wneuper/isa: src/HOL/Tools/Nitpick/nitpick

     1 (*  Title:      HOL/Tools/Nitpick/nitpick_mono.ML

     2     Author:     Jasmin Blanchette, TU Muenchen

     3     Copyright   2009, 2010

     5 Monotonicity inference for higher-order logic.

     6 *)

     8 signature NITPICK_MONO =

     9 sig

    10   type hol_context = Nitpick_HOL.hol_context

    12   val formulas_monotonic :

    13     hol_context -> bool -> typ -> term list * term list -> bool

    14   val finitize_funs :

    15     hol_context -> bool -> (typ option * bool option) list -> typ

    16     -> term list * term list -> term list * term list

    17 end;

    19 structure Nitpick_Mono : NITPICK_MONO =

    20 struct

    22 open Nitpick_Util

    23 open Nitpick_HOL

    25 type var = int

    27 datatype sign = Plus | Minus

    28 datatype sign_atom = S of sign | V of var

    30 type literal = var * sign

    32 datatype mtyp =

    33   MAlpha |

    34   MFun of mtyp * sign_atom * mtyp |

    35   MPair of mtyp * mtyp |

    36   MType of string * mtyp list |

    37   MRec of string * typ list

    39 datatype mterm =

    40   MRaw of term * mtyp |

    41   MAbs of string * typ * mtyp * sign_atom * mterm |

    42   MApp of mterm * mterm

    44 type mdata =

    45   {hol_ctxt: hol_context,

    46    binarize: bool,

    47    alpha_T: typ,

    48    no_harmless: bool,

    49    max_fresh: int Unsynchronized.ref,

    50    datatype_mcache: ((string * typ list) * mtyp) list Unsynchronized.ref,

    51    constr_mcache: (styp * mtyp) list Unsynchronized.ref}

    53 exception UNSOLVABLE of unit

    54 exception MTYPE of string * mtyp list * typ list

    55 exception MTERM of string * mterm list

    57 val debug_mono = false

    59 fun print_g f = () |> debug_mono ? tracing o f

    61 val string_for_var = signed_string_of_int

    62 fun string_for_vars sep [] = "0\<^bsub>" ^ sep ^ "\<^esub>"

    63   | string_for_vars sep xs = space_implode sep (map string_for_var xs)

    64 fun subscript_string_for_vars sep xs =

    65   if null xs then "" else "\<^bsub>" ^ string_for_vars sep xs ^ "\<^esub>"

    67 fun string_for_sign Plus = "+"

    68   | string_for_sign Minus = "-"

    70 fun xor sn1 sn2 = if sn1 = sn2 then Plus else Minus

    71 val negate = xor Minus

    73 fun string_for_sign_atom (S sn) = string_for_sign sn

    74   | string_for_sign_atom (V x) = string_for_var x

    76 fun string_for_literal (x, sn) = string_for_var x ^ " = " ^ string_for_sign sn

    78 val bool_M = MType (@{type_name bool}, [])

    79 val dummy_M = MType (nitpick_prefix ^ "dummy", [])

    81 fun is_MRec (MRec _) = true

    82   | is_MRec _ = false

    83 fun dest_MFun (MFun z) = z

    84   | dest_MFun M = raise MTYPE ("Nitpick_Mono.dest_MFun", [M], [])

    86 val no_prec = 100

    88 fun precedence_of_mtype (MFun _) = 1

    89   | precedence_of_mtype (MPair _) = 2

    90   | precedence_of_mtype _ = no_prec

    92 val string_for_mtype =

    93   let

    94     fun aux outer_prec M =

    95       let

    96         val prec = precedence_of_mtype M

    97         val need_parens = (prec < outer_prec)

    98       in

    99         (if need_parens then "(" else "") ^

   100         (if M = dummy_M then

   101            "_"

   102          else case M of

   103              MAlpha => "\<alpha>"

   104            | MFun (M1, a, M2) =>

   105              aux (prec + 1) M1 ^ " \<Rightarrow>\<^bsup>" ^

   106              string_for_sign_atom a ^ "\<^esup> " ^ aux prec M2

   107            | MPair (M1, M2) => aux (prec + 1) M1 ^ " \<times> " ^ aux prec M2

   108            | MType (s, []) =>

   109              if s = @{type_name prop} orelse s = @{type_name bool} then "o"

   110              else s

   111            | MType (s, Ms) => "(" ^ commas (map (aux 0) Ms) ^ ") " ^ s

   112            | MRec (s, _) => "[" ^ s ^ "]") ^

   113         (if need_parens then ")" else "")

   114       end

   115   in aux 0 end

   117 fun flatten_mtype (MPair (M1, M2)) = maps flatten_mtype [M1, M2]

   118   | flatten_mtype (MType (_, Ms)) = maps flatten_mtype Ms

   119   | flatten_mtype M = [M]

   121 fun precedence_of_mterm (MRaw _) = no_prec

   122   | precedence_of_mterm (MAbs _) = 1

   123   | precedence_of_mterm (MApp _) = 2

   125 fun string_for_mterm ctxt =

   126   let

   127     fun mtype_annotation M = "\<^bsup>" ^ string_for_mtype M ^ "\<^esup>"

   128     fun aux outer_prec m =

   129       let

   130         val prec = precedence_of_mterm m

   131         val need_parens = (prec < outer_prec)

   132       in

   133         (if need_parens then "(" else "") ^

   134         (case m of

   135            MRaw (t, M) => Syntax.string_of_term ctxt t ^ mtype_annotation M

   136          | MAbs (s, _, M, a, m) =>

   137            "\<lambda>" ^ s ^ mtype_annotation M ^ ".\<^bsup>" ^

   138            string_for_sign_atom a ^ "\<^esup> " ^ aux prec m

   139          | MApp (m1, m2) => aux prec m1 ^ " " ^ aux (prec + 1) m2) ^

   140         (if need_parens then ")" else "")

   141       end

   142   in aux 0 end

   144 fun mtype_of_mterm (MRaw (_, M)) = M

   145   | mtype_of_mterm (MAbs (_, _, M, a, m)) = MFun (M, a, mtype_of_mterm m)

   146   | mtype_of_mterm (MApp (m1, _)) =

   147     case mtype_of_mterm m1 of

   148       MFun (_, _, M12) => M12

   149     | M1 => raise MTYPE ("Nitpick_Mono.mtype_of_mterm", [M1], [])

   151 fun strip_mcomb (MApp (m1, m2)) = strip_mcomb m1 ||> (fn ms => append ms [m2])

   152   | strip_mcomb m = (m, [])

   154 fun initial_mdata hol_ctxt binarize no_harmless alpha_T =

   155   ({hol_ctxt = hol_ctxt, binarize = binarize, alpha_T = alpha_T,

   156     no_harmless = no_harmless, max_fresh = Unsynchronized.ref 0,

   157     datatype_mcache = Unsynchronized.ref [],

   158     constr_mcache = Unsynchronized.ref []} : mdata)

   160 fun could_exist_alpha_subtype alpha_T (T as Type (_, Ts)) =

   161     T = alpha_T orelse (not (is_fp_iterator_type T) andalso

   162                         exists (could_exist_alpha_subtype alpha_T) Ts)

   163   | could_exist_alpha_subtype alpha_T T = (T = alpha_T)

