src/Pure/term.ML
author wenzelm
Tue Nov 14 00:15:43 2006 +0100 (2006-11-14)
changeset 21353 cfee13454195
parent 21013 b9321724c2cc
child 21493 47050cdc1694
permissions -rw-r--r--
added dummyS;
wenzelm@9536
     1
(*  Title:      Pure/term.ML
clasohm@0
     2
    ID:         $Id$
wenzelm@9536
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0
     4
    Copyright   Cambridge University 1992
clasohm@1364
     5
wenzelm@4444
     6
Simply typed lambda-calculus: types, terms, and basic operations.
clasohm@0
     7
*)
clasohm@0
     8
clasohm@1364
     9
infix 9  $;
clasohm@1364
    10
infixr 5 -->;
wenzelm@4444
    11
infixr --->;
wenzelm@4444
    12
infix aconv;
clasohm@1364
    13
wenzelm@4444
    14
signature BASIC_TERM =
wenzelm@4444
    15
sig
wenzelm@4444
    16
  type indexname
wenzelm@4444
    17
  type class
wenzelm@4444
    18
  type sort
wenzelm@14829
    19
  type arity
wenzelm@4444
    20
  datatype typ =
wenzelm@4444
    21
    Type  of string * typ list |
wenzelm@4444
    22
    TFree of string * sort |
wenzelm@4444
    23
    TVar  of indexname * sort
wenzelm@16537
    24
  datatype term =
wenzelm@16537
    25
    Const of string * typ |
wenzelm@16537
    26
    Free of string * typ |
wenzelm@16537
    27
    Var of indexname * typ |
wenzelm@16537
    28
    Bound of int |
wenzelm@16537
    29
    Abs of string * typ * term |
wenzelm@17756
    30
    $ of term * term
wenzelm@16537
    31
  exception TYPE of string * typ list * term list
wenzelm@16537
    32
  exception TERM of string * term list
wenzelm@21353
    33
  val dummyS: sort
wenzelm@16710
    34
  val dummyT: typ
wenzelm@16710
    35
  val no_dummyT: typ -> typ
wenzelm@4444
    36
  val --> : typ * typ -> typ
wenzelm@4444
    37
  val ---> : typ list * typ -> typ
wenzelm@16710
    38
  val dest_Type: typ -> string * typ list
wenzelm@16710
    39
  val dest_TVar: typ -> indexname * sort
wenzelm@16710
    40
  val dest_TFree: typ -> string * sort
wenzelm@16710
    41
  val is_Bound: term -> bool
wenzelm@16710
    42
  val is_Const: term -> bool
wenzelm@16710
    43
  val is_Free: term -> bool
wenzelm@16710
    44
  val is_Var: term -> bool
wenzelm@4444
    45
  val is_TVar: typ -> bool
wenzelm@16710
    46
  val dest_Const: term -> string * typ
wenzelm@16710
    47
  val dest_Free: term -> string * typ
wenzelm@16710
    48
  val dest_Var: term -> indexname * typ
wenzelm@4444
    49
  val domain_type: typ -> typ
wenzelm@4480
    50
  val range_type: typ -> typ
wenzelm@4444
    51
  val binder_types: typ -> typ list
wenzelm@4444
    52
  val body_type: typ -> typ
wenzelm@4444
    53
  val strip_type: typ -> typ list * typ
wenzelm@16710
    54
  val type_of1: typ list * term -> typ
wenzelm@4444
    55
  val type_of: term -> typ
wenzelm@16710
    56
  val fastype_of1: typ list * term -> typ
wenzelm@4444
    57
  val fastype_of: term -> typ
wenzelm@10806
    58
  val list_abs: (string * typ) list * term -> term
haftmann@18927
    59
  val strip_abs: term -> (string * typ) list * term
wenzelm@4444
    60
  val strip_abs_body: term -> term
wenzelm@4444
    61
  val strip_abs_vars: term -> (string * typ) list
wenzelm@4444
    62
  val strip_qnt_body: string -> term -> term
wenzelm@4444
    63
  val strip_qnt_vars: string -> term -> (string * typ) list
wenzelm@4444
    64
  val list_comb: term * term list -> term
wenzelm@4444
    65
  val strip_comb: term -> term * term list
wenzelm@4444
    66
  val head_of: term -> term
wenzelm@4444
    67
  val size_of_term: term -> 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
haftmann@18927
    77
  val it_term_types: (typ * 'a -> 'a) -> term * 'a -> 'a
wenzelm@16943
    78
  val add_term_names: term * string list -> string list
wenzelm@16710
    79
  val aconv: term * term -> bool
wenzelm@16537
    80
  structure Vartab: TABLE
wenzelm@16537
    81
  structure Typtab: TABLE
wenzelm@16537
    82
  structure Termtab: TABLE
wenzelm@4444
    83
  val propT: typ
wenzelm@4444
    84
  val implies: term
wenzelm@4444
    85
  val all: typ -> term
wenzelm@4444
    86
  val equals: typ -> term
wenzelm@4444
    87
  val strip_all_body: term -> term
wenzelm@4444
    88
