src/HOL/Tools/Datatype/datatype_case.ML

formal markup of constants;

(*  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 * (term * (int * bool)) list
  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 (map mk_ty dts' ---> T))) constrs}
      end
  | NONE => NONE;


(*---------------------------------------------------------------------------
 * Each pattern carries with it a tag (i,b) where
 * i is the clause it came from and
 * b=true indicates that clause was given by the user
 * (or is an instantiation of a user supplied pattern)
 * b=false --> i = ~1
 *---------------------------------------------------------------------------*)

fun pattern_subst theta (tm, x) = (subst_free theta tm, x);

fun row_of_pat x = fst (snd x);

fun add_row_used ((prfx, pats), (tm, tag)) =
  fold Term.add_free_names (tm :: pats @ 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.free "fun" $ tT $ Syntax.free "dummy");    (* FIXME @{type_syntax} (!?) *)


(*---------------------------------------------------------------------------
 * Produce an instance of a constructor, plus genvars 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 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 :: rst), 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' @ rst), 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;

(*---------------------------------------------------------------------------
 * Partition the rows. Not efficient: we should use hashing.
 *---------------------------------------------------------------------------*)
fun partition _ _ _ _ _ _ _ [] = raise CASE_ERROR ("partition: no rows", ~1)
  | partition ty_match ty_inst type_of used constructors colty res_ty
        (rows as (((prfx, _ :: rstp), _) :: _)) =
      let
        fun part {constrs = [], rows = [], A} = rev A
          | part {constrs = [], rows = (_, (_, (i, _))) :: _, A} =
              raise CASE_ERROR ("Not a constructor pattern", i)
          | part {constrs = c :: crst, rows, A} =
              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 rstp;
                      val xs = Name.variant_list
                        (fold Term.add_free_names gvars used')
                        (replicate (length rstp) "x")
                    in
                      [((prfx, gvars @ map Free (xs ~~ Ts)),
                        (Const (@{const_name HOL.undefined}, res_ty), (~1, false)))]
                    end
                  else in_group
              in
                part{constrs = crst,
                  rows = not_in_group,
                  A = {constructor = c',
                    new_formals = gvars,
                    names = names,
                    constraints = cnstrts,
                    group = in_group'} :: A}
              end
      in part {constrs = constructors, rows = rows, A = []}
      end;

(*---------------------------------------------------------------------------
 * Misc. routines used in mk_case
 *---------------------------------------------------------------------------*)

fun mk_pat ((c, c'), l) =
  let
    val L = length (binder_types (fastype_of c))
    fun build (prfx, tag, plist) =
      let val (args, plist') = chop L plist
      in (prfx, tag, list_comb (c', args) :: plist') end
  in map build l end;

fun v_to_prfx (prfx, v::pats) = (v::prfx,pats)
  | v_to_prfx _ = raise CASE_ERROR ("mk_case: v_to_prfx", ~1);

fun v_to_pats (v::prfx,tag, pats) = (prfx, tag, v::pats)
  | v_to_pats _ = raise CASE_ERROR ("mk_case: v_to_pats", ~1);


(*----------------------------------------------------------------------------
 * Translation of pattern terms into nested case expressions.
 *
 * This performs the translation and also builds the full set of patterns.
 * Thus it supports the construction of induction theorems even when an
 * incomplete set of patterns is given.
 *---------------------------------------------------------------------------*)

fun mk_case tab ctxt ty_match ty_inst type_of used range_ty =
  let
    val name = Name.variant used "a";
    fun expand constructors used ty ((_, []), _) =
          raise CASE_ERROR ("mk_case: expand_var_row", ~1)
      | expand constructors used ty (row as ((prfx, p :: rst), rhs)) =
          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 :: rst), pattern_subst [(p, capp)] rhs)
                end
            in map expnd constructors end
          else [row]
    fun mk {rows = [], ...} = raise CASE_ERROR ("no rows", ~1)
      | mk {path = [], rows = ((prfx, []), (tm, tag)) :: _} =  (* Done *)
          ([(prfx, tag, [])], tm)
      | mk {path, rows as ((row as ((_, [Free _]), _)) :: _ :: _)} =
          mk {path = path, rows = [row]}
      | mk {path = u :: rstp, 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 ||>
                    pattern_subst [(v, u)] |>> v_to_prfx) (col0 ~~ rows);
                  val (pref_patl, tm) = mk {path = rstp, rows = rows'}
                in (map v_to_pats pref_patl, tm) 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 rstp 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 constructors' = map #constructor subproblems
                  val news = map (fn {new_formals, group, ...} =>
                    {path = new_formals @ rstp, rows = group}) subproblems;
                  val (pat_rect, dtrees) = split_list (map mk news);
                  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])
                  val pat_rect1 = maps mk_pat (constructors ~~ constructors' ~~ pat_rect)
                in (pat_rect1, 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, true)))) 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 (patts, case_tm) = mk_case tab ctxt ty_match ty_inst type_of
        used' rangeT {path = [x], rows = rows}
      handle CASE_ERROR (msg, i) => case_error (msg ^
        (if i < 0 then ""
         else "\nIn clause\n" ^ string_of_clause (nth clauses i)));
    val patts1 = map
      (fn (_, tag, [pat]) => (pat, tag)
        | _ => case_error "error in pattern-match translation") patts;
    val patts2 = Library.sort (int_ord o pairself row_of_pat) patts1
    val finals = map row_of_pat patts2
    val originals = map (row_of_pat o #2) rows
    val _ =
        case subtract (op =) finals originals 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, patts2)
  end;

fun make_case tab ctxt = gen_make_case
  (match_type (ProofContext.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 = ProofContext.theory_of ctxt;
      (* replace occurrences of dummy_pattern by distinct variables *)
      (* internalize constant names                                 *)
      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_name dummy_pattern}, T)) used =
            let val x = Name.variant used "x"
            in (Free (x, T), x :: used) end
        | prep_pat (Const (s, T)) used =
            (case try (unprefix Syntax.constN) s of
               SOME c => (Const (c, T), used)
             | NONE => (Const (Sign.intern_const thy s, T), used))
        | prep_pat (v as Free (s, T)) used =
            let val s' = Sign.intern_const thy 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 *)

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 HOL.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 (Name.variant 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 #> unprefix Syntax.constN)) (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 = ProofContext.theory_of ctxt;
    val consts = ProofContext.consts_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.mark_boundT p
              | Const (s, _) => Const (Consts.extern_early consts s, dummyT)
              | t => t) pat $
          map_aterms
            (fn x as Free (s, T) =>
                  if member (op =) xs (s, T) then Syntax.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;