   164 fun could_exist_alpha_sub_mtype _ (alpha_T as TFree _) T =

   165     could_exist_alpha_subtype alpha_T T

   166   | could_exist_alpha_sub_mtype ctxt alpha_T T =

   167     (T = alpha_T orelse is_datatype ctxt [(NONE, true)] T)

   169 fun exists_alpha_sub_mtype MAlpha = true

   170   | exists_alpha_sub_mtype (MFun (M1, _, M2)) =

   171     exists exists_alpha_sub_mtype [M1, M2]

   172   | exists_alpha_sub_mtype (MPair (M1, M2)) =

   173     exists exists_alpha_sub_mtype [M1, M2]

   174   | exists_alpha_sub_mtype (MType (_, Ms)) = exists exists_alpha_sub_mtype Ms

   175   | exists_alpha_sub_mtype (MRec _) = true

   177 fun exists_alpha_sub_mtype_fresh MAlpha = true

   178   | exists_alpha_sub_mtype_fresh (MFun (_, V _, _)) = true

   179   | exists_alpha_sub_mtype_fresh (MFun (_, _, M2)) =

   180     exists_alpha_sub_mtype_fresh M2

   181   | exists_alpha_sub_mtype_fresh (MPair (M1, M2)) =

   182     exists exists_alpha_sub_mtype_fresh [M1, M2]

   183   | exists_alpha_sub_mtype_fresh (MType (_, Ms)) =

   184     exists exists_alpha_sub_mtype_fresh Ms

   185   | exists_alpha_sub_mtype_fresh (MRec _) = true

   187 fun constr_mtype_for_binders z Ms =

   188   fold_rev (fn M => curry3 MFun M (S Minus)) Ms (MRec z)

   190 fun repair_mtype _ _ MAlpha = MAlpha

   191   | repair_mtype cache seen (MFun (M1, a, M2)) =

   192     MFun (repair_mtype cache seen M1, a, repair_mtype cache seen M2)

   193   | repair_mtype cache seen (MPair Mp) =

   194     MPair (pairself (repair_mtype cache seen) Mp)

   195   | repair_mtype cache seen (MType (s, Ms)) =

   196     MType (s, maps (flatten_mtype o repair_mtype cache seen) Ms)

   197   | repair_mtype cache seen (MRec (z as (s, _))) =

   198     case AList.lookup (op =) cache z |> the of

   199       MRec _ => MType (s, [])

   200     | M => if member (op =) seen M then MType (s, [])

   201            else repair_mtype cache (M :: seen) M

   203 fun repair_datatype_mcache cache =

   204   let

   205     fun repair_one (z, M) =

   206       Unsynchronized.change cache

   207           (AList.update (op =) (z, repair_mtype (!cache) [] M))

   208   in List.app repair_one (rev (!cache)) end

   210 fun repair_constr_mcache dtype_cache constr_mcache =

   211   let

   212     fun repair_one (x, M) =

   213       Unsynchronized.change constr_mcache

   214           (AList.update (op =) (x, repair_mtype dtype_cache [] M))

   215   in List.app repair_one (!constr_mcache) end

   217 fun is_fin_fun_supported_type @{typ prop} = true

   218   | is_fin_fun_supported_type @{typ bool} = true

   219   | is_fin_fun_supported_type (Type (@{type_name option}, _)) = true

   220   | is_fin_fun_supported_type _ = false

   221 fun fin_fun_body _ _ (t as @{term False}) = SOME t

   222   | fin_fun_body _ _ (t as Const (@{const_name None}, _)) = SOME t

   223   | fin_fun_body dom_T ran_T

   224                  ((t0 as Const (@{const_name If}, _))

   225                   $ (t1 as Const (@{const_name "op ="}, _) $ Bound 0 $ t1')

   226                   $ t2 $ t3) =

   227     (if loose_bvar1 (t1', 0) then

   228        NONE

   229      else case fin_fun_body dom_T ran_T t3 of

   230        NONE => NONE

   231      | SOME t3 =>

   232        SOME (t0 $ (Const (@{const_name is_unknown}, dom_T --> bool_T) $ t1')

   233                 $ (Const (@{const_name unknown}, ran_T)) $ (t0 $ t1 $ t2 $ t3)))

   234   | fin_fun_body _ _ _ = NONE

   236 fun fresh_mfun_for_fun_type (mdata as {max_fresh, ...} : mdata) all_minus

   237                             T1 T2 =

   238   let

   239     val M1 = fresh_mtype_for_type mdata all_minus T1

   240     val M2 = fresh_mtype_for_type mdata all_minus T2

   241     val a = if not all_minus andalso exists_alpha_sub_mtype_fresh M1 andalso

   242                is_fin_fun_supported_type (body_type T2) then

   243               V (Unsynchronized.inc max_fresh)

   244             else

   245               S Minus

   246   in (M1, a, M2) end

   247 and fresh_mtype_for_type (mdata as {hol_ctxt as {ctxt, ...}, binarize, alpha_T,

   248                                     datatype_mcache, constr_mcache, ...})

   249                          all_minus =

   250   let

   251     fun do_type T =

   252       if T = alpha_T then

   253         MAlpha

   254       else case T of

   255         Type (@{type_name fun}, [T1, T2]) =>

   256         MFun (fresh_mfun_for_fun_type mdata false T1 T2)

   257       | Type (@{type_name Product_Type.prod}, [T1, T2]) => MPair (pairself do_type (T1, T2))

   258       | Type (z as (s, _)) =>

   259         if could_exist_alpha_sub_mtype ctxt alpha_T T then

   260           case AList.lookup (op =) (!datatype_mcache) z of

   261             SOME M => M

   262           | NONE =>

   263             let

   264               val _ = Unsynchronized.change datatype_mcache (cons (z, MRec z))

   265               val xs = binarized_and_boxed_datatype_constrs hol_ctxt binarize T

   266               val (all_Ms, constr_Ms) =

   267                 fold_rev (fn (_, T') => fn (all_Ms, constr_Ms) =>

   268                              let

   269                                val binder_Ms = map do_type (binder_types T')

   270                                val new_Ms = filter exists_alpha_sub_mtype_fresh

   271                                                    binder_Ms

   272                                val constr_M = constr_mtype_for_binders z

   273                                                                        binder_Ms

   274                              in

   275                                (union (op =) new_Ms all_Ms,

   276                                 constr_M :: constr_Ms)

   277                              end)

   278                          xs ([], [])

   279               val M = MType (s, all_Ms)

   280               val _ = Unsynchronized.change datatype_mcache

   281                           (AList.update (op =) (z, M))

   282               val _ = Unsynchronized.change constr_mcache

   283                           (append (xs ~~ constr_Ms))

   284             in

   285               if forall (not o is_MRec o snd) (!datatype_mcache) then

   286                 (repair_datatype_mcache datatype_mcache;

   287                  repair_constr_mcache (!datatype_mcache) constr_mcache;

   288                  AList.lookup (op =) (!datatype_mcache) z |> the)

   289               else

   290                 M

   291             end

   292         else

   293           MType (s, [])

   294       | _ => MType (simple_string_of_typ T, [])

   295   in do_type end

   297 fun prodM_factors (MPair (M1, M2)) = maps prodM_factors [M1, M2]

   298   | prodM_factors M = [M]

   299 fun curried_strip_mtype (MFun (M1, _, M2)) =

   300     curried_strip_mtype M2 |>> append (prodM_factors M1)

   301   | curried_strip_mtype M = ([], M)

