(*  Title:      HOL/Tools/Datatype/datatype_case.ML

     Author:     Konrad Slind, Cambridge University Computer Laboratory

     Author:     Stefan Berghofer, TU Muenchen

 Datatype package: nested case expressions on datatypes.

 *)

 signature DATATYPE_CASE =

 sig

   datatype config = Error | Warning | Quiet

   type info = Datatype_Aux.info

   val make_case: (string * typ -> info option) ->

     Proof.context -> config -> string list -> term -> (term * term) list ->

     term

   val dest_case: (string -> info option) -> bool ->

     string list -> term -> (term * (term * term) list) option

   val strip_case: (string -> info option) -> bool ->

     term -> (term * (term * term) list) option

   val case_tr: bool -> (theory -> string * typ -> info option) ->

     Proof.context -> term list -> term

   val case_tr': (theory -> string -> info option) ->

     string -> Proof.context -> term list -> term

 end;

 structure Datatype_Case : DATATYPE_CASE =

 struct

 datatype config = Error | Warning | Quiet;

 type info = Datatype_Aux.info;

 exception CASE_ERROR of string * int;

 fun match_type thy pat ob = Sign.typ_match thy (pat, ob) Vartab.empty;

 (* Get information about datatypes *)

 fun ty_info tab sT =

   (case tab sT of

     SOME ({descr, case_name, index, sorts, ...} : info) =>

       let

         val (_, (tname, dts, constrs)) = nth descr index;

         val mk_ty = Datatype_Aux.typ_of_dtyp descr sorts;

         val T = Type (tname, map mk_ty dts);

       in

         SOME {case_name = case_name,

           constructors = map (fn (cname, dts') =>

             Const (cname, Logic.varifyT_global (map mk_ty dts' ---> T))) constrs}

       end

   | NONE => NONE);

 (*Each pattern carries with it a tag i, which denotes the clause it

 came from. i = ~1 indicates that the clause was added by pattern

 completion.*)

 fun add_row_used ((prfx, pats), (tm, tag)) =

   fold Term.add_free_names (tm :: pats @ map Free prfx);

 (*try to preserve names given by user*)

 fun default_names names ts =

   map (fn ("", Free (name', _)) => name' | (name, _) => name) (names ~~ ts);

 fun strip_constraints (Const (@{syntax_const "_constrain"}, _) $ t $ tT) =

       strip_constraints t ||> cons tT

   | strip_constraints t = (t, []);

 fun mk_fun_constrain tT t =

   Syntax.const @{syntax_const "_constrain"} $ t $

     (Syntax.const @{type_syntax fun} $ tT $ Syntax.const @{type_syntax dummy});

 (*Produce an instance of a constructor, plus fresh variables for its arguments.*)

 fun fresh_constr ty_match ty_inst colty used c =

   let

     val (_, Ty) = dest_Const c

     val Ts = binder_types Ty;

     val names = Name.variant_list used

       (Datatype_Prop.make_tnames (map Logic.unvarifyT_global Ts));

     val ty = body_type Ty;

     val ty_theta = ty_match ty colty handle Type.TYPE_MATCH =>

       raise CASE_ERROR ("type mismatch", ~1)

     val c' = ty_inst ty_theta c

     val gvars = map (ty_inst ty_theta o Free) (names ~~ Ts)

   in (c', gvars) end;

 (*Goes through a list of rows and picks out the ones beginning with a

  pattern with constructor = name.*)

 fun mk_group (name, T) rows =

   let val k = length (binder_types T) in

     fold (fn (row as ((prfx, p :: ps), rhs as (_, i))) =>

       fn ((in_group, not_in_group), (names, cnstrts)) =>

         (case strip_comb p of

           (Const (name', _), args) =>

             if name = name' then

               if length args = k then

                 let val (args', cnstrts') = split_list (map strip_constraints args)

                 in

                   ((((prfx, args' @ ps), rhs) :: in_group, not_in_group),

                    (default_names names args', map2 append cnstrts cnstrts'))

                 end

               else raise CASE_ERROR

                 ("Wrong number of arguments for constructor " ^ name, i)

             else ((in_group, row :: not_in_group), (names, cnstrts))

         | _ => raise CASE_ERROR ("Not a constructor pattern", i)))

     rows (([], []), (replicate k "", replicate k [])) |>> pairself rev

   end;

