src/Pure/term.ML
author wenzelm
Sun Mar 01 23:36:12 2009 +0100 (2009-03-01)
changeset 30190 479806475f3c
parent 30146 a77fc0209723
child 30242 aea5d7fa7ef5
permissions -rw-r--r--
use long names for old-style fold combinators;
wenzelm@9536
     1
(*  Title:      Pure/term.ML
wenzelm@9536
     2
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
wenzelm@29280
     3
    Author:     Makarius
clasohm@1364
     4
wenzelm@4444
     5
Simply typed lambda-calculus: types, terms, and basic operations.
clasohm@0
     6
*)
clasohm@0
     7
wenzelm@29257
     8
infix 9 $;
clasohm@1364
     9
infixr 5 -->;
wenzelm@4444
    10
infixr --->;
wenzelm@4444
    11
infix aconv;
clasohm@1364
    12
wenzelm@4444
    13
signature BASIC_TERM =
wenzelm@4444
    14
sig
wenzelm@22572
    15
  eqtype indexname
wenzelm@22572
    16
  eqtype class
wenzelm@22572
    17
  eqtype sort
wenzelm@22572
    18
  eqtype arity
wenzelm@4444
    19
  datatype typ =
wenzelm@4444
    20
    Type  of string * typ list |
wenzelm@4444
    21
    TFree of string * sort |
wenzelm@4444
    22
    TVar  of indexname * sort
wenzelm@16537
    23
  datatype term =
wenzelm@16537
    24
    Const of string * typ |
wenzelm@16537
    25
    Free of string * typ |
wenzelm@16537
    26
    Var of indexname * typ |
wenzelm@16537
    27
    Bound of int |
wenzelm@16537
    28
    Abs of string * typ * term |
wenzelm@17756
    29
    $ of term * term
wenzelm@16537
    30
  exception TYPE of string * typ list * term list
wenzelm@16537
    31
  exception TERM of string * term list
wenzelm@21353
    32
  val dummyS: sort
wenzelm@16710
    33
  val dummyT: typ
wenzelm@16710
    34
  val no_dummyT: typ -> typ
wenzelm@4444
    35
  val --> : typ * typ -> typ
wenzelm@4444
    36
  val ---> : typ list * typ -> typ
wenzelm@16710
    37
  val dest_Type: typ -> string * typ list
wenzelm@16710
    38
  val dest_TVar: typ -> indexname * sort
wenzelm@16710
    39
  val dest_TFree: typ -> string * sort
wenzelm@16710
    40
  val is_Bound: term -> bool
wenzelm@16710
    41
  val is_Const: term -> bool
wenzelm@16710
    42
  val is_Free: term -> bool
wenzelm@16710
    43
  val is_Var: term -> bool
wenzelm@4444
    44
  val is_TVar: typ -> bool
wenzelm@16710
    45
  val dest_Const: term -> string * typ
wenzelm@16710
    46
  val dest_Free: term -> string * typ
wenzelm@16710
    47
  val dest_Var: term -> indexname * typ
wenzelm@4444
    48
  val domain_type: typ -> typ
wenzelm@4480
    49
  val range_type: typ -> typ
wenzelm@4444
    50
  val binder_types: typ -> typ list
wenzelm@4444
    51
  val body_type: typ -> typ
wenzelm@4444
    52
  val strip_type: typ -> typ list * typ
wenzelm@16710
    53
  val type_of1: typ list * term -> typ
wenzelm@4444
    54
  val type_of: term -> typ
wenzelm@16710
    55
  val fastype_of1: typ list * term -> typ
wenzelm@4444
    56
  val fastype_of: term -> typ
wenzelm@10806
    57
  val list_abs: (string * typ) list * term -> term
haftmann@18927
    58
  val strip_abs: term -> (string * typ) list * term
wenzelm@4444
    59
  val strip_abs_body: term -> term
wenzelm@4444
    60
  val strip_abs_vars: term -> (string * typ) list
wenzelm@4444
    61
  val strip_qnt_body: string -> term -> term
wenzelm@4444
    62
  val strip_qnt_vars: string -> term -> (string * typ) list
wenzelm@4444
    63
  val list_comb: term * term list -> term
wenzelm@4444
    64
  val strip_comb: term -> term * term list
wenzelm@4444
    65
  val head_of: term -> term
wenzelm@4444
    66
  val size_of_term: term -> int
kleing@29882
    67
  val size_of_typ: typ -> int
haftmann@18847
    68
  val map_atyps: (typ -> typ) -> typ -> typ
haftmann@18847
    69
  val map_aterms: (term -> term) -> term -> term
wenzelm@4444
    70
  val map_type_tvar: (indexname * sort -> typ) -> typ -> typ
wenzelm@4444
    71
  val map_type_tfree: (string * sort -> typ) -> typ -> typ
wenzelm@20548
    72
  val map_types: (typ -> typ) -> term -> term
wenzelm@16943
    73
  val fold_atyps: (typ -> 'a -> 'a) -> typ -> 'a -> 'a
wenzelm@16943
    74
  val fold_aterms: (term -> 'a -> 'a) -> term -> 'a -> 'a
wenzelm@16943
    75
  val fold_term_types: (term -> typ -> 'a -> 'a) -> term -> 'a -> 'a
wenzelm@16943
    76
  val fold_types: (typ -> 'a -> 'a) -> term -> 'a -> 'a
wenzelm@24483
    77
  val burrow_types: (typ list -> typ list) -> term list -> term list
wenzelm@16710
    78
  val aconv: term * term -> bool
wenzelm@4444
    79
  val propT: typ
wenzelm@4444
    80
  val strip_all_body: term -> term
wenzelm@4444
    81
  val strip_all_vars: term -> (string * typ) list
wenzelm@4444
    82
  val incr_bv: int * int * term -> term
wenzelm@4444
    83
  val incr_boundvars: int -> term -> term
wenzelm@4444
    84
  val add_loose_bnos: term * int * int list -> int list
wenzelm@4444
    85
  val loose_bnos: term -> int list
wenzelm@4444
    86
  val loose_bvar: term * int -> bool
wenzelm@4444
    87
  val loose_bvar1: term * int -> bool
wenzelm@4444
    88
  val subst_bounds: term list * term -> term
wenzelm@4444
    89
  val subst_bound: term * term -> term
wenzelm@4444
    90
  val betapply: term * term -> term
wenzelm@18183
    91
  val betapplys: term * term list -> term
wenzelm@4444
    92
  val subst_free: (term * term) list -> term -> term
wenzelm@4444
    93
  val abstract_over: term * term -> term
wenzelm@11922
    94
  val lambda: term -> term -> term
wenzelm@4444
    95
  val absfree: string * typ * term -> term
wenzelm@17786
    96
  val absdummy: typ * term -> term
wenzelm@4444
    97
  val list_abs_free: (string * typ) list * term -> term
wenzelm@4444
    98
  val list_all_free: (string * typ) list * term -> term
wenzelm@4444
    99
  val list_all: (string * typ) list * term -> term
wenzelm@16710
   100
  val subst_atomic: (term * term) list -> term -> term
wenzelm@16710
   101
  val typ_subst_atomic: (typ * typ) list -> typ -> typ
wenzelm@16710
   102