   302 fun sel_mtype_from_constr_mtype s M =

   303   let val (arg_Ms, dataM) = curried_strip_mtype M in

   304     MFun (dataM, S Minus,

   305           case sel_no_from_name s of ~1 => bool_M | n => nth arg_Ms n)

   306   end

   308 fun mtype_for_constr (mdata as {hol_ctxt = {ctxt, ...}, alpha_T, constr_mcache,

   309                                 ...}) (x as (_, T)) =

   310   if could_exist_alpha_sub_mtype ctxt alpha_T T then

   311     case AList.lookup (op =) (!constr_mcache) x of

   312       SOME M => M

   313     | NONE => if T = alpha_T then

   314                 let val M = fresh_mtype_for_type mdata false T in

   315                   (Unsynchronized.change constr_mcache (cons (x, M)); M)

   316                 end

   317               else

   318                 (fresh_mtype_for_type mdata false (body_type T);

   319                  AList.lookup (op =) (!constr_mcache) x |> the)

   320   else

   321     fresh_mtype_for_type mdata false T

   322 fun mtype_for_sel (mdata as {hol_ctxt, binarize, ...}) (x as (s, _)) =

   323   x |> binarized_and_boxed_constr_for_sel hol_ctxt binarize

   324     |> mtype_for_constr mdata |> sel_mtype_from_constr_mtype s

   326 fun resolve_sign_atom lits (V x) =

   327     x |> AList.lookup (op =) lits |> Option.map S |> the_default (V x)

   328   | resolve_sign_atom _ a = a

   329 fun resolve_mtype lits =

   330   let

   331     fun aux MAlpha = MAlpha

   332       | aux (MFun (M1, a, M2)) = MFun (aux M1, resolve_sign_atom lits a, aux M2)

   333       | aux (MPair Mp) = MPair (pairself aux Mp)

   334       | aux (MType (s, Ms)) = MType (s, map aux Ms)

   335       | aux (MRec z) = MRec z

   336   in aux end

   338 datatype comp_op = Eq | Leq

   340 type comp = sign_atom * sign_atom * comp_op * var list

   341 type sign_expr = literal list

   343 type constraint_set = literal list * comp list * sign_expr list

   345 fun string_for_comp_op Eq = "="

   346   | string_for_comp_op Leq = "\<le>"

   348 fun string_for_sign_expr [] = "\<bot>"

   349   | string_for_sign_expr lits =

   350     space_implode " \<or> " (map string_for_literal lits)

   352 fun do_literal _ NONE = NONE

   353   | do_literal (x, sn) (SOME lits) =

   354     case AList.lookup (op =) lits x of

   355       SOME sn' => if sn = sn' then SOME lits else NONE

   356     | NONE => SOME ((x, sn) :: lits)

   358 fun do_sign_atom_comp Eq [] a1 a2 (accum as (lits, comps)) =

   359     (case (a1, a2) of

   360        (S sn1, S sn2) => if sn1 = sn2 then SOME accum else NONE

   361      | (V x1, S sn2) =>

   362        Option.map (rpair comps) (do_literal (x1, sn2) (SOME lits))

   363      | (V _, V _) => SOME (lits, insert (op =) (a1, a2, Eq, []) comps)

   364      | _ => do_sign_atom_comp Eq [] a2 a1 accum)

   365   | do_sign_atom_comp Leq [] a1 a2 (accum as (lits, comps)) =

   366     (case (a1, a2) of

   367        (_, S Minus) => SOME accum

   368      | (S Plus, _) => SOME accum

   369      | (S Minus, S Plus) => NONE

   370      | (V _, V _) => SOME (lits, insert (op =) (a1, a2, Leq, []) comps)

   371      | _ => do_sign_atom_comp Eq [] a1 a2 accum)

   372   | do_sign_atom_comp cmp xs a1 a2 (lits, comps) =

   373     SOME (lits, insert (op =) (a1, a2, cmp, xs) comps)

   375 fun do_mtype_comp _ _ _ _ NONE = NONE

   376   | do_mtype_comp _ _ MAlpha MAlpha accum = accum

   377   | do_mtype_comp Eq xs (MFun (M11, a1, M12)) (MFun (M21, a2, M22))

   378                   (SOME accum) =

   379      accum |> do_sign_atom_comp Eq xs a1 a2 |> do_mtype_comp Eq xs M11 M21

   380            |> do_mtype_comp Eq xs M12 M22

   381   | do_mtype_comp Leq xs (MFun (M11, a1, M12)) (MFun (M21, a2, M22))

   382                   (SOME accum) =

   383     (if exists_alpha_sub_mtype M11 then

   384        accum |> do_sign_atom_comp Leq xs a1 a2

   385              |> do_mtype_comp Leq xs M21 M11

   386              |> (case a2 of

   387                    S Minus => I

   388                  | S Plus => do_mtype_comp Leq xs M11 M21

   389                  | V x => do_mtype_comp Leq (x :: xs) M11 M21)

   390      else

   391        SOME accum)

   392     |> do_mtype_comp Leq xs M12 M22

   393   | do_mtype_comp cmp xs (M1 as MPair (M11, M12)) (M2 as MPair (M21, M22))

   394                   accum =

   395     (accum |> fold (uncurry (do_mtype_comp cmp xs)) [(M11, M21), (M12, M22)]

   396      handle Library.UnequalLengths =>

   397             raise MTYPE ("Nitpick_Mono.do_mtype_comp", [M1, M2], []))

   398   | do_mtype_comp _ _ (MType _) (MType _) accum =

   399     accum (* no need to compare them thanks to the cache *)

   400   | do_mtype_comp cmp _ M1 M2 _ =

   401     raise MTYPE ("Nitpick_Mono.do_mtype_comp (" ^ string_for_comp_op cmp ^ ")",

   402                  [M1, M2], [])

   404 fun add_mtype_comp cmp M1 M2 ((lits, comps, sexps) : constraint_set) =

   405     (print_g (fn () => "*** Add " ^ string_for_mtype M1 ^ " " ^

   406                        string_for_comp_op cmp ^ " " ^ string_for_mtype M2);

   407      case do_mtype_comp cmp [] M1 M2 (SOME (lits, comps)) of

   408        NONE => (print_g (K "**** Unsolvable"); raise UNSOLVABLE ())

   409      | SOME (lits, comps) => (lits, comps, sexps))

   411 val add_mtypes_equal = add_mtype_comp Eq

   412 val add_is_sub_mtype = add_mtype_comp Leq

   414 fun do_notin_mtype_fv _ _ _ NONE = NONE

   415   | do_notin_mtype_fv Minus _ MAlpha accum = accum

   416   | do_notin_mtype_fv Plus [] MAlpha _ = NONE

   417   | do_notin_mtype_fv Plus [(x, sn)] MAlpha (SOME (lits, sexps)) =

   418     SOME lits |> do_literal (x, sn) |> Option.map (rpair sexps)

   419   | do_notin_mtype_fv Plus sexp MAlpha (SOME (lits, sexps)) =

   420     SOME (lits, insert (op =) sexp sexps)

   421   | do_notin_mtype_fv sn sexp (MFun (M1, S sn', M2)) accum =

   422     accum |> (if sn' = Plus andalso sn = Plus then

   423                 do_notin_mtype_fv Plus sexp M1

   424               else

   425                 I)

   426           |> (if sn' = Minus orelse sn = Plus then

   427                 do_notin_mtype_fv Minus sexp M1

   428               else

   429                 I)

   430           |> do_notin_mtype_fv sn sexp M2

   431   | do_notin_mtype_fv Plus sexp (MFun (M1, V x, M2)) accum =

   432     accum |> (case do_literal (x, Minus) (SOME sexp) of

   433                 NONE => I

   434               | SOME sexp' => do_notin_mtype_fv Plus sexp' M1)