 (* Partitioning *)

 fun partition _ _ _ _ _ _ _ [] = raise CASE_ERROR ("partition: no rows", ~1)

   | partition ty_match ty_inst type_of used constructors colty res_ty

         (rows as (((prfx, _ :: ps), _) :: _)) =

       let

         fun part [] [] = []

           | part [] ((_, (_, i)) :: _) =

               raise CASE_ERROR ("Not a constructor pattern", i)

           | part (c :: cs) rows =

               let

                 val ((in_group, not_in_group), (names, cnstrts)) =

                   mk_group (dest_Const c) rows;

                 val used' = fold add_row_used in_group used;

                 val (c', gvars) = fresh_constr ty_match ty_inst colty used' c;

                 val in_group' =

                   if null in_group  (* Constructor not given *)

                   then

                     let

                       val Ts = map type_of ps;

                       val xs = Name.variant_list

                         (fold Term.add_free_names gvars used')

                         (replicate (length ps) "x")

                     in

                       [((prfx, gvars @ map Free (xs ~~ Ts)),

                         (Const (@{const_syntax undefined}, res_ty), ~1))]

                     end

                   else in_group

               in

                 {constructor = c',

                  new_formals = gvars,

                  names = names,

                  constraints = cnstrts,

                  group = in_group'} :: part cs not_in_group

               end

       in part constructors rows end;

 fun v_to_prfx (prfx, Free v::pats) = (v::prfx,pats)

   | v_to_prfx _ = raise CASE_ERROR ("mk_case: v_to_prfx", ~1);

 (* Translation of pattern terms into nested case expressions. *)

 fun mk_case tab ctxt ty_match ty_inst type_of used range_ty =

   let

     val name = singleton (Name.variant_list used) "a";

     fun expand constructors used ty ((_, []), _) =

           raise CASE_ERROR ("mk_case: expand_var_row", ~1)

       | expand constructors used ty (row as ((prfx, p :: ps), (rhs, tag))) =

           if is_Free p then

             let

               val used' = add_row_used row used;

               fun expnd c =

                 let val capp =

                   list_comb (fresh_constr ty_match ty_inst ty used' c)

                 in ((prfx, capp :: ps), (subst_free [(p, capp)] rhs, tag))

                 end

             in map expnd constructors end

           else [row]

     fun mk _ [] = raise CASE_ERROR ("no rows", ~1)

       | mk [] (((_, []), (tm, tag)) :: _) =  (* Done *)

           ([tag], tm)

       | mk path (rows as ((row as ((_, [Free _]), _)) :: _ :: _)) =

           mk path [row]

       | mk (u :: us) (rows as ((_, _ :: _), _) :: _) =

           let val col0 = map (fn ((_, p :: _), (_, i)) => (p, i)) rows in

             (case Option.map (apfst head_of) (find_first (not o is_Free o fst) col0) of

               NONE =>

                 let

                   val rows' = map (fn ((v, _), row) => row ||>

                     apfst (subst_free [(v, u)]) |>> v_to_prfx) (col0 ~~ rows);

                 in mk us rows' end

             | SOME (Const (cname, cT), i) =>

                 (case ty_info tab (cname, cT) of

                   NONE => raise CASE_ERROR ("Not a datatype constructor: " ^ cname, i)

                 | SOME {case_name, constructors} =>

                   let

                     val pty = body_type cT;

                     val used' = fold Term.add_free_names us used;

                     val nrows = maps (expand constructors used' pty) rows;

                     val subproblems = partition ty_match ty_inst type_of used'

                       constructors pty range_ty nrows;

                     val (pat_rect, dtrees) = split_list (map (fn {new_formals, group, ...} =>

                       mk (new_formals @ us) group) subproblems)

                     val case_functions = map2

                       (fn {new_formals, names, constraints, ...} =>

                          fold_rev (fn ((x as Free (_, T), s), cnstrts) => fn t =>

                            Abs (if s = "" then name else s, T,

                              abstract_over (x, t)) |>

                            fold mk_fun_constrain cnstrts)

                              (new_formals ~~ names ~~ constraints))

                       subproblems dtrees;

                     val types = map type_of (case_functions @ [u]);

                     val case_const = Const (case_name, types ---> range_ty)

                     val tree = list_comb (case_const, case_functions @ [u])

                   in (flat pat_rect, tree) end)

             | SOME (t, i) => raise CASE_ERROR ("Not a datatype constructor: " ^

                 Syntax.string_of_term ctxt t, i))

           end

       | mk _ _ = raise CASE_ERROR ("Malformed row matrix", ~1)

   in mk end;

 fun case_error s = error ("Error in case expression:\n" ^ s);