  val strip_all_vars: term -> (string * typ) list
wenzelm@4444
    89
  val incr_bv: int * int * term -> term
wenzelm@4444
    90
  val incr_boundvars: int -> term -> term
wenzelm@4444
    91
  val add_loose_bnos: term * int * int list -> int list
wenzelm@4444
    92
  val loose_bnos: term -> int list
wenzelm@4444
    93
  val loose_bvar: term * int -> bool
wenzelm@4444
    94
  val loose_bvar1: term * int -> bool
wenzelm@4444
    95
  val subst_bounds: term list * term -> term
wenzelm@4444
    96
  val subst_bound: term * term -> term
wenzelm@4444
    97
  val betapply: term * term -> term
wenzelm@18183
    98
  val betapplys: term * term list -> term
wenzelm@4444
    99
  val eq_ix: indexname * indexname -> bool
wenzelm@4444
   100
  val could_unify: term * term -> bool
wenzelm@4444
   101
  val subst_free: (term * term) list -> term -> term
wenzelm@4444
   102
  val abstract_over: term * term -> term
wenzelm@11922
   103
  val lambda: term -> term -> term
wenzelm@4444
   104
  val absfree: string * typ * term -> term
wenzelm@17786
   105
  val absdummy: typ * term -> term
wenzelm@4444
   106
  val list_abs_free: (string * typ) list * term -> term
wenzelm@4444
   107
  val list_all_free: (string * typ) list * term -> term
wenzelm@4444
   108
  val list_all: (string * typ) list * term -> term
wenzelm@16710
   109
  val subst_atomic: (term * term) list -> term -> term
wenzelm@16710
   110
  val typ_subst_atomic: (typ * typ) list -> typ -> typ
wenzelm@16710
   111
  val subst_atomic_types: (typ * typ) list -> term -> term
wenzelm@16710
   112
  val typ_subst_TVars: (indexname * typ) list -> typ -> typ
wenzelm@16710
   113
  val subst_TVars: (indexname * typ) list -> term -> term
wenzelm@16710
   114
  val subst_Vars: (indexname * term) list -> term -> term
wenzelm@16710
   115
  val subst_vars: (indexname * typ) list * (indexname * term) list -> term -> term
wenzelm@16710
   116
  val is_first_order: string list -> term -> bool
wenzelm@4444
   117
  val maxidx_of_typ: typ -> int
wenzelm@4444
   118
  val maxidx_of_typs: typ list -> int
wenzelm@4444
   119
  val maxidx_of_term: term -> int
wenzelm@4444
   120
  val add_term_consts: term * string list -> string list
nipkow@13646
   121
  val term_consts: term -> string list
wenzelm@19909
   122
  val exists_subtype: (typ -> bool) -> typ -> bool
wenzelm@20531
   123
  val exists_type: (typ -> bool) -> term -> bool
wenzelm@16943
   124
  val exists_subterm: (term -> bool) -> term -> bool
wenzelm@16710
   125
  val exists_Const: (string * typ -> bool) -> term -> bool
wenzelm@16710
   126
  val add_term_free_names: term * string list -> string list
wenzelm@16710
   127
  val add_typ_tvars: typ * (indexname * sort) list -> (indexname * sort) list
wenzelm@16710
   128
  val add_typ_tfree_names: typ * string list -> string list
wenzelm@16710
   129
  val add_typ_tfrees: typ * (string * sort) list -> (string * sort) list
wenzelm@16710
   130
  val add_typ_varnames: typ * string list -> string list
wenzelm@16710
   131
  val add_term_tvars: term * (indexname * sort) list -> (indexname * sort) list
wenzelm@16710
   132
  val add_term_tfrees: term * (string * sort) list -> (string * sort) list
wenzelm@16710
   133
  val add_term_tfree_names: term * string list -> string list
wenzelm@16710
   134
  val typ_tfrees: typ -> (string * sort) list
wenzelm@16710
   135
  val typ_tvars: typ -> (indexname * sort) list
wenzelm@16710
   136
  val term_tfrees: term -> (string * sort) list
wenzelm@16710
   137
  val term_tvars: term -> (indexname * sort) list
wenzelm@16710
   138
  val add_typ_ixns: indexname list * typ -> indexname list
wenzelm@16710
   139
  val add_term_tvar_ixns: term * indexname list -> indexname list
wenzelm@16710
   140
  val add_term_vars: term * term list -> term list
wenzelm@16710
   141
  val term_vars: term -> term list
wenzelm@4444
   142
  val add_term_frees: term * term list -> term list
wenzelm@4444
   143
  val term_frees: term -> term list
wenzelm@20160
   144
  val rename_wrt_term: term -> (string * 'a) list -> (string * 'a) list
wenzelm@15986
   145
  val show_question_marks: bool ref
wenzelm@4444
   146
end;
clasohm@0
   147
wenzelm@4444