   435           |> do_notin_mtype_fv Minus sexp M1

   436           |> do_notin_mtype_fv Plus sexp M2

   437   | do_notin_mtype_fv Minus sexp (MFun (M1, V x, M2)) accum =

   438     accum |> (case do_literal (x, Plus) (SOME sexp) of

   439                 NONE => I

   440               | SOME sexp' => do_notin_mtype_fv Plus sexp' M1)

   441           |> do_notin_mtype_fv Minus sexp M2

   442   | do_notin_mtype_fv sn sexp (MPair (M1, M2)) accum =

   443     accum |> fold (do_notin_mtype_fv sn sexp) [M1, M2]

   444   | do_notin_mtype_fv sn sexp (MType (_, Ms)) accum =

   445     accum |> fold (do_notin_mtype_fv sn sexp) Ms

   446   | do_notin_mtype_fv _ _ M _ =

   447     raise MTYPE ("Nitpick_Mono.do_notin_mtype_fv", [M], [])

   449 fun add_notin_mtype_fv sn M ((lits, comps, sexps) : constraint_set) =

   450     (print_g (fn () => "*** Add " ^ string_for_mtype M ^ " is " ^

   451                        (case sn of Minus => "concrete" | Plus => "complete") ^

   452                        ".");

   453      case do_notin_mtype_fv sn [] M (SOME (lits, sexps)) of

   454        NONE => (print_g (K "**** Unsolvable"); raise UNSOLVABLE ())

   455      | SOME (lits, sexps) => (lits, comps, sexps))

   457 val add_mtype_is_concrete = add_notin_mtype_fv Minus

   458 val add_mtype_is_complete = add_notin_mtype_fv Plus

   460 val bool_from_minus = true

   462 fun bool_from_sign Plus = not bool_from_minus

   463   | bool_from_sign Minus = bool_from_minus

   464 fun sign_from_bool b = if b = bool_from_minus then Minus else Plus

   466 fun prop_for_literal (x, sn) =

   467   (not (bool_from_sign sn) ? PropLogic.Not) (PropLogic.BoolVar x)

   468 fun prop_for_sign_atom_eq (S sn', sn) =

   469     if sn = sn' then PropLogic.True else PropLogic.False

   470   | prop_for_sign_atom_eq (V x, sn) = prop_for_literal (x, sn)

   471 fun prop_for_sign_expr xs = PropLogic.exists (map prop_for_literal xs)

   472 fun prop_for_exists_eq xs sn =

   473   PropLogic.exists (map (fn x => prop_for_literal (x, sn)) xs)

   474 fun prop_for_comp (a1, a2, Eq, []) =

   475     PropLogic.SAnd (prop_for_comp (a1, a2, Leq, []),

   476                     prop_for_comp (a2, a1, Leq, []))

   477   | prop_for_comp (a1, a2, Leq, []) =

   478     PropLogic.SOr (prop_for_sign_atom_eq (a1, Plus),

   479                    prop_for_sign_atom_eq (a2, Minus))

   480   | prop_for_comp (a1, a2, cmp, xs) =

   481     PropLogic.SOr (prop_for_exists_eq xs Minus, prop_for_comp (a1, a2, cmp, []))

   483 fun literals_from_assignments max_var assigns lits =

   484   fold (fn x => fn accum =>

   485            if AList.defined (op =) lits x then

   486              accum

   487            else case assigns x of

   488              SOME b => (x, sign_from_bool b) :: accum

   489            | NONE => accum) (max_var downto 1) lits

   491 fun string_for_comp (a1, a2, cmp, xs) =

   492   string_for_sign_atom a1 ^ " " ^ string_for_comp_op cmp ^

   493   subscript_string_for_vars " \<and> " xs ^ " " ^ string_for_sign_atom a2

   495 fun print_problem lits comps sexps =

   496   print_g (fn () => "*** Problem:\n" ^

   497                     cat_lines (map string_for_literal lits @

   498                                map string_for_comp comps @

   499                                map string_for_sign_expr sexps))

   501 fun print_solution lits =

   502   let val (pos, neg) = List.partition (curry (op =) Plus o snd) lits in

   503     print_g (fn () => "*** Solution:\n" ^

   504                       "+: " ^ commas (map (string_for_var o fst) pos) ^ "\n" ^

   505                       "-: " ^ commas (map (string_for_var o fst) neg))

   506   end

   508 fun solve max_var (lits, comps, sexps) =

   509     let

   510       fun do_assigns assigns =

   511         SOME (literals_from_assignments max_var assigns lits

   512               |> tap print_solution)

   513       val _ = print_problem lits comps sexps

   514       val prop = PropLogic.all (map prop_for_literal lits @

   515                                 map prop_for_comp comps @

   516                                 map prop_for_sign_expr sexps)

   517       val default_val = bool_from_sign Minus

   518     in

   519       if PropLogic.eval (K default_val) prop then

   520         do_assigns (K (SOME default_val))

   521       else

   522         let

   523           (* use the first ML solver (to avoid startup overhead) *)

   524           val solvers = !SatSolver.solvers

   525                         |> filter (member (op =) ["dptsat", "dpll"] o fst)

   526         in

   527           case snd (hd solvers) prop of

   528             SatSolver.SATISFIABLE assigns => do_assigns assigns

   529           | _ => NONE

   530         end

   531     end

   533 type mtype_schema = mtyp * constraint_set

   534 type mtype_context =

   535   {bound_Ts: typ list,

   536    bound_Ms: mtyp list,

   537    frees: (styp * mtyp) list,

   538    consts: (styp * mtyp) list}

   540 type accumulator = mtype_context * constraint_set

   542 val initial_gamma = {bound_Ts = [], bound_Ms = [], frees = [], consts = []}

   544 fun push_bound T M {bound_Ts, bound_Ms, frees, consts} =

   545   {bound_Ts = T :: bound_Ts, bound_Ms = M :: bound_Ms, frees = frees,

   546    consts = consts}

   547 fun pop_bound {bound_Ts, bound_Ms, frees, consts} =

   548   {bound_Ts = tl bound_Ts, bound_Ms = tl bound_Ms, frees = frees,

   549    consts = consts}

   550   handle List.Empty => initial_gamma (* FIXME: needed? *)

   552 fun consider_term (mdata as {hol_ctxt as {thy, ctxt, stds, fast_descrs,

   553                                           def_table, ...},

   554                              alpha_T, max_fresh, ...}) =

   555   let

   556     fun is_enough_eta_expanded t =

   557       case strip_comb t of

   558         (Const x, ts) =>

   559         the_default 0 (arity_of_built_in_const thy stds fast_descrs x)

   560         <= length ts

   561       | _ => true

   562     val mtype_for = fresh_mtype_for_type mdata false

   563     fun plus_set_mtype_for_dom M =

   564       MFun (M, S (if exists_alpha_sub_mtype M then Plus else Minus), bool_M)

   565     fun do_all T (gamma, cset) =

   566       let

   567         val abs_M = mtype_for (domain_type (domain_type T))

   568         val body_M = mtype_for (body_type T)

