(* Title: HOL/Tools/Ctr_Sugar/case_translation.ML
Author: Konrad Slind, Cambridge University Computer Laboratory
Author: Stefan Berghofer, TU Muenchen
Author: Dmitriy Traytel, TU Muenchen
Nested case expressions via a generic data slot for case combinators and constructors.
*)
signature CASE_TRANSLATION =
sig
val indexify_names: string list -> string list
val make_tnames: typ list -> string list
datatype config = Error | Warning | Quiet
val case_tr: bool -> Proof.context -> term list -> term
val lookup_by_constr: Proof.context -> string * typ -> (term * term list) option
val lookup_by_constr_permissive: Proof.context -> string * typ -> (term * term list) option
val lookup_by_case: Proof.context -> string -> (term * term list) option
val make_case: Proof.context -> config -> Name.context -> term -> (term * term) list -> term
val print_case_translations: Proof.context -> unit
val strip_case: Proof.context -> bool -> term -> (term * (term * term) list) option
val strip_case_full: Proof.context -> bool -> term -> term
val show_cases: bool Config.T
val register: term -> term list -> Context.generic -> Context.generic
end;
structure Case_Translation: CASE_TRANSLATION =
struct
(** general utilities **)
fun indexify_names names =
let
fun index (x :: xs) tab =
(case AList.lookup (op =) tab x of
NONE =>
if member (op =) xs x
then (x ^ "1") :: index xs ((x, 2) :: tab)
else x :: index xs tab
| SOME i => (x ^ string_of_int i) :: index xs ((x, i + 1) :: tab))
| index [] _ = [];
in index names [] end;
fun make_tnames Ts =
let
fun type_name (TFree (name, _)) = unprefix "'" name
| type_name (Type (name, _)) =
let val name' = Long_Name.base_name name
in if Symbol_Pos.is_identifier name' then name' else "x" end;
in indexify_names (map type_name Ts) end;
(** data management **)
datatype data = Data of
{constrs: (string * (term * term list)) list Symtab.table,
cases: (term * term list) Symtab.table};
fun make_data (constrs, cases) = Data {constrs = constrs, cases = cases};
structure Data = Generic_Data
(
type T = data;
val empty = make_data (Symtab.empty, Symtab.empty);
val extend = I;
fun merge
(Data {constrs = constrs1, cases = cases1},
Data {constrs = constrs2, cases = cases2}) =
make_data
(Symtab.join (K (AList.merge (op =) (K true))) (constrs1, constrs2),
Symtab.merge (K true) (cases1, cases2));
);
fun map_data f =
Data.map (fn Data {constrs, cases} => make_data (f (constrs, cases)));
fun map_constrs f = map_data (fn (constrs, cases) => (f constrs, cases));
fun map_cases f = map_data (fn (constrs, cases) => (constrs, f cases));
val rep_data = (fn Data args => args) o Data.get o Context.Proof;
fun T_of_data (comb, constrs : term list) =
fastype_of comb
|> funpow (length constrs) range_type
|> domain_type;
val Tname_of_data = fst o dest_Type o T_of_data;
val constrs_of = #constrs o rep_data;
val cases_of = #cases o rep_data;
fun lookup_by_constr ctxt (c, T) =
let
val tab = Symtab.lookup_list (constrs_of ctxt) c;
in
(case body_type T of
Type (tyco, _) => AList.lookup (op =) tab tyco
| _ => NONE)
end;
fun lookup_by_constr_permissive ctxt (c, T) =
let
val tab = Symtab.lookup_list (constrs_of ctxt) c;
val hint = (case body_type T of Type (tyco, _) => SOME tyco | _ => NONE);
val default = if null tab then NONE else SOME (snd (List.last tab));
(*conservative wrt. overloaded constructors*)
in
(case hint of
NONE => default
| SOME tyco =>