  val subst_atomic_types: (typ * typ) list -> term -> term
wenzelm@16710
   103
  val typ_subst_TVars: (indexname * typ) list -> typ -> typ
wenzelm@16710
   104
  val subst_TVars: (indexname * typ) list -> term -> term
wenzelm@16710
   105
  val subst_Vars: (indexname * term) list -> term -> term
wenzelm@16710
   106
  val subst_vars: (indexname * typ) list * (indexname * term) list -> term -> term
wenzelm@16710
   107
  val is_first_order: string list -> term -> bool
wenzelm@4444
   108
  val maxidx_of_typ: typ -> int
wenzelm@4444
   109
  val maxidx_of_typs: typ list -> int
wenzelm@4444
   110
  val maxidx_of_term: term -> int
wenzelm@19909
   111
  val exists_subtype: (typ -> bool) -> typ -> bool
wenzelm@20531
   112
  val exists_type: (typ -> bool) -> term -> bool
wenzelm@16943
   113
  val exists_subterm: (term -> bool) -> term -> bool
wenzelm@16710
   114
  val exists_Const: (string * typ -> bool) -> term -> bool
wenzelm@15986
   115
  val show_question_marks: bool ref
wenzelm@4444
   116
end;
clasohm@0
   117
wenzelm@4444
   118
signature TERM =
wenzelm@4444
   119
sig
wenzelm@4444
   120
  include BASIC_TERM
wenzelm@19394
   121
  val aT: sort -> typ
wenzelm@19394
   122
  val itselfT: typ -> typ
wenzelm@19394
   123
  val a_itselfT: typ
wenzelm@27335
   124
  val all: typ -> term
wenzelm@22908
   125
  val argument_type_of: term -> int -> typ
wenzelm@29257
   126
  val add_tvar_namesT: typ -> indexname list -> indexname list
wenzelm@29257
   127
  val add_tvar_names: term -> indexname list -> indexname list
wenzelm@16943
   128
  val add_tvarsT: typ -> (indexname * sort) list -> (indexname * sort) list
wenzelm@16943
   129
  val add_tvars: term -> (indexname * sort) list -> (indexname * sort) list
wenzelm@29257
   130
  val add_var_names: term -> indexname list -> indexname list
wenzelm@16943
   131
  val add_vars: term -> (indexname * typ) list -> (indexname * typ) list
wenzelm@29257
   132
  val add_tfree_namesT: typ -> string list -> string list
wenzelm@29257
   133
  val add_tfree_names: term -> string list -> string list
wenzelm@16943
   134
  val add_tfreesT: typ -> (string * sort) list -> (string * sort) list
wenzelm@16943
   135
  val add_tfrees: term -> (string * sort) list -> (string * sort) list
wenzelm@29257
   136
  val add_free_names: term -> string list -> string list
wenzelm@16943
   137
  val add_frees: term -> (string * typ) list -> (string * typ) list
wenzelm@29286
   138
  val add_const_names: term -> string list -> string list
wenzelm@29286
   139
  val add_consts: term -> (string * typ) list -> (string * typ) list
wenzelm@25050
   140
  val hidden_polymorphism: term -> (indexname * sort) list
wenzelm@29278
   141
  val declare_typ_names: typ -> Name.context -> Name.context
wenzelm@29278
   142
  val declare_term_names: term -> Name.context -> Name.context
wenzelm@29278
   143
  val declare_term_frees: term -> Name.context -> Name.context
wenzelm@29278
   144
  val variant_frees: term -> (string * 'a) list -> (string * 'a) list
wenzelm@29278
   145
  val rename_wrt_term: term -> (string * 'a) list -> (string * 'a) list
wenzelm@29269
   146
  val eq_ix: indexname * indexname -> bool
wenzelm@29269
   147
  val eq_tvar: (indexname * sort) * (indexname * sort) -> bool
wenzelm@29269
   148
  val eq_var: (indexname * typ) * (indexname * typ) -> bool
wenzelm@29269
   149
  val could_unify: term * term -> bool
haftmann@20109
   150
  val strip_abs_eta: int -> term -> (string * typ) list * term
wenzelm@12981
   151
  val match_bvars: (term * term) * (string * string) list -> (string * string) list
haftmann@22031
   152
  val map_abs_vars: (string -> string) -> term -> term
wenzelm@12981
   153
  val rename_abs: term -> term -> term -> term option
wenzelm@25050
   154
  val close_schematic_term: term -> term
wenzelm@16710
   155
  val maxidx_typ: typ -> int -> int
wenzelm@16710
   156
  val maxidx_typs: typ list -> int -> int
wenzelm@16710
   157
  val maxidx_term: term -> int -> int
wenzelm@24671
   158
  val has_abs: term -> bool
wenzelm@20239
   159
  val dest_abs: string * typ * term -> string * term
wenzelm@9536
   160
  val dummy_patternN: string
wenzelm@18253
   161
  val dummy_pattern: typ -> term
wenzelm@22723
   162
  val is_dummy_pattern: term -> bool
wenzelm@24733
   163
  val free_dummy_patterns: term -> Name.context -> term * Name.context
wenzelm@9536
   164
  val no_dummy_patterns: term -> term
wenzelm@24762
   165
  val replace_dummy_patterns: term -> int -> term * int
wenzelm@10552
   166
  val is_replaced_dummy_pattern: indexname -> bool
wenzelm@16035
   167
  val show_dummy_patterns: term -> term
wenzelm@14786
   168
  val string_of_vname: indexname -> string
wenzelm@14786
   169
  val string_of_vname': indexname -> string
wenzelm@4444
   170
end;
wenzelm@4444
   171
wenzelm@4444
   172
structure Term: TERM =
clasohm@1364
   173
struct
clasohm@0
   174
clasohm@0
   175
(*Indexnames can be quickly renamed by adding an offset to the integer part,
clasohm@0
   176
  for resolution.*)
wenzelm@16537
   177
type indexname = string * int;
clasohm@0
   178
wenzelm@4626
   179
(* Types are classified by sorts. *)
clasohm@0
   180
type class = string;
clasohm@0
   181
type sort  = class list;
wenzelm@14829
   182
type arity = string * sort list * sort;
clasohm@0
   183
clasohm@0
   184
(* The sorts attached to TFrees and TVars specify the sort of that variable *)
clasohm@0
   185
datatype typ = Type  of string * typ list
clasohm@0
   186
             | TFree of string * sort
wenzelm@9536
   187
             | TVar  of indexname * sort;
clasohm@0
   188
paulson@6033
   189
(*Terms.  Bound variables are indicated by depth number.
clasohm@0
   190
  Free variables, (scheme) variables and constants have names.
wenzelm@4626
   191
  An term is "closed" if every bound variable of level "lev"
wenzelm@13000
   192
  is enclosed by at least "lev" abstractions.