   148
signature TERM =
wenzelm@4444
   149
sig
wenzelm@4444
   150
  include BASIC_TERM
wenzelm@19394
   151
  val aT: sort -> typ
wenzelm@19394
   152
  val itselfT: typ -> typ
wenzelm@19394
   153
  val a_itselfT: typ
wenzelm@16710
   154
  val argument_type_of: term -> typ
wenzelm@16943
   155
  val add_tvarsT: typ -> (indexname * sort) list -> (indexname * sort) list
wenzelm@16943
   156
  val add_tvars: term -> (indexname * sort) list -> (indexname * sort) list
wenzelm@16943
   157
  val add_vars: term -> (indexname * typ) list -> (indexname * typ) list
wenzelm@16943
   158
  val add_tfreesT: typ -> (string * sort) list -> (string * sort) list
wenzelm@16943
   159
  val add_tfrees: term -> (string * sort) list -> (string * sort) list
wenzelm@16943
   160
  val add_frees: term -> (string * typ) list -> (string * typ) list
wenzelm@20199
   161
  val add_varnames: term -> indexname list -> indexname list
haftmann@20109
   162
  val strip_abs_eta: int -> term -> (string * typ) list * term
wenzelm@16678
   163
  val fast_indexname_ord: indexname * indexname -> order
wenzelm@16537
   164
  val indexname_ord: indexname * indexname -> order
wenzelm@16537
   165
  val sort_ord: sort * sort -> order
wenzelm@16537
   166
  val typ_ord: typ * typ -> order
wenzelm@16678
   167
  val fast_term_ord: term * term -> order
wenzelm@16537
   168
  val term_ord: term * term -> order
wenzelm@16537
   169
  val hd_ord: term * term -> order
wenzelm@16537
   170
  val termless: term * term -> bool
ballarin@20129
   171
  val term_lpo: (term -> int) -> term * term -> order
wenzelm@12981
   172
  val match_bvars: (term * term) * (string * string) list -> (string * string) list
wenzelm@12981
   173
  val rename_abs: term -> term -> term -> term option
wenzelm@16943
   174
  val eq_tvar: (indexname * sort) * (indexname * sort) -> bool
wenzelm@16882
   175
  val eq_var: (indexname * typ) * (indexname * typ) -> bool
wenzelm@16943
   176
  val tvar_ord: (indexname * sort) * (indexname * sort) -> order
wenzelm@16943
   177
  val var_ord: (indexname * typ) * (indexname * typ) -> order
wenzelm@16710
   178
  val maxidx_typ: typ -> int -> int
wenzelm@16710
   179
  val maxidx_typs: typ list -> int -> int
wenzelm@16710
   180
  val maxidx_term: term -> int -> int
wenzelm@20239
   181
  val dest_abs: string * typ * term -> string * term
wenzelm@20148
   182
  val declare_term_names: term -> Name.context -> Name.context
wenzelm@20160
   183
  val variant_frees: term -> (string * 'a) list -> (string * 'a) list
wenzelm@9536
   184
  val dummy_patternN: string
wenzelm@18253
   185
  val dummy_pattern: typ -> term
wenzelm@9536
   186
  val no_dummy_patterns: term -> term
wenzelm@9536
   187
  val replace_dummy_patterns: int * term -> int * term
wenzelm@10552
   188
  val is_replaced_dummy_pattern: indexname -> bool
wenzelm@16035
   189
  val show_dummy_patterns: term -> term
wenzelm@14786
   190
  val string_of_vname: indexname -> string
wenzelm@14786
   191
  val string_of_vname': indexname -> string
wenzelm@4444
   192
end;
wenzelm@4444
   193
wenzelm@4444
   194
structure Term: TERM =
clasohm@1364
   195
struct
clasohm@0
   196
clasohm@0
   197
(*Indexnames can be quickly renamed by adding an offset to the integer part,
clasohm@0
   198
  for resolution.*)
wenzelm@16537
   199
type indexname = string * int;
clasohm@0
   200
wenzelm@4626
   201
(* Types are classified by sorts. *)
clasohm@0
   202
type class = string;
clasohm@0
   203
type sort  = class list;
wenzelm@14829
   204
type arity = string * sort list * sort;
clasohm@0
   205
clasohm@0
   206
(* The sorts attached to TFrees and TVars specify the sort of that variable *)
clasohm@0
   207
datatype typ = Type  of string * typ list
clasohm@0
   208
             | TFree of string * sort
wenzelm@9536
   209
             | TVar  of indexname * sort;
clasohm@0
   210
paulson@6033
   211
(*Terms.  Bound variables are indicated by depth number.
clasohm@0
   212
  Free variables, (scheme) variables and constants have names.
wenzelm@4626
   213
  An term is "closed" if every bound variable of level "lev"
wenzelm@13000
   214
  is enclosed by at least "lev" abstractions.