(case AList.lookup (op =) tab tyco of
NONE => default (*permissive*)
| SOME info => SOME info))
end;
val lookup_by_case = Symtab.lookup o cases_of;
(** installation **)
fun case_error s = error ("Error in case expression:\n" ^ s);
val name_of = try (dest_Const #> fst);
(* parse translation *)
fun constrain_Abs tT t = Syntax.const @{syntax_const "_constrainAbs"} $ t $ tT;
fun case_tr err ctxt [t, u] =
let
val consts = Proof_Context.consts_of ctxt;
fun is_const s = can (Consts.the_constraint consts) (Consts.intern consts s);
fun variant_free x used =
let val (x', used') = Name.variant x used
in if is_const x' then variant_free x' used' else (x', used') end;
fun abs p tTs t =
Syntax.const @{const_syntax case_abs} $
fold constrain_Abs tTs (absfree p t);
fun abs_pat (Const (@{syntax_const "_constrain"}, _) $ t $ tT) tTs =
abs_pat t (tT :: tTs)
| abs_pat (Free (p as (x, _))) tTs =
if is_const x then I else abs p tTs
| abs_pat (t $ u) _ = abs_pat u [] #> abs_pat t []
| abs_pat _ _ = I;
(* replace occurrences of dummy_pattern by distinct variables *)
fun replace_dummies (Const (@{const_syntax Pure.dummy_pattern}, T)) used =
let val (x, used') = variant_free "x" used
in (Free (x, T), used') end
| replace_dummies (t $ u) used =
let
val (t', used') = replace_dummies t used;
val (u', used'') = replace_dummies u used';
in (t' $ u', used'') end
| replace_dummies t used = (t, used);
fun dest_case1 (t as Const (@{syntax_const "_case1"}, _) $ l $ r) =
let val (l', _) = replace_dummies l (Term.declare_term_frees t Name.context) in
abs_pat l' []
(Syntax.const @{const_syntax case_elem} $ Term_Position.strip_positions l' $ r)
end
| dest_case1 _ = case_error "dest_case1";
fun dest_case2 (Const (@{syntax_const "_case2"}, _) $ t $ u) = t :: dest_case2 u
| dest_case2 t = [t];
val errt = Syntax.const (if err then @{const_syntax True} else @{const_syntax False});
in
Syntax.const @{const_syntax case_guard} $ errt $ t $
(fold_rev
(fn t => fn u => Syntax.const @{const_syntax case_cons} $ dest_case1 t $ u)
(dest_case2 u)
(Syntax.const @{const_syntax case_nil}))
end
| case_tr _ _ _ = case_error "case_tr";
val _ = Theory.setup (Sign.parse_translation [(@{syntax_const "_case_syntax"}, case_tr true)]);
(* print translation *)
fun case_tr' (_ :: x :: t :: ts) =
let
fun mk_clause (Const (@{const_syntax case_abs}, _) $ Abs (s, T, t)) xs used =
let val (s', used') = Name.variant s used
in mk_clause t ((s', T) :: xs) used' end
| mk_clause (Const (@{const_syntax case_elem}, _) $ pat $ rhs) xs _ =
Syntax.const @{syntax_const "_case1"} $
subst_bounds (map Syntax_Trans.mark_bound_abs xs, pat) $
subst_bounds (map Syntax_Trans.mark_bound_body xs, rhs)
| mk_clause _ _ _ = raise Match;
fun mk_clauses (Const (@{const_syntax case_nil}, _)) = []
| mk_clauses (Const (@{const_syntax case_cons}, _) $ t $ u) =
mk_clause t [] (Term.declare_term_frees t Name.context) :: mk_clauses u
| mk_clauses _ = raise Match;
in
list_comb (Syntax.const @{syntax_const "_case_syntax"} $ x $
foldr1 (fn (t, u) => Syntax.const @{syntax_const "_case2"} $ t $ u)
(mk_clauses t), ts)
end
| case_tr' _ = raise Match;
val _ = Theory.setup (Sign.print_translation [(@{const_syntax "case_guard"}, K case_tr')]);
(* declarations *)
fun register raw_case_comb raw_constrs context =
let
val ctxt = Context.proof_of context;
val case_comb = singleton (Variable.polymorphic ctxt) raw_case_comb;