clasohm@0
   193
clasohm@0
   194
  It is possible to create meaningless terms containing loose bound vars
clasohm@0
   195
  or type mismatches.  But such terms are not allowed in rules. *)
clasohm@0
   196
wenzelm@13000
   197
datatype term =
clasohm@0
   198
    Const of string * typ
wenzelm@13000
   199
  | Free  of string * typ
clasohm@0
   200
  | Var   of indexname * typ
clasohm@0
   201
  | Bound of int
clasohm@0
   202
  | Abs   of string*typ*term
wenzelm@3965
   203
  | op $  of term*term;
clasohm@0
   204
wenzelm@16537
   205
(*Errors involving type mismatches*)
clasohm@0
   206
exception TYPE of string * typ list * term list;
clasohm@0
   207
wenzelm@16537
   208
(*Errors errors involving terms*)
clasohm@0
   209
exception TERM of string * term list;
clasohm@0
   210
clasohm@0
   211
(*Note variable naming conventions!
clasohm@0
   212
    a,b,c: string
clasohm@0
   213
    f,g,h: functions (including terms of function type)
clasohm@0
   214
    i,j,m,n: int
clasohm@0
   215
    t,u: term
clasohm@0
   216
    v,w: indexnames
clasohm@0
   217
    x,y: any
clasohm@0
   218
    A,B,C: term (denoting formulae)
clasohm@0
   219
    T,U: typ
clasohm@0
   220
*)
clasohm@0
   221
clasohm@0
   222
paulson@6033
   223
(** Types **)
paulson@6033
   224
wenzelm@21353
   225
(*dummies for type-inference etc.*)
wenzelm@21353
   226
val dummyS = [""];
wenzelm@16537
   227
val dummyT = Type ("dummy", []);
wenzelm@16537
   228
wenzelm@16537
   229
fun no_dummyT typ =
wenzelm@16537
   230
  let
wenzelm@16537
   231
    fun check (T as Type ("dummy", _)) =
wenzelm@16537
   232
          raise TYPE ("Illegal occurrence of '_' dummy type", [T], [])
wenzelm@16537
   233
      | check (Type (_, Ts)) = List.app check Ts
wenzelm@16537
   234
      | check _ = ();
wenzelm@16537
   235
  in check typ; typ end;
wenzelm@16537
   236
paulson@6033
   237
fun S --> T = Type("fun",[S,T]);
paulson@6033
   238
paulson@6033
   239
(*handy for multiple args: [T1,...,Tn]--->T  gives  T1-->(T2--> ... -->T)*)
skalberg@15570
   240
val op ---> = Library.foldr (op -->);
paulson@6033
   241
paulson@6033
   242
fun dest_Type (Type x) = x
paulson@6033
   243
  | dest_Type T = raise TYPE ("dest_Type", [T], []);
dixon@15914
   244
fun dest_TVar (TVar x) = x
dixon@15914
   245
  | dest_TVar T = raise TYPE ("dest_TVar", [T], []);
dixon@15914
   246
fun dest_TFree (TFree x) = x
dixon@15914
   247
  | dest_TFree T = raise TYPE ("dest_TFree", [T], []);
paulson@6033
   248
wenzelm@16537
   249
clasohm@0
   250
(** Discriminators **)
clasohm@0
   251
nipkow@7318
   252
fun is_Bound (Bound _) = true
nipkow@7318
   253
  | is_Bound _         = false;
nipkow@7318
   254
clasohm@0
   255
fun is_Const (Const _) = true
clasohm@0
   256
  | is_Const _ = false;
clasohm@0
   257
clasohm@0
   258
fun is_Free (Free _) = true
clasohm@0
   259
  | is_Free _ = false;
clasohm@0
   260
clasohm@0
   261
fun is_Var (Var _) = true
clasohm@0
   262
  | is_Var _ = false;
clasohm@0
   263
clasohm@0
   264
fun is_TVar (TVar _) = true
clasohm@0
   265
  | is_TVar _ = false;
clasohm@0
   266
wenzelm@16537
   267
clasohm@0
   268
(** Destructors **)
clasohm@0
   269
clasohm@0
   270
fun dest_Const (Const x) =  x
clasohm@0
   271
  | dest_Const t = raise TERM("dest_Const", [t]);
clasohm@0
   272
clasohm@0
   273
fun dest_Free (Free x) =  x
clasohm@0
   274
  | dest_Free t = raise TERM("dest_Free", [t]);
clasohm@0
   275
clasohm@0
   276
fun dest_Var (Var x) =  x
clasohm@0
   277
  | dest_Var t = raise TERM("dest_Var", [t]);
clasohm@0
   278
clasohm@0
   279
paulson@4464
   280
fun domain_type (Type("fun", [T,_])) = T
paulson@4464
   281
and range_type  (Type("fun", [_,T])) = T;
paulson@4064
   282
clasohm@0
   283
(* maps  [T1,...,Tn]--->T  to the list  [T1,T2,...,Tn]*)
clasohm@0
   284
fun binder_types (Type("fun",[S,T])) = S :: binder_types T
clasohm@0
   285
  | binder_types _   =  [];
clasohm@0
   286
clasohm@0
   287
(* maps  [T1,...,Tn]--->T  to T*)
clasohm@0
   288
fun body_type (Type("fun",[S,T])) = body_type T
clasohm@0
   289
  | body_type T   =  T;
clasohm@0
   290
clasohm@0
   291
(* maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T)  *)
clasohm@0
   292
fun strip_type T : typ list * typ =
clasohm@0
   293
  (binder_types T, body_type T);
clasohm@0
   294
clasohm@0
   295
clasohm@0
   296
(*Compute the type of the term, checking that combinations are well-typed
clasohm@0
   297
  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
clasohm@0
   298
fun type_of1 (Ts, Const (_,T)) = T
clasohm@0
   299
  | type_of1 (Ts, Free  (_,T)) = T
wenzelm@30146
   300
  | type_of1 (Ts, Bound i) = (nth Ts i
skalberg@15570
   301
        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
clasohm@0
   302
  | type_of1 (Ts, Var (_,T)) = T
clasohm@0
   303
  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
wenzelm@13000
   304
  | type_of1 (Ts, f$u) =
clasohm@0
   305
      let val U = type_of1(Ts,u)
clasohm@0
   306
          and T = type_of1(Ts,f)
clasohm@0
   307
      in case T of
wenzelm@9536
   308
            Type("fun",[T1,T2]) =>
wenzelm@9536
   309
              if T1=U then T2  else raise TYPE
wenzelm@9536
   310
                    ("type_of: type mismatch in application", [T1,U], [f$u])
wenzelm@13000
   311
          | _ => raise TYPE
wenzelm@9536
   312
                    ("type_of: function type is expected in application",
wenzelm@9536
   313
                     [T,U], [f$u])
clasohm@0
   314
      end;
clasohm@0
   315
clasohm@0
   316
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   317
clasohm@0
   318
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   319
fun fastype_of1 (Ts, f$u) =
lcp@61
   320
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   321
        Type("fun",[_,T]) => T
wenzelm@9536
   322
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   323
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   324
  | fastype_of1 (_, Free (_,T)) = T
wenzelm@30146
   325
  | fastype_of1 (Ts, Bound i) = (nth Ts i
skalberg@15570
   326
         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   327
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   328
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   329
lcp@61
   330
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   331
wenzelm@16678
   332
(*Determine the argument type of a function*)
wenzelm@22908
   333
fun argument_type_of tm k =
wenzelm@16678
   334
  let
wenzelm@16678
   335
    fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U
wenzelm@16678
   336
      | argT _ T = raise TYPE ("argument_type_of", [T], []);
wenzelm@16678
   337
wenzelm@16678
   338
    fun arg 0 _ (Abs (_, T, _)) = T
wenzelm@16678
   339
      | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t
wenzelm@16678
   340
      | arg i Ts (t $ _) = arg (i + 1) Ts t
wenzelm@16678
   341
      | arg i Ts a = argT i (fastype_of1 (Ts, a));
wenzelm@22908
   342
  in arg k [] tm end;
wenzelm@16678
   343
clasohm@0
   344
wenzelm@19473
   345
val list_abs = uncurry (fold_rev (fn (x, T) => fn t => Abs (x, T, t)));
wenzelm@10806
   346
haftmann@18927
   347
fun strip_abs (Abs (a, T, t)) =
haftmann@18927
   348
      let val (a', t') = strip_abs t