clasohm@0
   215
clasohm@0
   216
  It is possible to create meaningless terms containing loose bound vars
clasohm@0
   217
  or type mismatches.  But such terms are not allowed in rules. *)
clasohm@0
   218
wenzelm@13000
   219
datatype term =
clasohm@0
   220
    Const of string * typ
wenzelm@13000
   221
  | Free  of string * typ
clasohm@0
   222
  | Var   of indexname * typ
clasohm@0
   223
  | Bound of int
clasohm@0
   224
  | Abs   of string*typ*term
wenzelm@3965
   225
  | op $  of term*term;
clasohm@0
   226
wenzelm@16537
   227
(*Errors involving type mismatches*)
clasohm@0
   228
exception TYPE of string * typ list * term list;
clasohm@0
   229
wenzelm@16537
   230
(*Errors errors involving terms*)
clasohm@0
   231
exception TERM of string * term list;
clasohm@0
   232
clasohm@0
   233
(*Note variable naming conventions!
clasohm@0
   234
    a,b,c: string
clasohm@0
   235
    f,g,h: functions (including terms of function type)
clasohm@0
   236
    i,j,m,n: int
clasohm@0
   237
    t,u: term
clasohm@0
   238
    v,w: indexnames
clasohm@0
   239
    x,y: any
clasohm@0
   240
    A,B,C: term (denoting formulae)
clasohm@0
   241
    T,U: typ
clasohm@0
   242
*)
clasohm@0
   243
clasohm@0
   244
paulson@6033
   245
(** Types **)
paulson@6033
   246
wenzelm@21353
   247
(*dummies for type-inference etc.*)
wenzelm@21353
   248
val dummyS = [""];
wenzelm@16537
   249
val dummyT = Type ("dummy", []);
wenzelm@16537
   250
wenzelm@16537
   251
fun no_dummyT typ =
wenzelm@16537
   252
  let
wenzelm@16537
   253
    fun check (T as Type ("dummy", _)) =
wenzelm@16537
   254
          raise TYPE ("Illegal occurrence of '_' dummy type", [T], [])
wenzelm@16537
   255
      | check (Type (_, Ts)) = List.app check Ts
wenzelm@16537
   256
      | check _ = ();
wenzelm@16537
   257
  in check typ; typ end;
wenzelm@16537
   258
paulson@6033
   259
fun S --> T = Type("fun",[S,T]);
paulson@6033
   260
paulson@6033
   261
(*handy for multiple args: [T1,...,Tn]--->T  gives  T1-->(T2--> ... -->T)*)
skalberg@15570
   262
val op ---> = Library.foldr (op -->);
paulson@6033
   263
paulson@6033
   264
fun dest_Type (Type x) = x
paulson@6033
   265
  | dest_Type T = raise TYPE ("dest_Type", [T], []);
dixon@15914
   266
fun dest_TVar (TVar x) = x
dixon@15914
   267
  | dest_TVar T = raise TYPE ("dest_TVar", [T], []);
dixon@15914
   268
fun dest_TFree (TFree x) = x
dixon@15914
   269
  | dest_TFree T = raise TYPE ("dest_TFree", [T], []);
paulson@6033
   270
wenzelm@16537
   271
clasohm@0
   272
(** Discriminators **)
clasohm@0
   273
nipkow@7318
   274
fun is_Bound (Bound _) = true
nipkow@7318
   275
  | is_Bound _         = false;
nipkow@7318
   276
clasohm@0
   277
fun is_Const (Const _) = true
clasohm@0
   278
  | is_Const _ = false;
clasohm@0
   279
clasohm@0
   280
fun is_Free (Free _) = true
clasohm@0
   281
  | is_Free _ = false;
clasohm@0
   282
clasohm@0
   283
fun is_Var (Var _) = true
clasohm@0
   284
  | is_Var _ = false;
clasohm@0
   285
clasohm@0
   286
fun is_TVar (TVar _) = true
clasohm@0
   287
  | is_TVar _ = false;
clasohm@0
   288
wenzelm@16537
   289
clasohm@0
   290
(** Destructors **)
clasohm@0
   291
clasohm@0
   292
fun dest_Const (Const x) =  x
clasohm@0
   293
  | dest_Const t = raise TERM("dest_Const", [t]);
clasohm@0
   294
clasohm@0
   295
fun dest_Free (Free x) =  x
clasohm@0
   296
  | dest_Free t = raise TERM("dest_Free", [t]);
clasohm@0
   297
clasohm@0
   298
fun dest_Var (Var x) =  x
clasohm@0
   299
  | dest_Var t = raise TERM("dest_Var", [t]);
clasohm@0
   300
clasohm@0
   301
paulson@4464
   302
fun domain_type (Type("fun", [T,_])) = T
paulson@4464
   303
and range_type  (Type("fun", [_,T])) = T;
paulson@4064
   304
clasohm@0
   305
(* maps  [T1,...,Tn]--->T  to the list  [T1,T2,...,Tn]*)
clasohm@0
   306
fun binder_types (Type("fun",[S,T])) = S :: binder_types T
clasohm@0
   307