val constrs = Variable.polymorphic ctxt raw_constrs;
val case_key = case_comb |> dest_Const |> fst;
val constr_keys = map (fst o dest_Const) constrs;
val data = (case_comb, constrs);
val Tname = Tname_of_data data;
val update_constrs = fold (fn key => Symtab.cons_list (key, (Tname, data))) constr_keys;
val update_cases = Symtab.update (case_key, data);
in
context
|> map_constrs update_constrs
|> map_cases update_cases
end;
val _ = Theory.setup
(Attrib.setup @{binding case_translation}
(Args.term -- Scan.repeat1 Args.term >>
(fn (t, ts) => Thm.declaration_attribute (K (register t ts))))
"declaration of case combinators and constructors");
(* (Un)check phases *)
datatype config = Error | Warning | Quiet;
exception CASE_ERROR of string * int;
(*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, _)) =
fold Term.declare_term_frees (tm :: pats @ map Free prfx);
(*try to preserve names given by user*)
fun default_name "" (Free (name', _)) = name'
| default_name name _ = name;
(*Produce an instance of a constructor, plus fresh variables for its arguments.*)
fun fresh_constr colty used c =
let
val (_, T) = dest_Const c;
val Ts = binder_types T;
val (names, _) =
fold_map Name.variant (make_tnames (map Logic.unvarifyT_global Ts)) used;
val ty = body_type T;
val ty_theta = Type.raw_match (ty, colty) Vartab.empty
handle Type.TYPE_MATCH => raise CASE_ERROR ("type mismatch", ~1);
val c' = Envir.subst_term_types ty_theta c;
val gvars = map (Envir.subst_term_types ty_theta o Free) (names ~~ Ts);
in (c', gvars) end;
(*Go through a list of rows and pick 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) =>
(case strip_comb p of
(Const (name', _), args) =>
if name = name' then
if length args = k then
((((prfx, args @ ps), rhs) :: in_group, not_in_group),
map2 default_name names args)
else raise CASE_ERROR ("Wrong number of arguments for constructor " ^ quote name, i)
else ((in_group, row :: not_in_group), names)
| _ => raise CASE_ERROR ("Not a constructor pattern", i)))
rows (([], []), replicate k "") |>> apply2 rev
end;
(* Partitioning *)
fun partition _ _ _ _ [] = raise CASE_ERROR ("partition: no rows", ~1)
| partition 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) = mk_group (dest_Const c) rows;
val used' = fold add_row_used in_group used;
val (c', gvars) = fresh_constr colty used' c;
val in_group' =
if null in_group (* Constructor not given *)
then
let
val Ts = map fastype_of ps;
val (xs, _) =
fold_map Name.variant
(replicate (length ps) "x")
(fold Term.declare_term_frees gvars used');
in
[((prfx, gvars @ map Free (xs ~~ Ts)),
(Const (@{const_name undefined}, res_ty), ~1))]
end
else in_group;
in
{constructor = c',
new_formals = gvars,
names = names,
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 ctxt used range_ty =
let
val get_info = lookup_by_constr_permissive ctxt;
fun expand _ _ _ ((_, []), _) = raise CASE_ERROR ("mk_case: expand", ~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 used' c)
in ((prfx, capp :: ps), (subst_free [(p, capp)] rhs, tag)) end;
in map expnd constructors end
else [row];
val (name, _) = Name.variant "a" used;
fun mk _ [] = raise CASE_ERROR ("no rows", ~1)
| mk [] (((_, []), (tm, tag)) :: _) = ([tag], tm) (* Done *)
| mk path ((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 get_info (cname, cT) of
NONE => raise CASE_ERROR ("Not a datatype constructor: " ^ quote cname, i)