haftmann@18927
   349
      in ((a, T) :: a', t') end
haftmann@18927
   350
  | strip_abs t = ([], t);
haftmann@18927
   351
clasohm@0
   352
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   353
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   354
  | strip_abs_body u  =  u;
clasohm@0
   355
clasohm@0
   356
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   357
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   358
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   359
clasohm@0
   360
clasohm@0
   361
fun strip_qnt_body qnt =
clasohm@0
   362
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   363
      | strip t = t
clasohm@0
   364
in strip end;
clasohm@0
   365
clasohm@0
   366
fun strip_qnt_vars qnt =
clasohm@0
   367
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   368
      | strip t  =  [] : (string*typ) list
clasohm@0
   369
in strip end;
clasohm@0
   370
clasohm@0
   371
clasohm@0
   372
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   373
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   374
clasohm@0
   375
clasohm@0
   376
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   377
fun strip_comb u : term * term list =
clasohm@0
   378
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   379
        |   stripc  x =  x
clasohm@0
   380
    in  stripc(u,[])  end;
clasohm@0
   381
clasohm@0
   382
clasohm@0
   383
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   384
fun head_of (f$t) = head_of f
clasohm@0
   385
  | head_of u = u;
clasohm@0
   386
wenzelm@16599
   387
(*number of atoms and abstractions in a term*)
wenzelm@16599
   388
fun size_of_term tm =
wenzelm@16599
   389
  let
wenzelm@30144
   390
    fun add_size (t $ u) n = add_size t (add_size u n)
wenzelm@30144
   391
      | add_size (Abs (_ ,_, t)) n = add_size t (n + 1)
wenzelm@30144
   392
      | add_size _ n = n + 1;
wenzelm@30144
   393
  in add_size tm 0 end;
clasohm@0
   394
wenzelm@30144
   395
(*number of atoms and constructors in a type*)
kleing@29882
   396
fun size_of_typ ty =
kleing@29882
   397
  let
wenzelm@30144
   398
    fun add_size (Type (_, tys)) n = fold add_size tys (n + 1)
wenzelm@30144
   399
      | add_size _ n = n + 1;
wenzelm@30144
   400
  in add_size ty 0 end;
kleing@29882
   401
haftmann@18847
   402
fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts)
haftmann@18976
   403
  | map_atyps f T = f T;
haftmann@18847
   404
haftmann@18847
   405
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u
haftmann@18847
   406
  | map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t)
haftmann@18847
   407
  | map_aterms f t = f t;
haftmann@18847
   408
wenzelm@18981
   409
fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T);
wenzelm@18981
   410
fun map_type_tfree f = map_atyps (fn TFree x => f x | T => T);
nipkow@949
   411
wenzelm@20548
   412
fun map_types f =
wenzelm@16678
   413
  let
wenzelm@16678
   414
    fun map_aux (Const (a, T)) = Const (a, f T)
wenzelm@16678
   415
      | map_aux (Free (a, T)) = Free (a, f T)
wenzelm@16678
   416
      | map_aux (Var (v, T)) = Var (v, f T)
wenzelm@16678
   417
      | map_aux (t as Bound _)  = t
wenzelm@16678
   418
      | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t)
wenzelm@16678
   419
      | map_aux (t $ u) = map_aux t $ map_aux u;
wenzelm@16678
   420
  in map_aux end;
clasohm@0
   421
clasohm@0
   422
wenzelm@16943
   423
(* fold types and terms *)
wenzelm@16943
   424
wenzelm@16943
   425
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts
wenzelm@16943
   426
  | fold_atyps f T = f T;
wenzelm@16943
   427
wenzelm@16943
   428
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u
wenzelm@16943
   429
  | fold_aterms f (Abs (_, _, t)) = fold_aterms f t
wenzelm@16943
   430
  | fold_aterms f a = f a;
wenzelm@16943
   431
wenzelm@16943
   432
fun fold_term_types f (t as Const (_, T)) = f t T
wenzelm@16943
   433
  | fold_term_types f (t as Free (_, T)) = f t T
wenzelm@16943
   434
  | fold_term_types f (t as Var (_, T)) = f t T
wenzelm@16943
   435
  | fold_term_types f (Bound _) = I
wenzelm@16943
   436
  | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b
wenzelm@16943
   437
  | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u;
wenzelm@16943
   438
wenzelm@16943
   439
fun fold_types f = fold_term_types (K f);
wenzelm@16943
   440
wenzelm@24483
   441
fun replace_types (Const (c, _)) (T :: Ts) = (Const (c, T), Ts)
wenzelm@24483
   442
  | replace_types (Free (x, _)) (T :: Ts) = (Free (x, T), Ts)
wenzelm@24483
   443
  | replace_types (Var (xi, _)) (T :: Ts) = (Var (xi, T), Ts)
wenzelm@24483
   444
  | replace_types (Bound i) Ts = (Bound i, Ts)
wenzelm@24483
   445
  | replace_types (Abs (x, _, b)) (T :: Ts) =
wenzelm@24483
   446
      let val (b', Ts') = replace_types b Ts
wenzelm@24483
   447
      in (Abs (x, T, b'), Ts') end
wenzelm@24483
   448
  | replace_types (t $ u) Ts =
wenzelm@24483
   449
      let
wenzelm@24483
   450
        val (t', Ts') = replace_types t Ts;
wenzelm@24483
   451
        val (u', Ts'') = replace_types u Ts';
wenzelm@24483
   452
      in (t' $ u', Ts'') end;
wenzelm@24483
   453
wenzelm@24483
   454
fun burrow_types f ts =
wenzelm@24483
   455
  let
wenzelm@24483
   456
    val Ts = rev (fold (fold_types cons) ts []);
wenzelm@24483
   457
    val Ts' = f Ts;
wenzelm@24483
   458
    val (ts', []) = fold_map replace_types ts Ts';
wenzelm@24483
   459
  in ts' end;
wenzelm@24483
   460
wenzelm@16943
   461
(*collect variables*)
wenzelm@29257
   462
val add_tvar_namesT = fold_atyps (fn TVar (xi, _) => insert (op =) xi | _ => I);
wenzelm@29257
   463
val add_tvar_names = fold_types add_tvar_namesT;
wenzelm@16943
   464
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I);
wenzelm@16943
   465
val add_tvars = fold_types add_tvarsT;
wenzelm@29257
   466
val add_var_names = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I);
wenzelm@16943
   467
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I);
wenzelm@29257
   468
val add_tfree_namesT = fold_atyps (fn TFree (xi, _) => insert (op =) xi | _ => I);
wenzelm@29257
   469
val add_tfree_names = fold_types add_tfree_namesT;
wenzelm@16943
   470
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I);
wenzelm@16943
   471
val add_tfrees = fold_types add_tfreesT;
wenzelm@29257
   472
val add_free_names = fold_aterms (fn Free (x, _) => insert (op =) x | _ => I);
wenzelm@16943
   473
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I);
wenzelm@29286
   474
val add_const_names = fold_aterms (fn Const (c, _) => insert (op =) c | _ => I);
wenzelm@29286
   475
val add_consts = fold_aterms (fn Const c => insert (op =) c | _ => I);
wenzelm@16943
   476
wenzelm@25050
   477
(*extra type variables in a term, not covered by its type*)
wenzelm@25050
   478
fun hidden_polymorphism t =
wenzelm@21682
   479
  let
wenzelm@25050
   480
    val T = fastype_of t;
wenzelm@21682
   481
    val tvarsT = add_tvarsT T [];
wenzelm@21682
   482
    val extra_tvars = fold_types (fold_atyps
wenzelm@21682
   483
      (fn TVar v => if member (op =) tvarsT v then I else insert (op =) v | _ => I)) t [];
wenzelm@21682
   484