   569       in

   570         (MFun (MFun (abs_M, S Minus, body_M), S Minus, body_M),

   571          (gamma, cset |> add_mtype_is_complete abs_M))

   572       end

   573     fun do_equals T (gamma, cset) =

   574       let val M = mtype_for (domain_type T) in

   575         (MFun (M, S Minus, MFun (M, V (Unsynchronized.inc max_fresh),

   576                                  mtype_for (nth_range_type 2 T))),

   577          (gamma, cset |> add_mtype_is_concrete M))

   578       end

   579     fun do_robust_set_operation T (gamma, cset) =

   580       let

   581         val set_T = domain_type T

   582         val M1 = mtype_for set_T

   583         val M2 = mtype_for set_T

   584         val M3 = mtype_for set_T

   585       in

   586         (MFun (M1, S Minus, MFun (M2, S Minus, M3)),

   587          (gamma, cset |> add_is_sub_mtype M1 M3 |> add_is_sub_mtype M2 M3))

   588       end

   589     fun do_fragile_set_operation T (gamma, cset) =

   590       let

   591         val set_T = domain_type T

   592         val set_M = mtype_for set_T

   593         fun custom_mtype_for (T as Type (@{type_name fun}, [T1, T2])) =

   594             if T = set_T then set_M

   595             else MFun (custom_mtype_for T1, S Minus, custom_mtype_for T2)

   596           | custom_mtype_for T = mtype_for T

   597       in

   598         (custom_mtype_for T, (gamma, cset |> add_mtype_is_concrete set_M))

   599       end

   600     fun do_pair_constr T accum =

   601       case mtype_for (nth_range_type 2 T) of

   602         M as MPair (a_M, b_M) =>

   603         (MFun (a_M, S Minus, MFun (b_M, S Minus, M)), accum)

   604       | M => raise MTYPE ("Nitpick_Mono.consider_term.do_pair_constr", [M], [])

   605     fun do_nth_pair_sel n T =

   606       case mtype_for (domain_type T) of

   607         M as MPair (a_M, b_M) =>

   608         pair (MFun (M, S Minus, if n = 0 then a_M else b_M))

   609       | M => raise MTYPE ("Nitpick_Mono.consider_term.do_nth_pair_sel", [M], [])

   610     fun do_bounded_quantifier t0 abs_s abs_T connective_t bound_t body_t accum =

   611       let

   612         val abs_M = mtype_for abs_T

   613         val (bound_m, accum) =

   614           accum |>> push_bound abs_T abs_M |> do_term bound_t

   615         val expected_bound_M = plus_set_mtype_for_dom abs_M

   616         val (body_m, accum) =

   617           accum ||> add_mtypes_equal expected_bound_M (mtype_of_mterm bound_m)

   618                 |> do_term body_t ||> apfst pop_bound

   619         val bound_M = mtype_of_mterm bound_m

   620         val (M1, a, M2) = dest_MFun bound_M

   621       in

   622         (MApp (MRaw (t0, MFun (bound_M, S Minus, bool_M)),

   623                MAbs (abs_s, abs_T, M1, a,

   624                      MApp (MApp (MRaw (connective_t,

   625                                        mtype_for (fastype_of connective_t)),

   626                                  MApp (bound_m, MRaw (Bound 0, M1))),

   627                            body_m))), accum)

   628       end

   629     and do_term t (accum as (gamma as {bound_Ts, bound_Ms, frees, consts},

   630                              cset)) =

   631         (print_g (fn () => "  \<Gamma> \<turnstile> " ^

   632                            Syntax.string_of_term ctxt t ^ " : _?");

   633          case t of

   634            Const (x as (s, T)) =>

   635            (case AList.lookup (op =) consts x of

   636               SOME M => (M, accum)

   637             | NONE =>

   638               if not (could_exist_alpha_subtype alpha_T T) then

   639                 (mtype_for T, accum)

   640               else case s of

   641                 @{const_name all} => do_all T accum

   642               | @{const_name "=="} => do_equals T accum

   643               | @{const_name All} => do_all T accum

   644               | @{const_name Ex} =>

   645                 let val set_T = domain_type T in

   646                   do_term (Abs (Name.uu, set_T,

   647                                 @{const Not} $ (HOLogic.mk_eq

   648                                     (Abs (Name.uu, domain_type set_T,

   649                                           @{const False}),

   650                                      Bound 0)))) accum

   651                   |>> mtype_of_mterm

   652                 end

   653               | @{const_name "op ="} => do_equals T accum

   654               | @{const_name The} =>

   655                 (print_g (K "*** The"); raise UNSOLVABLE ())

   656               | @{const_name Eps} =>

   657                 (print_g (K "*** Eps"); raise UNSOLVABLE ())

   658               | @{const_name If} =>

   659                 do_robust_set_operation (range_type T) accum

   660                 |>> curry3 MFun bool_M (S Minus)

   661               | @{const_name Pair} => do_pair_constr T accum

   662               | @{const_name fst} => do_nth_pair_sel 0 T accum

   663               | @{const_name snd} => do_nth_pair_sel 1 T accum

   664               | @{const_name Id} =>

   665                 (MFun (mtype_for (domain_type T), S Minus, bool_M), accum)

   666               | @{const_name converse} =>

   667                 let

   668                   val x = Unsynchronized.inc max_fresh

   669                   fun mtype_for_set T =

   670                     MFun (mtype_for (domain_type T), V x, bool_M)

   671                   val ab_set_M = domain_type T |> mtype_for_set

   672                   val ba_set_M = range_type T |> mtype_for_set

   673                 in (MFun (ab_set_M, S Minus, ba_set_M), accum) end

   674               | @{const_name trancl} => do_fragile_set_operation T accum

   675               | @{const_name rel_comp} =>

   676                 let

   677                   val x = Unsynchronized.inc max_fresh

   678                   fun mtype_for_set T =

   679                     MFun (mtype_for (domain_type T), V x, bool_M)

   680                   val bc_set_M = domain_type T |> mtype_for_set

   681                   val ab_set_M = domain_type (range_type T) |> mtype_for_set

   682                   val ac_set_M = nth_range_type 2 T |> mtype_for_set

   683                 in

   684                   (MFun (bc_set_M, S Minus, MFun (ab_set_M, S Minus, ac_set_M)),

   685                    accum)

   686                 end

   687               | @{const_name image} =>

   688                 let

   689                   val a_M = mtype_for (domain_type (domain_type T))

   690                   val b_M = mtype_for (range_type (domain_type T))

   691                 in

   692                   (MFun (MFun (a_M, S Minus, b_M), S Minus,

   693                          MFun (plus_set_mtype_for_dom a_M, S Minus,

   694                                plus_set_mtype_for_dom b_M)), accum)

   695                 end

   696               | @{const_name finite} =>

   697                 let val M1 = mtype_for (domain_type (domain_type T)) in

   698                   (MFun (plus_set_mtype_for_dom M1, S Minus, bool_M), accum)

   699                 end

   700               | @{const_name Sigma} =>

   701                 let

   702                   val x = Unsynchronized.inc max_fresh

   703                   fun mtype_for_set T =

   704                     MFun (mtype_for (domain_type T), V x, bool_M)

   705                   val a_set_T = domain_type T

   706                   val a_M = mtype_for (domain_type a_set_T)

   707                   val b_set_M = mtype_for_set (range_type (domain_type

   708                                                                (range_type T)))