| SOME (case_comb, constructors) =>
let
val pty = body_type cT;
val used' = fold Term.declare_term_frees us used;
val nrows = maps (expand constructors used' pty) rows;
val subproblems = partition 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, ...} =>
fold_rev (fn (x as Free (_, T), s) => fn t =>
Abs (if s = "" then name else s, T, abstract_over (x, t)))
(new_formals ~~ names))
subproblems dtrees;
val types = map fastype_of (case_functions @ [u]);
val case_const = Const (name_of case_comb |> the, 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;
(*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 make_case ctxt config used x clauses =
let
fun string_of_clause (pat, rhs) =
Syntax.unparse_term ctxt
(Term.list_comb (Syntax.const @{syntax_const "_case1"},
Syntax.uncheck_terms ctxt [pat, rhs]))
|> Pretty.string_of;
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 (fastype_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 ctxt 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 =>
if config = Quiet then ()
else
(if config = Error then case_error else warning (*FIXME lack of syntactic context!?*))
("The following clauses are redundant (covered by preceding clauses):\n" ^
cat_lines (map (string_of_clause o nth clauses) is)));
in
case_tm
end;
(* term check *)
fun decode_clause (Const (@{const_name case_abs}, _) $ Abs (s, T, t)) xs used =
let val (s', used') = Name.variant s used
in decode_clause t (Free (s', T) :: xs) used' end
| decode_clause (Const (@{const_name case_elem}, _) $ t $ u) xs _ =
(subst_bounds (xs, t), subst_bounds (xs, u))
| decode_clause _ _ _ = case_error "decode_clause";
fun decode_cases (Const (@{const_name case_nil}, _)) = []
| decode_cases (Const (@{const_name case_cons}, _) $ t $ u) =
decode_clause t [] (Term.declare_term_frees t Name.context) ::
decode_cases u
| decode_cases _ = case_error "decode_cases";
fun check_case ctxt =
let
fun decode_case (Const (@{const_name case_guard}, _) $ b $ u $ t) =
make_case ctxt (if b = @{term True} then Error else Warning)
Name.context (decode_case u) (decode_cases t)
| decode_case (t $ u) = decode_case t $ decode_case u
| decode_case (Abs (x, T, u)) =
let val (x', u') = Term.dest_abs (x, T, u);
in Term.absfree (x', T) (decode_case u') end
| decode_case t = t;
in
map decode_case
end;
val _ = Context.>> (Syntax_Phases.term_check 1 "case" check_case);
(* Pretty printing of nested case expressions *)
(* destruct one level of pattern matching *)
fun dest_case ctxt 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 j = length zs;
val (xs, ys) =
if j < i then (zs @
map (pair "x") (drop j (take i (binder_types (fastype_of t)))), [])
else chop i zs;
val u = fold_rev Term.abs ys (strip_abs_body t);
val xs' = map Free
((fold_map Name.variant (map fst xs)
(Term.declare_term_names u used) |> fst) ~~
map snd xs);
val (xs1, xs2) = chop j xs'
in (xs', list_comb (subst_bounds (rev xs1, u), xs2)) 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);
val get_info = lookup_by_case ctxt;
in
(case get_info cname of
SOME (_, constructors) =>
if length fs = length constructors then
let
val R = fastype_of x;
val cases = map (fn (Const (s, U), t) =>
let
val Us = binder_types U;
val k = length Us;
val p as (xs, _) = strip_abs k t;
in
(Const (s, map fastype_of xs ---> R), p, is_dependent k t)
end) (constructors ~~ fs);
val cases' =
sort (int_ord o swap o apply2 (length o snd))