  in extra_tvars end;
wenzelm@21682
   485
wenzelm@16943
   486
wenzelm@29278
   487
(* renaming variables *)
wenzelm@29278
   488
wenzelm@29278
   489
val declare_typ_names = fold_atyps (fn TFree (a, _) => Name.declare a | _ => I);
wenzelm@29278
   490
wenzelm@29278
   491
fun declare_term_names tm =
wenzelm@29278
   492
  fold_aterms
wenzelm@29278
   493
    (fn Const (a, _) => Name.declare (NameSpace.base a)
wenzelm@29278
   494
      | Free (a, _) => Name.declare a
wenzelm@29278
   495
      | _ => I) tm #>
wenzelm@29278
   496
  fold_types declare_typ_names tm;
wenzelm@29278
   497
wenzelm@29278
   498
val declare_term_frees = fold_aterms (fn Free (x, _) => Name.declare x | _ => I);
wenzelm@29278
   499
wenzelm@29278
   500
fun variant_frees t frees =
wenzelm@29278
   501
  fst (Name.variants (map fst frees) (declare_term_names t Name.context)) ~~ map snd frees;
wenzelm@29278
   502
wenzelm@29278
   503
fun rename_wrt_term t frees = rev (variant_frees t frees);  (*reversed result!*)
wenzelm@29278
   504
wenzelm@29278
   505
wenzelm@25050
   506
wenzelm@29269
   507
(** Comparing terms **)
wenzelm@29269
   508
wenzelm@29269
   509
(* variables *)
wenzelm@29269
   510
wenzelm@29269
   511
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y;
wenzelm@16537
   512
wenzelm@29269
   513
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S';
wenzelm@29269
   514
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T';
wenzelm@29269
   515
wenzelm@29269
   516
wenzelm@29269
   517
(* alpha equivalence *)
wenzelm@20511
   518
wenzelm@20511
   519
fun tm1 aconv tm2 =
wenzelm@20511
   520
  pointer_eq (tm1, tm2) orelse
wenzelm@20511
   521
    (case (tm1, tm2) of
wenzelm@20511
   522
      (t1 $ u1, t2 $ u2) => t1 aconv t2 andalso u1 aconv u2
wenzelm@20511
   523
    | (Abs (_, T1, t1), Abs (_, T2, t2)) => t1 aconv t2 andalso T1 = T2
wenzelm@20511
   524
    | (a1, a2) => a1 = a2);
wenzelm@20511
   525
wenzelm@20511
   526
wenzelm@29269
   527
(*A fast unification filter: true unless the two terms cannot be unified.
wenzelm@29269
   528
  Terms must be NORMAL.  Treats all Vars as distinct. *)
wenzelm@29269
   529
fun could_unify (t, u) =
wenzelm@29269
   530
  let
wenzelm@29269
   531
    fun matchrands (f $ t) (g $ u) = could_unify (t, u) andalso matchrands f g
wenzelm@29269
   532
      | matchrands _ _ = true;
wenzelm@29269
   533
  in
wenzelm@29269
   534
    case (head_of t, head_of u) of
wenzelm@29269
   535
      (_, Var _) => true
wenzelm@29269
   536
    | (Var _, _) => true
wenzelm@29269
   537
    | (Const (a, _), Const (b, _)) => a = b andalso matchrands t u
wenzelm@29269
   538
    | (Free (a, _), Free (b, _)) => a = b andalso matchrands t u
wenzelm@29269
   539
    | (Bound i, Bound j) => i = j andalso matchrands t u
wenzelm@29269
   540
    | (Abs _, _) => true   (*because of possible eta equality*)
wenzelm@29269
   541
    | (_, Abs _) => true
wenzelm@29269
   542
    | _ => false
wenzelm@29269
   543
  end;
wenzelm@16678
   544
nipkow@16570
   545
wenzelm@16537
   546
clasohm@0
   547
(** Connectives of higher order logic **)
clasohm@0
   548
wenzelm@24850
   549
fun aT S = TFree (Name.aT, S);
wenzelm@19394
   550
wenzelm@375
   551
fun itselfT ty = Type ("itself", [ty]);
wenzelm@24850
   552
val a_itselfT = itselfT (TFree (Name.aT, []));
wenzelm@375
   553
clasohm@0
   554
val propT : typ = Type("prop",[]);
clasohm@0
   555
clasohm@0
   556
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   557
clasohm@0
   558
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   559
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   560
  | strip_all_body t  =  t;
clasohm@0
   561
clasohm@0
   562
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   563
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   564
                (a,T) :: strip_all_vars t
clasohm@0
   565
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   566
clasohm@0
   567
(*increments a term's non-local bound variables
clasohm@0
   568
  required when moving a term within abstractions
clasohm@0
   569
     inc is  increment for bound variables
clasohm@0
   570
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   571
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   572
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   573
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   574
  | incr_bv (inc, lev, f$t) =
clasohm@0
   575
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   576
  | incr_bv (inc, lev, u) = u;
clasohm@0
   577
clasohm@0
   578
fun incr_boundvars  0  t = t
clasohm@0
   579
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   580
wenzelm@12981
   581
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   582
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   583
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   584
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   585
                                          else (x,y)::al)
wenzelm@12981
   586
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   587
  | match_bvs(_,_,al) = al;
wenzelm@12981
   588
wenzelm@12981
   589
(* strip abstractions created by parameters *)
wenzelm@12981
   590
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   591
haftmann@22031
   592
fun map_abs_vars f (t $ u) = map_abs_vars f t $ map_abs_vars f u
haftmann@22031
   593
  | map_abs_vars f (Abs (a, T, t)) = Abs (f a, T, map_abs_vars f t)
haftmann@22031
   594
  | map_abs_vars f t = t;
haftmann@22031
   595
wenzelm@12981
   596
fun rename_abs pat obj t =
wenzelm@12981
   597
  let
wenzelm@12981
   598
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   599
    fun ren_abs (Abs (x, T, b)) =
wenzelm@18942
   600
          Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b)
wenzelm@12981
   601
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   602
      | ren_abs t = t
skalberg@15531
   603
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   604
clasohm@0
   605
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   606
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   607
fun add_loose_bnos (Bound i, lev, js) =
haftmann@20854
   608
        if i<lev then js else insert (op =) (i - lev) js
clasohm@0
   609
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   610
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   611
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   612
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   613
clasohm@0
   614
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   615
clasohm@0
   616
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   617
   level k or beyond. *)
clasohm@0
   618
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   619
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   620
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   621
  | loose_bvar _ = false;
clasohm@0
   622
nipkow@2792
   623
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   624
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   625
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   626
  | loose_bvar1 _ = false;
clasohm@0
   627
clasohm@0
   628
(*Substitute arguments for loose bound variables.