  | binder_types _   =  [];
clasohm@0
   308
clasohm@0
   309
(* maps  [T1,...,Tn]--->T  to T*)
clasohm@0
   310
fun body_type (Type("fun",[S,T])) = body_type T
clasohm@0
   311
  | body_type T   =  T;
clasohm@0
   312
clasohm@0
   313
(* maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T)  *)
clasohm@0
   314
fun strip_type T : typ list * typ =
clasohm@0
   315
  (binder_types T, body_type T);
clasohm@0
   316
clasohm@0
   317
clasohm@0
   318
(*Compute the type of the term, checking that combinations are well-typed
clasohm@0
   319
  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
clasohm@0
   320
fun type_of1 (Ts, Const (_,T)) = T
clasohm@0
   321
  | type_of1 (Ts, Free  (_,T)) = T
skalberg@15570
   322
  | type_of1 (Ts, Bound i) = (List.nth (Ts,i)
skalberg@15570
   323
        handle Subscript => raise TYPE("type_of: bound variable", [], [Bound i]))
clasohm@0
   324
  | type_of1 (Ts, Var (_,T)) = T
clasohm@0
   325
  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
wenzelm@13000
   326
  | type_of1 (Ts, f$u) =
clasohm@0
   327
      let val U = type_of1(Ts,u)
clasohm@0
   328
          and T = type_of1(Ts,f)
clasohm@0
   329
      in case T of
wenzelm@9536
   330
            Type("fun",[T1,T2]) =>
wenzelm@9536
   331
              if T1=U then T2  else raise TYPE
wenzelm@9536
   332
                    ("type_of: type mismatch in application", [T1,U], [f$u])
wenzelm@13000
   333
          | _ => raise TYPE
wenzelm@9536
   334
                    ("type_of: function type is expected in application",
wenzelm@9536
   335
                     [T,U], [f$u])
clasohm@0
   336
      end;
clasohm@0
   337
clasohm@0
   338
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   339
clasohm@0
   340
(*Determines the type of a term, with minimal checking*)
wenzelm@13000
   341
fun fastype_of1 (Ts, f$u) =
lcp@61
   342
    (case fastype_of1 (Ts,f) of
wenzelm@9536
   343
        Type("fun",[_,T]) => T
wenzelm@9536
   344
        | _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   345
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   346
  | fastype_of1 (_, Free (_,T)) = T
skalberg@15570
   347
  | fastype_of1 (Ts, Bound i) = (List.nth(Ts,i)
skalberg@15570
   348
         handle Subscript => raise TERM("fastype_of: Bound", [Bound i]))
wenzelm@13000
   349
  | fastype_of1 (_, Var (_,T)) = T
lcp@61
   350
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   351
lcp@61
   352
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   353
wenzelm@16678
   354
(*Determine the argument type of a function*)
wenzelm@16678
   355
fun argument_type_of tm =
wenzelm@16678
   356
  let
wenzelm@16678
   357
    fun argT i (Type ("fun", [T, U])) = if i = 0 then T else argT (i - 1) U
wenzelm@16678
   358
      | argT _ T = raise TYPE ("argument_type_of", [T], []);
wenzelm@16678
   359
wenzelm@16678
   360
    fun arg 0 _ (Abs (_, T, _)) = T
wenzelm@16678
   361
      | arg i Ts (Abs (_, T, t)) = arg (i - 1) (T :: Ts) t
wenzelm@16678
   362
      | arg i Ts (t $ _) = arg (i + 1) Ts t
wenzelm@16678
   363
      | arg i Ts a = argT i (fastype_of1 (Ts, a));
wenzelm@16678
   364
  in arg 0 [] tm end;
wenzelm@16678
   365
clasohm@0
   366
wenzelm@19473
   367
val list_abs = uncurry (fold_rev (fn (x, T) => fn t => Abs (x, T, t)));
wenzelm@10806
   368
haftmann@18927
   369
fun strip_abs (Abs (a, T, t)) =
haftmann@18927
   370
      let val (a', t') = strip_abs t
haftmann@18927
   371
      in ((a, T) :: a', t') end
haftmann@18927
   372
  | strip_abs t = ([], t);
haftmann@18927
   373
clasohm@0
   374
(* maps  (x1,...,xn)t   to   t  *)
wenzelm@13000
   375
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t
clasohm@0
   376
  | strip_abs_body u  =  u;
clasohm@0
   377
clasohm@0
   378
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
wenzelm@13000
   379
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t