(fold_rev count_cases cases []);
val dummy =
if d then Term.dummy_pattern R
else Free (Name.variant "x" used |> fst, 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
else NONE
| _ => NONE)
end
| _ => NONE);
(* destruct nested patterns *)
fun encode_clause recur S T (pat, rhs) =
fold (fn x as (_, U) => fn t =>
let val T = fastype_of t;
in Const (@{const_name case_abs}, (U --> T) --> T) $ Term.absfree x t end)
(Term.add_frees pat [])
(Const (@{const_name case_elem}, S --> T --> S --> T) $ pat $ recur rhs);
fun encode_cases _ S T [] = Const (@{const_name case_nil}, S --> T)
| encode_cases recur S T (p :: ps) =
Const (@{const_name case_cons}, (S --> T) --> (S --> T) --> S --> T) $
encode_clause recur S T p $ encode_cases recur S T ps;
fun encode_case recur (t, ps as (pat, rhs) :: _) =
let
val tT = fastype_of t;
val T = fastype_of rhs;
in
Const (@{const_name case_guard}, @{typ bool} --> tT --> (tT --> T) --> T) $
@{term True} $ t $ (encode_cases recur (fastype_of pat) (fastype_of rhs) ps)
end
| encode_case _ _ = case_error "encode_case";
fun strip_case' ctxt d (pat, rhs) =
(case dest_case ctxt d (Term.declare_term_frees pat Name.context) rhs of
SOME (exp as Free _, clauses) =>
if Term.exists_subterm (curry (op aconv) exp) pat andalso
not (exists (fn (_, rhs') =>
Term.exists_subterm (curry (op aconv) exp) rhs') clauses)
then
maps (strip_case' ctxt d) (map (fn (pat', rhs') =>
(subst_free [(exp, pat')] pat, rhs')) clauses)
else [(pat, rhs)]
| _ => [(pat, rhs)]);
fun strip_case ctxt d t =
(case dest_case ctxt d Name.context t of
SOME (x, clauses) => SOME (x, maps (strip_case' ctxt d) clauses)
| NONE => NONE);
fun strip_case_full ctxt d t =
(case dest_case ctxt d Name.context t of
SOME (x, clauses) =>
encode_case (strip_case_full ctxt d)
(strip_case_full ctxt d x, maps (strip_case' ctxt d) clauses)
| NONE =>
(case t of
t $ u => strip_case_full ctxt d t $ strip_case_full ctxt d u
| Abs (x, T, u) =>
let val (x', u') = Term.dest_abs (x, T, u);
in Term.absfree (x', T) (strip_case_full ctxt d u') end
| _ => t));
(* term uncheck *)
val show_cases = Attrib.setup_config_bool @{binding show_cases} (K true);
fun uncheck_case ctxt ts =
if Config.get ctxt show_cases
then map (fn t => if can Term.type_of t then strip_case_full ctxt true t else t) ts
else ts;
val _ = Context.>> (Syntax_Phases.term_uncheck 1 "case" uncheck_case);
(* outer syntax commands *)
fun print_case_translations ctxt =
let
val cases = map snd (Symtab.dest (cases_of ctxt));
val type_space = Proof_Context.type_space ctxt;
val pretty_term = Syntax.pretty_term ctxt;
fun pretty_data (data as (comb, ctrs)) =
let
val name = Tname_of_data data;
val xname = Name_Space.extern ctxt type_space name;
val markup = Name_Space.markup type_space name;
val prt =
(Pretty.block o Pretty.fbreaks)
[Pretty.block [Pretty.mark_str (markup, xname), Pretty.str ":"],
Pretty.block [Pretty.str "combinator:", Pretty.brk 1, pretty_term comb],
Pretty.block (Pretty.str "constructors:" :: Pretty.brk 1 ::
Pretty.commas (map pretty_term ctrs))];
in (xname, prt) end;
in
Pretty.big_list "case translations:" (map #2 (sort_by #1 (map pretty_data cases)))
|> Pretty.writeln
end;
val _ =
Outer_Syntax.command @{command_keyword print_case_translations}
"print registered case combinators and constructors"
(Scan.succeed (Toplevel.keep (print_case_translations o Toplevel.context_of)))
end;