--- a/src/HOL/Tools/datatype_case.ML Tue Jun 16 00:01:32 2009 -0700
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,469 +0,0 @@
-(* Title: HOL/Tools/datatype_case.ML
- Author: Konrad Slind, Cambridge University Computer Laboratory
- Author: Stefan Berghofer, TU Muenchen
-
-Nested case expressions on datatypes.
-*)
-
-signature DATATYPE_CASE =
-sig
- val make_case: (string -> DatatypeAux.datatype_info option) ->
- Proof.context -> bool -> string list -> term -> (term * term) list ->
- term * (term * (int * bool)) list
- val dest_case: (string -> DatatypeAux.datatype_info option) -> bool ->
- string list -> term -> (term * (term * term) list) option
- val strip_case: (string -> DatatypeAux.datatype_info option) -> bool ->
- term -> (term * (term * term) list) option
- val case_tr: bool -> (theory -> string -> DatatypeAux.datatype_info option)
- -> Proof.context -> term list -> term
- val case_tr': (theory -> string -> DatatypeAux.datatype_info option) ->
- string -> Proof.context -> term list -> term
-end;
-
-structure DatatypeCase : DATATYPE_CASE =
-struct
-
-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 : string -> DatatypeAux.datatype_info option) s =
- case tab s of
- SOME {descr, case_name, index, sorts, ...} =>
- let
- val (_, (tname, dts, constrs)) = nth descr index;
- val mk_ty = DatatypeAux.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 ("_constrain", _) $ t $ tT) =
- strip_constraints t ||> cons tT
- | strip_constraints t = (t, []);
-
-fun mk_fun_constrain tT t = Syntax.const "_constrain" $ t $
- (Syntax.free "fun" $ tT $ Syntax.free "dummy");
-
-
-(*---------------------------------------------------------------------------
- * 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
- (DatatypeProp.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 ("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 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 new_formals = map #new_formals subproblems
- 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 = flat (map 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 err used x clauses =
- let
- fun string_of_clause (pat, rhs) = Syntax.string_of_term ctxt
- (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 (Library.int_ord o Library.pairself row_of_pat) patts1
- val finals = map row_of_pat patts2
- val originals = map (row_of_pat o #2) rows
- val _ = case originals \\ finals of
- [] => ()
- | is => (if err then case_error else warning)
- ("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_TVars 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 ("_constrain", _)) $ t $ tT) used =
- let val (t', used') = prep_pat t used
- in (c $ t' $ tT, used') end
- | prep_pat (Const ("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 ("_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 ("_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 err []
- (fold (fn tT => fn t => 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 "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 ("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 "_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 "_case_syntax" $ x $
- foldr1 (fn (t, u) => Syntax.const "_case2" $ t $ u)
- (map mk_clause clauses)
- | NONE => raise Match
- end;
-
-end;