clasohm@0
   380
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   381
clasohm@0
   382
clasohm@0
   383
fun strip_qnt_body qnt =
clasohm@0
   384
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   385
      | strip t = t
clasohm@0
   386
in strip end;
clasohm@0
   387
clasohm@0
   388
fun strip_qnt_vars qnt =
clasohm@0
   389
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   390
      | strip t  =  [] : (string*typ) list
clasohm@0
   391
in strip end;
clasohm@0
   392
clasohm@0
   393
clasohm@0
   394
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
skalberg@15570
   395
val list_comb : term * term list -> term = Library.foldl (op $);
clasohm@0
   396
clasohm@0
   397
clasohm@0
   398
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
wenzelm@13000
   399
fun strip_comb u : term * term list =
clasohm@0
   400
    let fun stripc (f$t, ts) = stripc (f, t::ts)
wenzelm@13000
   401
        |   stripc  x =  x
clasohm@0
   402
    in  stripc(u,[])  end;
clasohm@0
   403
clasohm@0
   404
clasohm@0
   405
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   406
fun head_of (f$t) = head_of f
clasohm@0
   407
  | head_of u = u;
clasohm@0
   408
clasohm@0
   409
wenzelm@16599
   410
(*number of atoms and abstractions in a term*)
wenzelm@16599
   411
fun size_of_term tm =
wenzelm@16599
   412
  let
wenzelm@16678
   413
    fun add_size (t $ u, n) = add_size (t, add_size (u, n))
wenzelm@16678
   414
      | add_size (Abs (_ ,_, t), n) = add_size (t, n + 1)
wenzelm@16678
   415
      | add_size (_, n) = n + 1;
wenzelm@16678
   416
  in add_size (tm, 0) end;
clasohm@0
   417
haftmann@18847
   418
fun map_atyps f (Type (a, Ts)) = Type (a, map (map_atyps f) Ts)
haftmann@18976
   419
  | map_atyps f T = f T;
haftmann@18847
   420
haftmann@18847
   421
fun map_aterms f (t $ u) = map_aterms f t $ map_aterms f u
haftmann@18847
   422
  | map_aterms f (Abs (a, T, t)) = Abs (a, T, map_aterms f t)
haftmann@18847
   423
  | map_aterms f t = f t;
haftmann@18847
   424
wenzelm@18981
   425
fun map_type_tvar f = map_atyps (fn TVar x => f x | T => T);
wenzelm@18981
   426
fun map_type_tfree f = map_atyps (fn TFree x => f x | T => T);
nipkow@949
   427
wenzelm@20548
   428
fun map_types f =
wenzelm@16678
   429
  let
wenzelm@16678
   430
    fun map_aux (Const (a, T)) = Const (a, f T)
wenzelm@16678
   431
      | map_aux (Free (a, T)) = Free (a, f T)
wenzelm@16678
   432
      | map_aux (Var (v, T)) = Var (v, f T)
wenzelm@16678
   433
      | map_aux (t as Bound _)  = t
wenzelm@16678
   434
      | map_aux (Abs (a, T, t)) = Abs (a, f T, map_aux t)
wenzelm@16678
   435
      | map_aux (t $ u) = map_aux t $ map_aux u;
wenzelm@16678
   436
  in map_aux end;
clasohm@0
   437
clasohm@0
   438
(* iterate a function over all types in a term *)
clasohm@0
   439
fun it_term_types f =
clasohm@0
   440
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   441
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   442
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   443
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   444
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   445
      | iter(Bound _, a) = a
clasohm@0
   446
in iter end
clasohm@0
   447
clasohm@0
   448
wenzelm@16943
   449
(* fold types and terms *)
wenzelm@16943
   450
wenzelm@16943
   451
(*fold atoms of type*)
wenzelm@16943
   452
fun fold_atyps f (Type (_, Ts)) = fold (fold_atyps f) Ts
wenzelm@16943
   453
  | fold_atyps f T = f T;
wenzelm@16943
   454
wenzelm@16943
   455
(*fold atoms of term*)
wenzelm@16943
   456
fun fold_aterms f (t $ u) = fold_aterms f t #> fold_aterms f u
wenzelm@16943
   457
  | fold_aterms f (Abs (_, _, t)) = fold_aterms f t
wenzelm@16943
   458
  | fold_aterms f a = f a;
wenzelm@16943
   459
wenzelm@16943
   460
(*fold types of term*)
wenzelm@16943
   461
fun fold_term_types f (t as Const (_, T)) = f t T