 (*Repeated variable occurrences in a pattern are not allowed.*)

 fun no_repeat_vars ctxt pat = fold_aterms

   (fn x as Free (s, _) => (fn xs =>

         if member op aconv xs x then

           case_error (quote s ^ " occurs repeatedly in the pattern " ^

             quote (Syntax.string_of_term ctxt pat))

         else x :: xs)

     | _ => I) pat [];

 fun gen_make_case ty_match ty_inst type_of tab ctxt config used x clauses =

   let

     fun string_of_clause (pat, rhs) =

       Syntax.string_of_term ctxt (Syntax.const @{syntax_const "_case1"} $ pat $ rhs);

     val _ = map (no_repeat_vars ctxt o fst) clauses;

     val rows = map_index (fn (i, (pat, rhs)) =>

       (([], [pat]), (rhs, i))) clauses;

     val rangeT =

       (case distinct op = (map (type_of o snd) clauses) of

         [] => case_error "no clauses given"

       | [T] => T

       | _ => case_error "all cases must have the same result type");

     val used' = fold add_row_used rows used;

     val (tags, case_tm) = mk_case tab ctxt ty_match ty_inst type_of

         used' rangeT [x] rows

       handle CASE_ERROR (msg, i) => case_error (msg ^

         (if i < 0 then ""

          else "\nIn clause\n" ^ string_of_clause (nth clauses i)));

     val _ =

       (case subtract (op =) tags (map (snd o snd) rows) of

         [] => ()

       | is =>

           (case config of Error => case_error | Warning => warning | Quiet => fn _ => {})

             ("The following clauses are redundant (covered by preceding clauses):\n" ^

              cat_lines (map (string_of_clause o nth clauses) is)));

   in

     case_tm

   end;

 fun make_case tab ctxt = gen_make_case

   (match_type (Proof_Context.theory_of ctxt)) Envir.subst_term_types fastype_of tab ctxt;

 val make_case_untyped = gen_make_case (K (K Vartab.empty))

   (K (Term.map_types (K dummyT))) (K dummyT);

 (* parse translation *)

 fun case_tr err tab_of ctxt [t, u] =

       let

         val thy = Proof_Context.theory_of ctxt;

         val intern_const_syntax = Consts.intern_syntax (Proof_Context.consts_of ctxt);

         (* replace occurrences of dummy_pattern by distinct variables *)

         (* internalize constant names                                 *)

         (* FIXME proper name context!? *)

         fun prep_pat ((c as Const (@{syntax_const "_constrain"}, _)) $ t $ tT) used =

               let val (t', used') = prep_pat t used

               in (c $ t' $ tT, used') end

           | prep_pat (Const (@{const_syntax dummy_pattern}, T)) used =

               let val x = singleton (Name.variant_list used) "x"

               in (Free (x, T), x :: used) end

           | prep_pat (Const (s, T)) used =

               (Const (intern_const_syntax s, T), used)

           | prep_pat (v as Free (s, T)) used =

               let val s' = Proof_Context.intern_const ctxt s in

                 if Sign.declared_const thy s' then

                   (Const (s', T), used)

                 else (v, used)

               end

           | prep_pat (t $ u) used =

               let

                 val (t', used') = prep_pat t used;

                 val (u', used'') = prep_pat u used';

               in

                 (t' $ u', used'')

               end

           | prep_pat t used = case_error ("Bad pattern: " ^ Syntax.string_of_term ctxt t);

         fun dest_case1 (t as Const (@{syntax_const "_case1"}, _) $ l $ r) =

               let val (l', cnstrts) = strip_constraints l

               in ((fst (prep_pat l' (Term.add_free_names t [])), r), cnstrts) end

           | dest_case1 t = case_error "dest_case1";

         fun dest_case2 (Const (@{syntax_const "_case2"}, _) $ t $ u) = t :: dest_case2 u

           | dest_case2 t = [t];

         val (cases, cnstrts) = split_list (map dest_case1 (dest_case2 u));

         val case_tm = make_case_untyped (tab_of thy) ctxt

           (if err then Error else Warning) []

           (fold (fn tT => fn t => Syntax.const @{syntax_const "_constrain"} $ t $ tT)

              (flat cnstrts) t) cases;

       in case_tm end

   | case_tr _ _ _ ts = case_error "case_tr";

 (* Pretty printing of nested case expressions *)

 (* destruct one level of pattern matching *)

