************************************************************************)

(*********** monadic notation and pattern matching compilation ***********)

(*************************************************************************)

fun add_names (Const(a,_), bs) = insert (op =) (Sign.base_name a) bs

  | add_names (Free(a,_) , bs) = insert (op =) a bs

  | add_names (f $ u     , bs) = add_names (f, add_names(u, bs))

  | add_names (Abs(a,_,t), bs) = add_names (t, insert (op =) a bs)

  | add_names (_         , bs) = bs;

fun add_terms ts xs = foldr add_names xs ts;

(* builds a monadic term for matching a constructor pattern *)

fun pre_build pat rhs vs taken =

  case pat of

    Const("Cfun.Rep_CFun",_)$f$(v as Free(n,T)) =>

      pre_build f rhs (v::vs) taken

  | Const("Cfun.Rep_CFun",_)$f$x =>

      let val (rhs', v, taken') = pre_build x rhs [] taken;

      in pre_build f rhs' (v::vs) taken' end

  | Const(c,T) =>

      let

        val n = Name.variant taken "v";

        fun result_type (Type("Cfun.->",[_,T])) (x::xs) = result_type T xs

          | result_type T _ = T;

        val v = Free(n, result_type T vs);

        val m = "match_"^(extern_name(Sign.base_name c));

        val k = lambda_ctuple vs rhs;

      in

        (%%:"Fixrec.bind"`(%%:m`v)`k, v, n::taken)

      end

  | Free(n,_) => fixrec_err ("expected constructor, found free variable " ^ quote n)

  | _ => fixrec_err "pre_build: invalid pattern";

(* builds a monadic term for matching a function definition pattern *)

(* returns (name, arity, matcher) *)

fun building pat rhs vs taken =

  case pat of

    Const("Cfun.Rep_CFun", _)$f$(v as Free(n,T)) =>

      building f rhs (v::vs) taken

  | Const("Cfun.Rep_CFun", _)$f$x =>

      let val (rhs', v, taken') = pre_build x rhs [] taken;

      in building f rhs' (v::vs) taken' end

  | Const(name,_) => (name, length vs, big_lambdas vs rhs)

  | _ => fixrec_err "function is not declared as constant in theory";

fun match_eq eq = 

  let val (lhs,rhs) = dest_eqs eq;

  in building lhs (%%:"Fixrec.return"`rhs) [] (add_terms [eq] []) end;

(* returns the sum (using +++) of the terms in ms *)

(* also applies "run" to the result! *)

fun fatbar arity ms =

  let

    fun unLAM 0 t = t

      | unLAM n (_$Abs(_,_,t)) = unLAM (n-1) t

      | unLAM _ _ = fixrec_err "fatbar: internal error, not enough LAMs";

    fun reLAM 0 t = t

      | reLAM n t = reLAM (n-1) (%%:"Cfun.Abs_CFun" $ Abs("",dummyT,t));

    fun mplus (x,y) = %%:"Fixrec.mplus"`x`y;

    val msum = foldr1 mplus (map (unLAM arity) ms);

  in

    reLAM arity (%%:"Fixrec.run"`msum)

  end;

fun unzip3 [] = ([],[],[])

  | unzip3 ((x,y,z)::ts) =

      let val (xs,ys,zs) = unzip3 ts

      in (x::xs, y::ys, z::zs) end;

(* this is the pattern-matching compiler function *)

fun compile_pats eqs = 

  let

    val ((n::names),(a::arities),mats) = unzip3 (map match_eq eqs);

    val cname = if forall (fn x => n=x) names then n

          else fixrec_err "all equations in block must define the same function";

    val arity = if forall (fn x => a=x) arities then a

          else fixrec_err "all equations in block must have the same arity";

    val rhs = fatbar arity mats;

  in

    mk_trp (%%:cname === rhs)

  end;

(*************************************************************************)

(********************** Proving associated theorems **********************)

(*************************************************************************)

(* proves a block of pattern matching equations as theorems, using unfold *)

fun make_simps thy (unfold_thm, eqns) =

  let

    val tacs = [rtac (unfold_thm RS ssubst_lhs) 1, asm_simp_tac (simpset_of thy) 1];

    fun prove_term t = Goal.prove_global thy [] [] t (K (EVERY tacs));

    fun prove_eqn ((name, eqn_t), atts) = ((name, prove_term eqn_t), atts);

  in

    map prove_eqn eqns

  end;