wenzelm@16943
   462
  | fold_term_types f (t as Free (_, T)) = f t T
wenzelm@16943
   463
  | fold_term_types f (t as Var (_, T)) = f t T
wenzelm@16943
   464
  | fold_term_types f (Bound _) = I
wenzelm@16943
   465
  | fold_term_types f (t as Abs (_, T, b)) = f t T #> fold_term_types f b
wenzelm@16943
   466
  | fold_term_types f (t $ u) = fold_term_types f t #> fold_term_types f u;
wenzelm@16943
   467
wenzelm@16943
   468
fun fold_types f = fold_term_types (K f);
wenzelm@16943
   469
wenzelm@16943
   470
(*collect variables*)
wenzelm@16943
   471
val add_tvarsT = fold_atyps (fn TVar v => insert (op =) v | _ => I);
wenzelm@16943
   472
val add_tvars = fold_types add_tvarsT;
wenzelm@16943
   473
val add_vars = fold_aterms (fn Var v => insert (op =) v | _ => I);
wenzelm@20199
   474
val add_varnames = fold_aterms (fn Var (xi, _) => insert (op =) xi | _ => I);
wenzelm@16943
   475
val add_tfreesT = fold_atyps (fn TFree v => insert (op =) v | _ => I);
wenzelm@16943
   476
val add_tfrees = fold_types add_tfreesT;
wenzelm@16943
   477
val add_frees = fold_aterms (fn Free v => insert (op =) v | _ => I);
wenzelm@16943
   478
wenzelm@16943
   479
wenzelm@16678
   480
(** Comparing terms, types, sorts etc. **)
wenzelm@16537
   481
wenzelm@20511
   482
(* alpha equivalence -- tuned for equalities *)
wenzelm@20511
   483
wenzelm@20511
   484
fun tm1 aconv tm2 =
wenzelm@20511
   485
  pointer_eq (tm1, tm2) orelse
wenzelm@20511
   486
    (case (tm1, tm2) of
wenzelm@20511
   487
      (t1 $ u1, t2 $ u2) => t1 aconv t2 andalso u1 aconv u2
wenzelm@20511
   488
    | (Abs (_, T1, t1), Abs (_, T2, t2)) => t1 aconv t2 andalso T1 = T2
wenzelm@20511
   489
    | (a1, a2) => a1 = a2);
wenzelm@20511
   490
wenzelm@20511
   491
wenzelm@20511
   492
(* fast syntactic ordering -- tuned for inequalities *)
wenzelm@16678
   493
wenzelm@16678
   494
fun fast_indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   495
  (case int_ord (i, j) of EQUAL => fast_string_ord (x, y) | ord => ord);
wenzelm@16537
   496
wenzelm@16599
   497
fun sort_ord SS =
wenzelm@16599
   498
  if pointer_eq SS then EQUAL
wenzelm@16990
   499
  else dict_ord fast_string_ord SS;
wenzelm@16678
   500
wenzelm@16678
   501
local
wenzelm@16537
   502
wenzelm@16678
   503
fun cons_nr (TVar _) = 0
wenzelm@16678
   504
  | cons_nr (TFree _) = 1
wenzelm@16678
   505
  | cons_nr (Type _) = 2;
wenzelm@16537
   506
wenzelm@16678
   507
in
wenzelm@16537
   508
wenzelm@16537
   509
fun typ_ord TU =
wenzelm@16537
   510
  if pointer_eq TU then EQUAL
wenzelm@16537
   511
  else
wenzelm@16537
   512
    (case TU of
wenzelm@16678
   513
      (Type (a, Ts), Type (b, Us)) =>
wenzelm@16990
   514
        (case fast_string_ord (a, b) of EQUAL => dict_ord typ_ord (Ts, Us) | ord => ord)
wenzelm@16678
   515
    | (TFree (a, S), TFree (b, S')) =>
wenzelm@16678
   516
        (case fast_string_ord (a, b) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   517
    | (TVar (xi, S), TVar (yj, S')) =>
wenzelm@16678
   518
        (case fast_indexname_ord (xi, yj) of EQUAL => sort_ord (S, S') | ord => ord)
wenzelm@16678
   519
    | (T, U) => int_ord (cons_nr T, cons_nr U));
wenzelm@16678
   520
wenzelm@16678
   521
end;
wenzelm@16678
   522
wenzelm@16678
   523
local
wenzelm@16678
   524
wenzelm@16678
   525
fun cons_nr (Const _) = 0
wenzelm@16678
   526
  | cons_nr (Free _) = 1
wenzelm@16678
   527
  | cons_nr (Var _) = 2
wenzelm@16678
   528
  | cons_nr (Bound _) = 3
wenzelm@16678
   529
  | cons_nr (Abs _) = 4
wenzelm@16678
   530
  | cons_nr (_ $ _) = 5;
wenzelm@16678
   531
wenzelm@16678
   532
fun struct_ord (Abs (_, _, t), Abs (_, _, u)) = struct_ord (t, u)
wenzelm@16678
   533
  | struct_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   534
      (case struct_ord (t1, u1) of EQUAL => struct_ord (t2, u2) | ord => ord)
wenzelm@16678
   535