 (* FIXME proper name context!? *)

 fun gen_dest_case name_of type_of tab d used t =

   (case apfst name_of (strip_comb t) of

     (SOME cname, ts as _ :: _) =>

       let

         val (fs, x) = split_last ts;

         fun strip_abs i t =

           let

             val zs = strip_abs_vars t;

             val _ = if length zs < i then raise CASE_ERROR ("", 0) else ();

             val (xs, ys) = chop i zs;

             val u = list_abs (ys, strip_abs_body t);

             val xs' = map Free (Name.variant_list (OldTerm.add_term_names (u, used))

               (map fst xs) ~~ map snd xs)

           in (xs', subst_bounds (rev xs', u)) end;

         fun is_dependent i t =

           let val k = length (strip_abs_vars t) - i

           in k < 0 orelse exists (fn j => j >= k) (loose_bnos (strip_abs_body t)) end;

         fun count_cases (_, _, true) = I

           | count_cases (c, (_, body), false) =

               AList.map_default op aconv (body, []) (cons c);

         val is_undefined = name_of #> equal (SOME @{const_name undefined});

         fun mk_case (c, (xs, body), _) = (list_comb (c, xs), body)

       in

         (case ty_info tab cname of

           SOME {constructors, case_name} =>

             if length fs = length constructors then

               let

                 val cases = map (fn (Const (s, U), t) =>

                   let

                     val k = length (binder_types U);

                     val p as (xs, _) = strip_abs k t

                   in

                     (Const (s, map type_of xs ---> type_of x),

                      p, is_dependent k t)

                   end) (constructors ~~ fs);

                 val cases' = sort (int_ord o swap o pairself (length o snd))

                   (fold_rev count_cases cases []);

                 val R = type_of t;

                 val dummy =

                   if d then Const (@{const_name dummy_pattern}, R)

                   else Free (singleton (Name.variant_list used) "x", R);

               in

                 SOME (x,

                   map mk_case

                     (case find_first (is_undefined o fst) cases' of

                       SOME (_, cs) =>

                       if length cs = length constructors then [hd cases]

                       else filter_out (fn (_, (_, body), _) => is_undefined body) cases

                     | NONE => case cases' of

                       [] => cases

                     | (default, cs) :: _ =>

                       if length cs = 1 then cases

                       else if length cs = length constructors then

                         [hd cases, (dummy, ([], default), false)]

                       else

                         filter_out (fn (c, _, _) => member op aconv cs c) cases @

                         [(dummy, ([], default), false)]))

               end handle CASE_ERROR _ => NONE

             else NONE

         | _ => NONE)

       end

   | _ => NONE);

 val dest_case = gen_dest_case (try (dest_Const #> fst)) fastype_of;

 val dest_case' = gen_dest_case (try (dest_Const #> fst #> Lexicon.unmark_const)) (K dummyT);

 (* destruct nested patterns *)

 fun strip_case'' dest (pat, rhs) =

   (case dest (Term.add_free_names pat []) rhs of

     SOME (exp as Free _, clauses) =>

       if member op aconv (OldTerm.term_frees pat) exp andalso

         not (exists (fn (_, rhs') =>

           member op aconv (OldTerm.term_frees rhs') exp) clauses)

       then

         maps (strip_case'' dest) (map (fn (pat', rhs') =>

           (subst_free [(exp, pat')] pat, rhs')) clauses)

       else [(pat, rhs)]

   | _ => [(pat, rhs)]);

 fun gen_strip_case dest t =

   (case dest [] t of

     SOME (x, clauses) =>

       SOME (x, maps (strip_case'' dest) clauses)

   | NONE => NONE);

 val strip_case = gen_strip_case oo dest_case;

 val strip_case' = gen_strip_case oo dest_case';

 (* print translation *)

 fun case_tr' tab_of cname ctxt ts =

   let

     val thy = Proof_Context.theory_of ctxt;

     fun mk_clause (pat, rhs) =

       let val xs = Term.add_frees pat [] in

         Syntax.const @{syntax_const "_case1"} $

           map_aterms

             (fn Free p => Syntax_Trans.mark_boundT p

               | Const (s, _) => Syntax.const (Lexicon.mark_const s)

               | t => t) pat $

           map_aterms

             (fn x as Free (s, T) =>

                   if member (op =) xs (s, T) then Syntax_Trans.mark_bound s else x

               | t => t) rhs

       end;

   in

     (case strip_case' (tab_of thy) true (list_comb (Syntax.const cname, ts)) of

       SOME (x, clauses) =>

         Syntax.const @{syntax_const "_case_syntax"} $ x $

           foldr1 (fn (t, u) => Syntax.const @{syntax_const "_case2"} $ t $ u)

             (map mk_clause clauses)

     | NONE => raise Match)

   end;

 end;