(*************************************************************************)

(************************* Main fixrec function **************************)

(*************************************************************************)

fun gen_add_fixrec prep_prop prep_attrib strict blocks thy =

  let

    val eqns = List.concat blocks;

    val lengths = map length blocks;

    val ((names, srcss), strings) = apfst split_list (split_list eqns);

    val atts = map (map (prep_attrib thy)) srcss;

    val eqn_ts = map (prep_prop thy) strings;

    val rec_ts = map (fn eq => chead_of (fst (dest_eqs (Logic.strip_imp_concl eq)))

      handle TERM _ => fixrec_eq_err thy "not a proper equation" eq) eqn_ts;

    val (_, eqn_ts') = PrimrecPackage.unify_consts thy rec_ts eqn_ts;

    fun unconcat [] _ = []

      | unconcat (n::ns) xs = List.take (xs,n) :: unconcat ns (List.drop (xs,n));

    val pattern_blocks = unconcat lengths (map Logic.strip_imp_concl eqn_ts');

    val compiled_ts = map (legacy_infer_term thy o compile_pats) pattern_blocks;

    val (thy', cnames, fixdef_thms, unfold_thms) = add_fixdefs compiled_ts thy;

  in

    if strict then let (* only prove simp rules if strict = true *)

      val eqn_blocks = unconcat lengths ((names ~~ eqn_ts') ~~ atts);

      val simps = List.concat (map (make_simps thy') (unfold_thms ~~ eqn_blocks));

      val (simp_thms, thy'') = PureThy.add_thms simps thy';

      val simp_names = map (fn name => name^"_simps") cnames;

      val simp_attribute = rpair [Simplifier.simp_add];

      val simps' = map simp_attribute (simp_names ~~ unconcat lengths simp_thms);

    in

      (snd o PureThy.add_thmss simps') thy''

    end

    else thy'

  end;

val add_fixrec = gen_add_fixrec Syntax.read_prop_global Attrib.attribute;

val add_fixrec_i = gen_add_fixrec Sign.cert_prop (K I);

(*************************************************************************)

(******************************** Fixpat *********************************)

(*************************************************************************)

fun fix_pat thy t = 

  let

    val T = fastype_of t;

    val eq = mk_trp (HOLogic.eq_const T $ t $ Var (("x",0),T));

    val cname = case chead_of t of Const(c,_) => c | _ =>

              fixrec_err "function is not declared as constant in theory";

    val unfold_thm = PureThy.get_thm thy (Name (cname^"_unfold"));

    val simp = Goal.prove_global thy [] [] eq

          (fn _ => EVERY [stac unfold_thm 1, simp_tac (simpset_of thy) 1]);

  in simp end;

fun gen_add_fixpat prep_term prep_attrib ((name, srcs), strings) thy =

  let

    val atts = map (prep_attrib thy) srcs;

    val ts = map (prep_term thy) strings;

    val simps = map (fix_pat thy) ts;

  in

    (snd o PureThy.add_thmss [((name, simps), atts)]) thy

  end;

val add_fixpat = gen_add_fixpat Syntax.read_term_global Attrib.attribute;

val add_fixpat_i = gen_add_fixpat Sign.cert_term (K I);

(*************************************************************************)

(******************************** Parsers ********************************)

(*************************************************************************)

local structure P = OuterParse and K = OuterKeyword in

val fixrec_eqn = SpecParse.opt_thm_name ":" -- P.prop;

val fixrec_strict = P.opt_keyword "permissive" >> not;

val fixrec_decl = fixrec_strict -- P.and_list1 (Scan.repeat1 fixrec_eqn);

(* this builds a parser for a new keyword, fixrec, whose functionality 

is defined by add_fixrec *)

val _ =

  OuterSyntax.command "fixrec" "define recursive functions (HOLCF)" K.thy_decl

    (fixrec_decl >> (Toplevel.theory o uncurry add_fixrec));

(* fixpat parser *)

val fixpat_decl = SpecParse.opt_thm_name ":" -- Scan.repeat1 P.prop;

val _ =

  OuterSyntax.command "fixpat" "define rewrites for fixrec functions" K.thy_decl

    (fixpat_decl >> (Toplevel.theory o add_fixpat));

end;

end;