clasohm@0
   629
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   630
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   631
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   632
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   633
     compensate for the disappearance of lambdas.
clasohm@0
   634
*)
wenzelm@13000
   635
fun subst_bounds (args: term list, t) : term =
wenzelm@19065
   636
  let
wenzelm@19065
   637
    exception SAME;
wenzelm@19065
   638
    val n = length args;
wenzelm@19065
   639
    fun subst (t as Bound i, lev) =
wenzelm@19065
   640
         (if i < lev then raise SAME   (*var is locally bound*)
wenzelm@30146
   641
          else incr_boundvars lev (nth args (i - lev))
wenzelm@19065
   642
            handle Subscript => Bound (i - n))  (*loose: change it*)
wenzelm@19065
   643
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   644
      | subst (f $ t, lev) =
wenzelm@19065
   645
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   646
      | subst _ = raise SAME;
wenzelm@19065
   647
  in case args of [] => t | _ => (subst (t, 0) handle SAME => t) end;
clasohm@0
   648
paulson@2192
   649
(*Special case: one argument*)
wenzelm@13000
   650
fun subst_bound (arg, t) : term =
wenzelm@19065
   651
  let
wenzelm@19065
   652
    exception SAME;
wenzelm@19065
   653
    fun subst (Bound i, lev) =
wenzelm@19065
   654
          if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   655
          else if i = lev then incr_boundvars lev arg
wenzelm@19065
   656
          else Bound (i - 1)   (*loose: change it*)
wenzelm@19065
   657
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   658
      | subst (f $ t, lev) =
wenzelm@19065
   659
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   660
      | subst _ = raise SAME;
wenzelm@19065
   661
  in subst (t, 0) handle SAME => t end;
paulson@2192
   662
clasohm@0
   663
(*beta-reduce if possible, else form application*)
paulson@2192
   664
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   665
  | betapply (f,u) = f$u;
clasohm@0
   666
wenzelm@18183
   667
val betapplys = Library.foldl betapply;
wenzelm@18183
   668
wenzelm@14786
   669
haftmann@20109
   670
(*unfolding abstractions with substitution
haftmann@20109
   671
  of bound variables and implicit eta-expansion*)
haftmann@20109
   672
fun strip_abs_eta k t =
haftmann@20109
   673
  let
wenzelm@29278
   674
    val used = fold_aterms declare_term_frees t Name.context;
haftmann@20109
   675
    fun strip_abs t (0, used) = (([], t), (0, used))
haftmann@20109
   676
      | strip_abs (Abs (v, T, t)) (k, used) =
haftmann@20109
   677
          let
wenzelm@20122
   678
            val ([v'], used') = Name.variants [v] used;
haftmann@21013
   679
            val t' = subst_bound (Free (v', T), t);
wenzelm@20122
   680
            val ((vs, t''), (k', used'')) = strip_abs t' (k - 1, used');
wenzelm@20122
   681
          in (((v', T) :: vs, t''), (k', used'')) end
haftmann@20109
   682
      | strip_abs t (k, used) = (([], t), (k, used));
haftmann@20109
   683
    fun expand_eta [] t _ = ([], t)
haftmann@20109
   684
      | expand_eta (T::Ts) t used =
haftmann@20109
   685
          let
wenzelm@20122
   686
            val ([v], used') = Name.variants [""] used;
wenzelm@20122
   687
            val (vs, t') = expand_eta Ts (t $ Free (v, T)) used';
haftmann@20109
   688
          in ((v, T) :: vs, t') end;
haftmann@20109
   689
    val ((vs1, t'), (k', used')) = strip_abs t (k, used);
haftmann@20109
   690
    val Ts = (fst o chop k' o fst o strip_type o fastype_of) t';
haftmann@20109
   691
    val (vs2, t'') = expand_eta Ts t' used';
haftmann@20109
   692
  in (vs1 @ vs2, t'') end;
haftmann@20109
   693
haftmann@20109
   694
clasohm@0
   695
(*Substitute new for free occurrences of old in a term*)
wenzelm@29256
   696
fun subst_free [] = I
clasohm@0
   697
  | subst_free pairs =
wenzelm@13000
   698
      let fun substf u =
haftmann@17314
   699
            case AList.lookup (op aconv) pairs u of
skalberg@15531
   700
                SOME u' => u'
skalberg@15531
   701
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   702
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   703
                                 | _ => u)
clasohm@0
   704
      in  substf  end;
clasohm@0
   705
wenzelm@13000
   706
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   707
    which must contain no loose bound variables.
clasohm@0
   708
  The resulting term is ready to become the body of an Abs.*)
wenzelm@16882
   709
fun abstract_over (v, body) =
wenzelm@16882
   710
  let
wenzelm@16990
   711
    exception SAME;
wenzelm@16990
   712
    fun abs lev tm =
wenzelm@16990
   713
      if v aconv tm then Bound lev
wenzelm@16882
   714
      else
wenzelm@16990
   715
        (case tm of
wenzelm@16990
   716
          Abs (a, T, t) => Abs (a, T, abs (lev + 1) t)
wenzelm@16990
   717
        | t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u)
wenzelm@16990
   718
        | _ => raise SAME);
wenzelm@16990
   719
  in abs 0 body handle SAME => body end;
clasohm@0
   720
wenzelm@21975
   721
fun lambda v t =
wenzelm@21975
   722
  let val x =
wenzelm@21975
   723
    (case v of
wenzelm@21975
   724
      Const (x, _) => NameSpace.base x
wenzelm@21975
   725
    | Free (x, _) => x
wenzelm@21975
   726
    | Var ((x, _), _) => x
wenzelm@24850
   727
    | _ => Name.uu)
wenzelm@21975
   728
  in Abs (x, fastype_of v, abstract_over (v, t)) end;
clasohm@0
   729
clasohm@0
   730
(*Form an abstraction over a free variable.*)
wenzelm@21975
   731
fun absfree (a,T,body) = Abs (a, T, abstract_over (Free (a, T), body));
wenzelm@24850
   732
fun absdummy (T, body) = Abs (Name.internal Name.uu, T, body);
clasohm@0
   733
clasohm@0
   734
(*Abstraction over a list of free variables*)
clasohm@0
   735
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   736
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   737
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   738
clasohm@0
   739
(*Quantification over a list of free variables*)
clasohm@0
   740
fun list_all_free ([], t: term) = t
wenzelm@13000
   741
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   742
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   743
clasohm@0
   744
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   745
fun list_all ([], t) = t
wenzelm@13000
   746
  | list_all ((a,T)::vars, t) =
clasohm@0
   747
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   748
wenzelm@16678
   749
(*Replace the ATOMIC term ti by ui;    inst = [(t1,u1), ..., (tn,un)].