   709                   val a_set_M = mtype_for_set a_set_T

   710                   val a_to_b_set_M = MFun (a_M, S Minus, b_set_M)

   711                   val ab_set_M = mtype_for_set (nth_range_type 2 T)

   712                 in

   713                   (MFun (a_set_M, S Minus,

   714                          MFun (a_to_b_set_M, S Minus, ab_set_M)), accum)

   715                 end

   716               | _ =>

   717                 if s = @{const_name safe_The} orelse

   718                    s = @{const_name safe_Eps} then

   719                   let

   720                     val a_set_M = mtype_for (domain_type T)

   721                     val a_M = dest_MFun a_set_M |> #1

   722                   in (MFun (a_set_M, S Minus, a_M), accum) end

   723                 else if s = @{const_name ord_class.less_eq} andalso

   724                         is_set_type (domain_type T) then

   725                   do_fragile_set_operation T accum

   726                 else if is_sel s then

   727                   (mtype_for_sel mdata x, accum)

   728                 else if is_constr ctxt stds x then

   729                   (mtype_for_constr mdata x, accum)

   730                 else if is_built_in_const thy stds fast_descrs x then

   731                   (fresh_mtype_for_type mdata true T, accum)

   732                 else

   733                   let val M = mtype_for T in

   734                     (M, ({bound_Ts = bound_Ts, bound_Ms = bound_Ms,

   735                           frees = frees, consts = (x, M) :: consts}, cset))

   736                   end) |>> curry MRaw t

   737          | Free (x as (_, T)) =>

   738            (case AList.lookup (op =) frees x of

   739               SOME M => (M, accum)

   740             | NONE =>

   741               let val M = mtype_for T in

   742                 (M, ({bound_Ts = bound_Ts, bound_Ms = bound_Ms,

   743                       frees = (x, M) :: frees, consts = consts}, cset))

   744               end) |>> curry MRaw t

   745          | Var _ => (print_g (K "*** Var"); raise UNSOLVABLE ())

   746          | Bound j => (MRaw (t, nth bound_Ms j), accum)

   747          | Abs (s, T, t') =>

   748            (case fin_fun_body T (fastype_of1 (T :: bound_Ts, t')) t' of

   749               SOME t' =>

   750               let

   751                 val M = mtype_for T

   752                 val a = V (Unsynchronized.inc max_fresh)

   753                 val (m', accum) = do_term t' (accum |>> push_bound T M)

   754               in (MAbs (s, T, M, a, m'), accum |>> pop_bound) end

   755             | NONE =>

   756               ((case t' of

   757                   t1' $ Bound 0 =>

   758                   if not (loose_bvar1 (t1', 0)) andalso

   759                      is_enough_eta_expanded t1' then

   760                     do_term (incr_boundvars ~1 t1') accum

   761                   else

   762                     raise SAME ()

   763                 | (t11 as Const (@{const_name "op ="}, _)) $ Bound 0 $ t13 =>

   764                   if not (loose_bvar1 (t13, 0)) then

   765                     do_term (incr_boundvars ~1 (t11 $ t13)) accum

   766                   else

   767                     raise SAME ()

   768                 | _ => raise SAME ())

   769                handle SAME () =>

   770                       let

   771                         val M = mtype_for T

   772                         val (m', accum) = do_term t' (accum |>> push_bound T M)

   773                       in

   774                         (MAbs (s, T, M, S Minus, m'), accum |>> pop_bound)

   775                       end))

   776          | (t0 as Const (@{const_name All}, _))

   777            $ Abs (s', T', (t10 as @{const "op -->"}) $ (t11 $ Bound 0) $ t12) =>

   778            do_bounded_quantifier t0 s' T' t10 t11 t12 accum

   779          | (t0 as Const (@{const_name Ex}, _))

   780            $ Abs (s', T', (t10 as @{const "op &"}) $ (t11 $ Bound 0) $ t12) =>

   781            do_bounded_quantifier t0 s' T' t10 t11 t12 accum

   782          | Const (@{const_name Let}, _) $ t1 $ t2 =>

   783            do_term (betapply (t2, t1)) accum

   784          | t1 $ t2 =>

   785            let

   786              val (m1, accum) = do_term t1 accum

   787              val (m2, accum) = do_term t2 accum

   788            in

   789              let

   790                val T11 = domain_type (fastype_of1 (bound_Ts, t1))

   791                val T2 = fastype_of1 (bound_Ts, t2)

   792                val M11 = mtype_of_mterm m1 |> dest_MFun |> #1

   793                val M2 = mtype_of_mterm m2

   794              in (MApp (m1, m2), accum ||> add_is_sub_mtype M2 M11) end

   795            end)

   796         |> tap (fn (m, _) => print_g (fn () => "  \<Gamma> \<turnstile> " ^

   797                                                string_for_mterm ctxt m))

   798   in do_term end

   800 fun force_minus_funs 0 _ = I

   801   | force_minus_funs n (M as MFun (M1, _, M2)) =

   802     add_mtypes_equal M (MFun (M1, S Minus, M2))

   803     #> force_minus_funs (n - 1) M2

   804   | force_minus_funs _ M =

   805     raise MTYPE ("Nitpick_Mono.force_minus_funs", [M], [])

   806 fun consider_general_equals mdata def (x as (_, T)) t1 t2 accum =

   807   let

   808     val (m1, accum) = consider_term mdata t1 accum

   809     val (m2, accum) = consider_term mdata t2 accum

   810     val M1 = mtype_of_mterm m1

   811     val M2 = mtype_of_mterm m2

   812     val accum = accum ||> add_mtypes_equal M1 M2

   813     val body_M = fresh_mtype_for_type mdata false (nth_range_type 2 T)

   814     val m = MApp (MApp (MRaw (Const x,

   815                 MFun (M1, S Minus, MFun (M2, S Minus, body_M))), m1), m2)

   816   in

   817     (m, if def then

   818           let val (head_m, arg_ms) = strip_mcomb m1 in

   819             accum ||> force_minus_funs (length arg_ms) (mtype_of_mterm head_m)

   820           end

   821         else

   822           accum)

   823   end

   825 fun consider_general_formula (mdata as {hol_ctxt = {ctxt, ...}, ...}) =

   826   let

   827     val mtype_for = fresh_mtype_for_type mdata false

   828     val do_term = consider_term mdata

   829     fun do_formula sn t accum =

   830         let

   831           fun do_quantifier (quant_x as (quant_s, _)) abs_s abs_T body_t =

   832             let

   833               val abs_M = mtype_for abs_T

   834               val side_cond = ((sn = Minus) = (quant_s = @{const_name Ex}))

   835               val (body_m, accum) =

   836                 accum ||> side_cond ? add_mtype_is_complete abs_M

   837                       |>> push_bound abs_T abs_M |> do_formula sn body_t

   838               val body_M = mtype_of_mterm body_m

   839             in

   840               (MApp (MRaw (Const quant_x,

   841                            MFun (MFun (abs_M, S Minus, body_M), S Minus,

   842                                  body_M)),

   843                      MAbs (abs_s, abs_T, abs_M, S Minus, body_m)),

   844                accum |>> pop_bound)

   845             end

   846           fun do_equals x t1 t2 =

   847             case sn of

   848               Plus => do_term t accum

   849             | Minus => consider_general_equals mdata false x t1 t2 accum

   850         in

   851           (print_g (fn () => "  \<Gamma> \<turnstile> " ^

   852                            Syntax.string_of_term ctxt t ^ " : o\<^sup>" ^

   853                            string_for_sign sn ^ "?");