clasohm@0
   750
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
wenzelm@16678
   751
fun subst_atomic [] tm = tm
wenzelm@16678
   752
  | subst_atomic inst tm =
wenzelm@16678
   753
      let
wenzelm@16678
   754
        fun subst (Abs (a, T, body)) = Abs (a, T, subst body)
wenzelm@16678
   755
          | subst (t $ u) = subst t $ subst u
wenzelm@18942
   756
          | subst t = the_default t (AList.lookup (op aconv) inst t);
wenzelm@16678
   757
      in subst tm end;
clasohm@0
   758
wenzelm@16678
   759
(*Replace the ATOMIC type Ti by Ui;    inst = [(T1,U1), ..., (Tn,Un)].*)
wenzelm@16678
   760
fun typ_subst_atomic [] ty = ty
wenzelm@16678
   761
  | typ_subst_atomic inst ty =
wenzelm@16678
   762
      let
wenzelm@16678
   763
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   764
          | subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T);
wenzelm@16678
   765
      in subst ty end;
berghofe@15797
   766
wenzelm@16678
   767
fun subst_atomic_types [] tm = tm
wenzelm@20548
   768
  | subst_atomic_types inst tm = map_types (typ_subst_atomic inst) tm;
wenzelm@16678
   769
wenzelm@16678
   770
fun typ_subst_TVars [] ty = ty
wenzelm@16678
   771
  | typ_subst_TVars inst ty =
wenzelm@16678
   772
      let
wenzelm@16678
   773
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   774
          | subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi)
wenzelm@16678
   775
          | subst T = T;
wenzelm@16678
   776
      in subst ty end;
clasohm@0
   777
wenzelm@16678
   778
fun subst_TVars [] tm = tm
wenzelm@20548
   779
  | subst_TVars inst tm = map_types (typ_subst_TVars inst) tm;
clasohm@0
   780
wenzelm@16678
   781
fun subst_Vars [] tm = tm
wenzelm@16678
   782
  | subst_Vars inst tm =
wenzelm@16678
   783
      let
wenzelm@18942
   784
        fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi)
wenzelm@16678
   785
          | subst (Abs (a, T, t)) = Abs (a, T, subst t)
wenzelm@16678
   786
          | subst (t $ u) = subst t $ subst u
wenzelm@16678
   787
          | subst t = t;
wenzelm@16678
   788
      in subst tm end;
clasohm@0
   789
wenzelm@16678
   790
fun subst_vars ([], []) tm = tm
wenzelm@16678
   791
  | subst_vars ([], inst) tm = subst_Vars inst tm
wenzelm@16678
   792
  | subst_vars (instT, inst) tm =
wenzelm@16678
   793
      let
wenzelm@16678
   794
        fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T)
wenzelm@16678
   795
          | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T)
wenzelm@16678
   796
          | subst (t as Var (xi, T)) =
haftmann@17271
   797
              (case AList.lookup (op =) inst xi of
wenzelm@16678
   798
                NONE => Var (xi, typ_subst_TVars instT T)
wenzelm@16678
   799
              | SOME t => t)
wenzelm@16678
   800
          | subst (t as Bound _) = t
wenzelm@16678
   801
          | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t)
wenzelm@16678
   802
          | subst (t $ u) = subst t $ subst u;
wenzelm@16678
   803
      in subst tm end;
clasohm@0
   804
wenzelm@25050
   805
fun close_schematic_term t =
wenzelm@25050
   806
  let
wenzelm@25050
   807
    val extra_types = map (fn v => Const ("TYPE", itselfT (TVar v))) (hidden_polymorphism t);
wenzelm@25050
   808
    val extra_terms = map Var (rev (add_vars t []));
wenzelm@25050
   809
  in fold_rev lambda (extra_types @ extra_terms) t end;
wenzelm@25050
   810
wenzelm@25050
   811
clasohm@0
   812
paulson@15573
   813
(** Identifying first-order terms **)
paulson@15573
   814
wenzelm@20199
   815
(*Differs from proofterm/is_fun in its treatment of TVar*)
wenzelm@29256
   816
fun is_funtype (Type ("fun", [_, _])) = true
wenzelm@20199
   817
  | is_funtype _ = false;
wenzelm@20199
   818
paulson@15573
   819
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
wenzelm@29256
   820
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts, t)));
paulson@15573
   821
wenzelm@16537
   822
(*First order means in all terms of the form f(t1,...,tn) no argument has a
paulson@16589
   823
  function type. The supplied quantifiers are excluded: their argument always
paulson@16589
   824
  has a function type through a recursive call into its body.*)
wenzelm@16667
   825
fun is_first_order quants =
paulson@16589
   826
  let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
wenzelm@16667
   827
        | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) =
wenzelm@20664
   828
            member (op =) quants q  andalso   (*it is a known quantifier*)
paulson@16589
   829
            not (is_funtype T)   andalso first_order1 (T::Ts) body
wenzelm@16667
   830
        | first_order1 Ts t =
wenzelm@16667
   831
            case strip_comb t of
wenzelm@16667
   832
                 (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   833
               | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   834
               | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   835
               | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   836
               | (Abs _, ts) => false (*not in beta-normal form*)
wenzelm@16667
   837
               | _ => error "first_order: unexpected case"
paulson@16589
   838
    in  first_order1 []  end;
paulson@15573
   839
wenzelm@16710
   840
wenzelm@16990
   841
(* maximum index of typs and terms *)
clasohm@0
   842
wenzelm@16710
   843
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j)
wenzelm@16710
   844
  | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i
wenzelm@16710
   845
  | maxidx_typ (TFree _) i = i
wenzelm@16710
   846
and maxidx_typs [] i = i
wenzelm@16710
   847
  | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i);
clasohm@0
   848
wenzelm@16710
   849
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j))
wenzelm@16710
   850
  | maxidx_term (Const (_, T)) i = maxidx_typ T i
wenzelm@16710
   851
  | maxidx_term (Free (_, T)) i = maxidx_typ T i
wenzelm@16710
   852
  | maxidx_term (Bound _) i = i
wenzelm@16710
   853
  | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i)
wenzelm@16710
   854
  | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i);
clasohm@0
   855
wenzelm@16710
   856
fun maxidx_of_typ T = maxidx_typ T ~1;
wenzelm@16710
   857
fun maxidx_of_typs Ts = maxidx_typs Ts ~1;
wenzelm@16710
   858
fun maxidx_of_term t = maxidx_term t ~1;
berghofe@13665
   859
clasohm@0
   860
clasohm@0
   861
wenzelm@29270
   862
(** misc syntax operations **)
clasohm@0
   863
wenzelm@19909
   864
(* substructure *)
wenzelm@4017
   865
wenzelm@19909
   866
fun exists_subtype P =
wenzelm@19909
   867
  let
wenzelm@19909
   868
    fun ex ty = P ty orelse
wenzelm@19909
   869
      (case ty of Type (_, Ts) => exists ex Ts | _ => false);
wenzelm@19909
   870
  in ex end;
nipkow@13646
   871
wenzelm@20531
   872
fun exists_type P =
wenzelm@20531
   873
  let
wenzelm@20531
   874
    fun ex (Const (_, T)) = P T
wenzelm@20531
   875
      | ex (Free (_, T)) = P T
wenzelm@20531
   876
      | ex (Var (_, T)) = P T
wenzelm@20531
   877
      | ex (Bound _) = false
wenzelm@20531
   878
      | ex (Abs (_, T, t)) = P T orelse ex t
wenzelm@20531
   879
      | ex (t $ u) = ex t orelse ex u;
wenzelm@20531
   880
  in ex end;
wenzelm@20531
   881
wenzelm@16943
   882
fun exists_subterm P =
wenzelm@16943
   883
  let
wenzelm@16943
   884
    fun ex tm = P tm orelse
wenzelm@16943
   885
      (case tm of
wenzelm@16943
   886
        t $ u => ex t orelse ex u
wenzelm@16943
   887
      | Abs (_, _, t) => ex t
wenzelm@16943
   888
      | _ => false);
wenzelm@16943
   889
  in ex end;
obua@16108
   890
wenzelm@29270
   891
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false);
wenzelm@29270
   892
wenzelm@24671
   893
fun has_abs (Abs _) = true
wenzelm@24671
   894
  | has_abs (t $ u) = has_abs t orelse has_abs u
wenzelm@24671
   895
  | has_abs _ = false;
wenzelm@24671
   896
wenzelm@24671
   897
wenzelm@20199
   898
(* dest abstraction *)
clasohm@0
   899
wenzelm@16678
   900
fun dest_abs (x, T, body) =
wenzelm@16678
   901
  let
wenzelm@16678
   902
    fun name_clash (Free (y, _)) = (x = y)
wenzelm@16678
   903
      | name_clash (t $ u) = name_clash t orelse name_clash u
wenzelm@16678
   904
      | name_clash (Abs (_, _, t)) = name_clash t
wenzelm@16678
   905
      | name_clash _ = false;
wenzelm@16678
   906
  in
wenzelm@27335
   907
    if name_clash body then dest_abs (Name.variant [x] x, T, body)    (*potentially slow*)
wenzelm@16678
   908
    else (x, subst_bound (Free (x, T), body))
wenzelm@16678
   909
  end;
wenzelm@16678
   910
wenzelm@20160
   911
wenzelm@9536
   912
(* dummy patterns *)
wenzelm@9536
   913
wenzelm@9536
   914
val dummy_patternN = "dummy_pattern";
wenzelm@9536
   915
wenzelm@18253
   916
fun dummy_pattern T = Const (dummy_patternN, T);
wenzelm@18253
   917
wenzelm@9536
   918
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
   919
  | is_dummy_pattern _ = false;
wenzelm@9536
   920
wenzelm@9536
   921
fun no_dummy_patterns tm =
haftmann@16787
   922
  if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm
wenzelm@9536
   923
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
   924
wenzelm@24733
   925
fun free_dummy_patterns (Const ("dummy_pattern", T)) used =
wenzelm@24850
   926
      let val [x] = Name.invents used Name.uu 1
wenzelm@24733
   927
      in (Free (Name.internal x, T), Name.declare x used) end
wenzelm@24733
   928
  | free_dummy_patterns (Abs (x, T, b)) used =
wenzelm@24733
   929
      let val (b', used') = free_dummy_patterns b used
wenzelm@24733
   930
      in (Abs (x, T, b'), used') end
wenzelm@24733
   931
  | free_dummy_patterns (t $ u) used =
wenzelm@24733
   932
      let
wenzelm@24733
   933
        val (t', used') = free_dummy_patterns t used;
wenzelm@24733
   934
        val (u', used'') = free_dummy_patterns u used';
wenzelm@24733
   935
      in (t' $ u', used'') end
wenzelm@24733
   936
  | free_dummy_patterns a used = (a, used);
wenzelm@24733
   937
wenzelm@24762
   938
fun replace_dummy Ts (Const ("dummy_pattern", T)) i =
wenzelm@24762
   939
      (list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)), i + 1)
wenzelm@24762
   940
  | replace_dummy Ts (Abs (x, T, t)) i =
wenzelm@24762
   941
      let val (t', i') = replace_dummy (T :: Ts) t i
wenzelm@24762
   942
      in (Abs (x, T, t'), i') end
wenzelm@24762
   943
  | replace_dummy Ts (t $ u) i =
wenzelm@24762
   944
      let
wenzelm@24762
   945
        val (t', i') = replace_dummy Ts t i;
wenzelm@24762
   946
        val (u', i'') = replace_dummy Ts u i';
wenzelm@24762
   947
      in (t' $ u', i'') end
wenzelm@24762
   948
  | replace_dummy _ a i = (a, i);
wenzelm@11903
   949
wenzelm@11903
   950
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
   951
wenzelm@10552
   952
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
   953
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
   954
wenzelm@16035
   955
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
wenzelm@16035
   956
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
   957
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
   958
  | show_dummy_patterns a = a;
wenzelm@16035
   959
wenzelm@13484
   960
wenzelm@20100
   961
(* display variables *)
wenzelm@20100
   962
wenzelm@15986
   963
val show_question_marks = ref true;
berghofe@15472
   964
wenzelm@14786
   965
fun string_of_vname (x, i) =
wenzelm@14786
   966
  let
wenzelm@15986
   967
    val question_mark = if ! show_question_marks then "?" else "";
wenzelm@15986
   968
    val idx = string_of_int i;
wenzelm@15986
   969
    val dot =
wenzelm@15986
   970
      (case rev (Symbol.explode x) of
wenzelm@15986
   971
        _ :: "\\<^isub>" :: _ => false
wenzelm@15986
   972
      | _ :: "\\<^isup>" :: _ => false
wenzelm@15986
   973
      | c :: _ => Symbol.is_digit c
wenzelm@15986
   974
      | _ => true);
wenzelm@14786
   975
  in
wenzelm@15986
   976
    if dot then question_mark ^ x ^ "." ^ idx
wenzelm@15986
   977
    else if i <> 0 then question_mark ^ x ^ idx
wenzelm@15986
   978
    else question_mark ^ x
wenzelm@14786
   979
  end;
wenzelm@14786
   980
wenzelm@14786
   981
fun string_of_vname' (x, ~1) = x
wenzelm@14786
   982
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
   983
clasohm@1364
   984
end;
clasohm@1364
   985
wenzelm@4444
   986
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
   987
open BasicTerm;