   854            case t of

   855              Const (x as (@{const_name all}, _)) $ Abs (s1, T1, t1) =>

   856              do_quantifier x s1 T1 t1

   857            | Const (x as (@{const_name "=="}, _)) $ t1 $ t2 => do_equals x t1 t2

   858            | @{const Trueprop} $ t1 =>

   859              let val (m1, accum) = do_formula sn t1 accum in

   860                (MApp (MRaw (@{const Trueprop}, mtype_for (bool_T --> prop_T)),

   861                       m1), accum)

   862              end

   863            | @{const Not} $ t1 =>

   864              let val (m1, accum) = do_formula (negate sn) t1 accum in

   865                (MApp (MRaw (@{const Not}, mtype_for (bool_T --> bool_T)), m1),

   866                 accum)

   867              end

   868            | Const (x as (@{const_name All}, _)) $ Abs (s1, T1, t1) =>

   869              do_quantifier x s1 T1 t1

   870            | Const (x0 as (s0 as @{const_name Ex}, T0))

   871              $ (t1 as Abs (s1, T1, t1')) =>

   872              (case sn of

   873                 Plus => do_quantifier x0 s1 T1 t1'

   874               | Minus =>

   875                 (* FIXME: Move elsewhere *)

   876                 do_term (@{const Not}

   877                          $ (HOLogic.eq_const (domain_type T0) $ t1

   878                             $ Abs (Name.uu, T1, @{const False}))) accum)

   879            | Const (x as (@{const_name "op ="}, _)) $ t1 $ t2 =>

   880              do_equals x t1 t2

   881            | Const (@{const_name Let}, _) $ t1 $ t2 =>

   882              do_formula sn (betapply (t2, t1)) accum

   883            | (t0 as Const (s0, _)) $ t1 $ t2 =>

   884              if s0 = @{const_name "==>"} orelse s0 = @{const_name "op &"} orelse

   885                 s0 = @{const_name "op |"} orelse

   886                 s0 = @{const_name "op -->"} then

   887                let

   888                  val impl = (s0 = @{const_name "==>"} orelse

   889                              s0 = @{const_name "op -->"})

   890                  val (m1, accum) = do_formula (sn |> impl ? negate) t1 accum

   891                  val (m2, accum) = do_formula sn t2 accum

   892                in

   893                  (MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2),

   894                   accum)

   895                end

   896              else

   897                do_term t accum

   898            | _ => do_term t accum)

   899         end

   900         |> tap (fn (m, _) =>

   901                    print_g (fn () => "\<Gamma> \<turnstile> " ^

   902                                      string_for_mterm ctxt m ^ " : o\<^sup>" ^

   903                                      string_for_sign sn))

   904   in do_formula end

   906 (* The harmless axiom optimization below is somewhat too aggressive in the face

   907    of (rather peculiar) user-defined axioms. *)

   908 val harmless_consts =

   909   [@{const_name ord_class.less}, @{const_name ord_class.less_eq}]

   910 val bounteous_consts = [@{const_name bisim}]

   912 fun is_harmless_axiom ({no_harmless = true, ...} : mdata) _ = false

   913   | is_harmless_axiom {hol_ctxt = {thy, stds, fast_descrs, ...}, ...} t =

   914     Term.add_consts t []

   915     |> filter_out (is_built_in_const thy stds fast_descrs)

   916     |> (forall (member (op =) harmless_consts o original_name o fst) orf

   917         exists (member (op =) bounteous_consts o fst))

   919 fun consider_nondefinitional_axiom mdata t =

   920   if is_harmless_axiom mdata t then pair (MRaw (t, dummy_M))

   921   else consider_general_formula mdata Plus t

   923 fun consider_definitional_axiom (mdata as {hol_ctxt = {ctxt, ...}, ...}) t =

   924   if not (is_constr_pattern_formula ctxt t) then

   925     consider_nondefinitional_axiom mdata t

   926   else if is_harmless_axiom mdata t then

   927     pair (MRaw (t, dummy_M))

   928   else

   929     let

   930       val mtype_for = fresh_mtype_for_type mdata false

   931       val do_term = consider_term mdata

   932       fun do_all quant_t abs_s abs_T body_t accum =

   933         let

   934           val abs_M = mtype_for abs_T

   935           val (body_m, accum) =

   936             accum |>> push_bound abs_T abs_M |> do_formula body_t

   937           val body_M = mtype_of_mterm body_m

   938         in

   939           (MApp (MRaw (quant_t,

   940                        MFun (MFun (abs_M, S Minus, body_M), S Minus, body_M)),

   941                  MAbs (abs_s, abs_T, abs_M, S Minus, body_m)),

   942            accum |>> pop_bound)

   943         end

   944       and do_conjunction t0 t1 t2 accum =

   945         let

   946           val (m1, accum) = do_formula t1 accum

   947           val (m2, accum) = do_formula t2 accum

   948         in

   949           (MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2), accum)

   950         end

   951       and do_implies t0 t1 t2 accum =

   952         let

   953           val (m1, accum) = do_term t1 accum

   954           val (m2, accum) = do_formula t2 accum

   955         in

   956           (MApp (MApp (MRaw (t0, mtype_for (fastype_of t0)), m1), m2), accum)

   957         end

   958       and do_formula t accum =

   959           case t of

   960             (t0 as Const (@{const_name all}, _)) $ Abs (s1, T1, t1) =>

   961             do_all t0 s1 T1 t1 accum

   962           | @{const Trueprop} $ t1 =>

   963             let val (m1, accum) = do_formula t1 accum in

   964               (MApp (MRaw (@{const Trueprop}, mtype_for (bool_T --> prop_T)),

   965                      m1), accum)

   966             end

   967           | Const (x as (@{const_name "=="}, _)) $ t1 $ t2 =>

   968             consider_general_equals mdata true x t1 t2 accum

   969           | (t0 as @{const "==>"}) $ t1 $ t2 => do_implies t0 t1 t2 accum

   970           | (t0 as @{const Pure.conjunction}) $ t1 $ t2 =>

   971             do_conjunction t0 t1 t2 accum

   972           | (t0 as Const (@{const_name All}, _)) $ Abs (s0, T1, t1) =>

   973             do_all t0 s0 T1 t1 accum

   974           | Const (x as (@{const_name "op ="}, _)) $ t1 $ t2 =>

   975             consider_general_equals mdata true x t1 t2 accum

   976           | (t0 as @{const "op &"}) $ t1 $ t2 => do_conjunction t0 t1 t2 accum

   977           | (t0 as @{const "op -->"}) $ t1 $ t2 => do_implies t0 t1 t2 accum

   978           | _ => raise TERM ("Nitpick_Mono.consider_definitional_axiom.\

   979                              \do_formula", [t])

   980     in do_formula t end

   982 fun string_for_mtype_of_term ctxt lits t M =

   983   Syntax.string_of_term ctxt t ^ " : " ^ string_for_mtype (resolve_mtype lits M)

   985 fun print_mtype_context ctxt lits ({frees, consts, ...} : mtype_context) =

   986   print_g (fn () =>

   987       map (fn (x, M) => string_for_mtype_of_term ctxt lits (Free x) M) frees @

   988       map (fn (x, M) => string_for_mtype_of_term ctxt lits (Const x) M) consts

   989       |> cat_lines)

   991 fun amass f t (ms, accum) =

   992   let val (m, accum) = f t accum in (m :: ms, accum) end

   994 fun infer which no_harmless (hol_ctxt as {ctxt, ...}) binarize alpha_T

   995           (nondef_ts, def_ts) =

   996   let

   997     val _ = print_g (fn () => "****** " ^ which ^ " analysis: " ^

   998                               string_for_mtype MAlpha ^ " is " ^

   999                               Syntax.string_of_typ ctxt alpha_T)

  1000     val mdata as {max_fresh, constr_mcache, ...} =

  1001       initial_mdata hol_ctxt binarize no_harmless alpha_T

  1002     val accum = (initial_gamma, ([], [], []))

  1003     val (nondef_ms, accum) =

  1004       ([], accum) |> amass (consider_general_formula mdata Plus) (hd nondef_ts)

  1005                   |> fold (amass (consider_nondefinitional_axiom mdata))

  1006                           (tl nondef_ts)

  1007     val (def_ms, (gamma, cset)) =

  1008       ([], accum) |> fold (amass (consider_definitional_axiom mdata)) def_ts

  1009   in

  1010     case solve (!max_fresh) cset of

  1011       SOME lits => (print_mtype_context ctxt lits gamma;

  1012                     SOME (lits, (nondef_ms, def_ms), !constr_mcache))

  1013     | _ => NONE

  1014   end

  1015   handle UNSOLVABLE () => NONE

  1016        | MTYPE (loc, Ms, Ts) =>

  1017          raise BAD (loc, commas (map string_for_mtype Ms @

  1018                                  map (Syntax.string_of_typ ctxt) Ts))

  1019        | MTERM (loc, ms) =>

  1020          raise BAD (loc, commas (map (string_for_mterm ctxt) ms))

  1022 val formulas_monotonic = is_some oooo infer "Monotonicity" false

  1024 fun fin_fun_constr T1 T2 =

  1025   (@{const_name FinFun}, (T1 --> T2) --> Type (@{type_name fin_fun}, [T1, T2]))

  1027 fun finitize_funs (hol_ctxt as {thy, ctxt, stds, fast_descrs, constr_cache,

  1028                                 ...})

  1029                   binarize finitizes alpha_T tsp =

  1030   case infer "Finiteness" true hol_ctxt binarize alpha_T tsp of

  1031     SOME (lits, msp, constr_mtypes) =>

  1032     if forall (curry (op =) Minus o snd) lits then

  1033       tsp

  1034     else

  1035       let

  1036         fun should_finitize T a =

  1037           case triple_lookup (type_match thy) finitizes T of

  1038             SOME (SOME false) => false

  1039           | _ => resolve_sign_atom lits a = S Plus

  1040         fun type_from_mtype T M =

  1041           case (M, T) of

  1042             (MAlpha, _) => T

  1043           | (MFun (M1, a, M2), Type (@{type_name fun}, Ts)) =>

  1044             Type (if should_finitize T a then @{type_name fin_fun}

  1045                   else @{type_name fun}, map2 type_from_mtype Ts [M1, M2])

  1046           | (MPair (M1, M2), Type (@{type_name Product_Type.prod}, Ts)) =>

  1047             Type (@{type_name Product_Type.prod}, map2 type_from_mtype Ts [M1, M2])

  1048           | (MType _, _) => T

  1049           | _ => raise MTYPE ("Nitpick_Mono.finitize_funs.type_from_mtype",

  1050                               [M], [T])

  1051         fun finitize_constr (x as (s, T)) =

  1052           (s, case AList.lookup (op =) constr_mtypes x of

  1053                 SOME M => type_from_mtype T M

  1054               | NONE => T)

  1055         fun term_from_mterm new_Ts old_Ts m =

  1056           case m of

  1057             MRaw (t, M) =>

  1058             let

  1059               val T = fastype_of1 (old_Ts, t)

  1060               val T' = type_from_mtype T M

  1061             in

  1062               case t of

  1063                 Const (x as (s, _)) =>

  1064                 if s = @{const_name finite} then

  1065                   case domain_type T' of

  1066                     set_T' as Type (@{type_name fin_fun}, _) =>

  1067                     Abs (Name.uu, set_T', @{const True})

  1068                   | _ => Const (s, T')

  1069                 else if s = @{const_name "=="} orelse

  1070                         s = @{const_name "op ="} then

  1071                   let

  1072                     val T =

  1073                       case T' of

  1074                         Type (_, [T1, Type (_, [T2, T3])]) =>

  1075                         T1 --> T2 --> T3

  1076                       | _ => raise TYPE ("Nitpick_Mono.finitize_funs.\

  1077                                          \term_from_mterm", [T, T'], [])

  1078                   in coerce_term hol_ctxt new_Ts T' T (Const (s, T)) end

  1079                 else if is_built_in_const thy stds fast_descrs x then

  1080                   coerce_term hol_ctxt new_Ts T' T t

  1081                 else if is_constr ctxt stds x then

  1082                   Const (finitize_constr x)

  1083                 else if is_sel s then

  1084                   let

  1085                     val n = sel_no_from_name s

  1086                     val x' =

  1087                       x |> binarized_and_boxed_constr_for_sel hol_ctxt binarize

  1088                         |> finitize_constr

  1089                     val x'' =

  1090                       binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize

  1091                                                              x' n

  1092                   in Const x'' end

  1093                 else

  1094                   Const (s, T')

  1095               | Free (s, T) => Free (s, type_from_mtype T M)

  1096               | Bound _ => t

  1097               | _ => raise MTERM ("Nitpick_Mono.finitize_funs.term_from_mterm",

  1098                                   [m])

  1099             end

  1100           | MApp (m1, m2) =>

  1101             let

  1102               val (t1, t2) = pairself (term_from_mterm new_Ts old_Ts) (m1, m2)

  1103               val (T1, T2) = pairself (curry fastype_of1 new_Ts) (t1, t2)

  1104               val (t1', T2') =

  1105                 case T1 of

  1106                   Type (s, [T11, T12]) =>

  1107                   (if s = @{type_name fin_fun} then

  1108                      select_nth_constr_arg ctxt stds (fin_fun_constr T11 T12) t1

  1109                                            0 (T11 --> T12)

  1110                    else

  1111                      t1, T11)

  1112                 | _ => raise TYPE ("Nitpick_Mono.finitize_funs.term_from_mterm",

  1113                                    [T1], [])

  1114             in betapply (t1', coerce_term hol_ctxt new_Ts T2' T2 t2) end

  1115           | MAbs (s, old_T, M, a, m') =>

  1116             let

  1117               val new_T = type_from_mtype old_T M

  1118               val t' = term_from_mterm (new_T :: new_Ts) (old_T :: old_Ts) m'

  1119               val T' = fastype_of1 (new_T :: new_Ts, t')

  1120             in

  1121               Abs (s, new_T, t')

  1122               |> should_finitize (new_T --> T') a

  1123                  ? construct_value ctxt stds (fin_fun_constr new_T T') o single

  1124             end

  1125       in

  1126         Unsynchronized.change constr_cache (map (apsnd (map finitize_constr)));

  1127         pairself (map (term_from_mterm [] [])) msp

  1128       end

  1129   | NONE => tsp

  1131 end;

author	blanchet
	Sat, 03 Jul 2010 00:50:35 +0200
changeset 37695	c6161bee8486
parent 37678	0040bafffdef
child 38406	7207321df8af
permissions	-rw-r--r--