  | struct_ord (t, u) = int_ord (cons_nr t, cons_nr u);
wenzelm@16678
   536
wenzelm@16678
   537
fun atoms_ord (Abs (_, _, t), Abs (_, _, u)) = atoms_ord (t, u)
wenzelm@16678
   538
  | atoms_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   539
      (case atoms_ord (t1, u1) of EQUAL => atoms_ord (t2, u2) | ord => ord)
wenzelm@16678
   540
  | atoms_ord (Const (a, _), Const (b, _)) = fast_string_ord (a, b)
wenzelm@16678
   541
  | atoms_ord (Free (x, _), Free (y, _)) = fast_string_ord (x, y)
wenzelm@16678
   542
  | atoms_ord (Var (xi, _), Var (yj, _)) = fast_indexname_ord (xi, yj)
wenzelm@16678
   543
  | atoms_ord (Bound i, Bound j) = int_ord (i, j)
wenzelm@16678
   544
  | atoms_ord _ = sys_error "atoms_ord";
wenzelm@16678
   545
wenzelm@16678
   546
fun types_ord (Abs (_, T, t), Abs (_, U, u)) =
wenzelm@16678
   547
      (case typ_ord (T, U) of EQUAL => types_ord (t, u) | ord => ord)
wenzelm@16678
   548
  | types_ord (t1 $ t2, u1 $ u2) =
wenzelm@16678
   549
      (case types_ord (t1, u1) of EQUAL => types_ord (t2, u2) | ord => ord)
wenzelm@16678
   550
  | types_ord (Const (_, T), Const (_, U)) = typ_ord (T, U)
wenzelm@16678
   551
  | types_ord (Free (_, T), Free (_, U)) = typ_ord (T, U)
wenzelm@16678
   552
  | types_ord (Var (_, T), Var (_, U)) = typ_ord (T, U)
wenzelm@16678
   553
  | types_ord (Bound _, Bound _) = EQUAL
wenzelm@16678
   554
  | types_ord _ = sys_error "types_ord";
wenzelm@16678
   555
wenzelm@16678
   556
in
wenzelm@16678
   557
wenzelm@16678
   558
fun fast_term_ord tu =
wenzelm@16678
   559
  if pointer_eq tu then EQUAL
wenzelm@16678
   560
  else
wenzelm@16678
   561
    (case struct_ord tu of
wenzelm@16678
   562
      EQUAL => (case atoms_ord tu of EQUAL => types_ord tu | ord => ord)
wenzelm@16678
   563
    | ord => ord);
wenzelm@16678
   564
wenzelm@16678
   565
structure Vartab = TableFun(type key = indexname val ord = fast_indexname_ord);
wenzelm@16678
   566
structure Typtab = TableFun(type key = typ val ord = typ_ord);
wenzelm@16678
   567
structure Termtab = TableFun(type key = term val ord = fast_term_ord);
wenzelm@16678
   568
wenzelm@16678
   569
end;
wenzelm@16537
   570
wenzelm@16537
   571
wenzelm@16537
   572
(* term_ord *)
wenzelm@16537
   573
wenzelm@16537
   574
(*a linear well-founded AC-compatible ordering for terms:
wenzelm@16537
   575
  s < t <=> 1. size(s) < size(t) or
wenzelm@16537
   576
            2. size(s) = size(t) and s=f(...) and t=g(...) and f<g or
wenzelm@16537
   577
            3. size(s) = size(t) and s=f(s1..sn) and t=f(t1..tn) and
wenzelm@16537
   578
               (s1..sn) < (t1..tn) (lexicographically)*)
wenzelm@16678
   579
wenzelm@16678
   580
fun indexname_ord ((x, i), (y, j)) =
wenzelm@16678
   581
  (case int_ord (i, j) of EQUAL => string_ord (x, y) | ord => ord);
wenzelm@16678
   582
wenzelm@16667
   583
local
wenzelm@16667
   584
wenzelm@16667
   585
fun hd_depth (t $ _, n) = hd_depth (t, n + 1)
wenzelm@16667
   586
  | hd_depth p = p;
wenzelm@16537
   587
wenzelm@16537
   588
fun dest_hd (Const (a, T)) = (((a, 0), T), 0)
wenzelm@16537
   589
  | dest_hd (Free (a, T)) = (((a, 0), T), 1)
wenzelm@16537
   590
  | dest_hd (Var v) = (v, 2)
wenzelm@16537
   591
  | dest_hd (Bound i) = ((("", i), dummyT), 3)
wenzelm@16537
   592
  | dest_hd (Abs (_, T, _)) = ((("", 0), T), 4);
wenzelm@16537
   593
wenzelm@16667
   594
in
wenzelm@16667
   595
wenzelm@16537
   596
fun term_ord tu =
wenzelm@16537
   597
  if pointer_eq tu then EQUAL
wenzelm@16537
   598
  else
wenzelm@16537
   599
    (case tu of
wenzelm@16537
   600
      (Abs (_, T, t), Abs(_, U, u)) =>
wenzelm@16537
   601
        (case term_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
wenzelm@16667
   602
    | (t, u) =>
wenzelm@16537
   603
        (case int_ord (size_of_term t, size_of_term u) of
wenzelm@16537
   604
          EQUAL =>
wenzelm@16943
   605
            (case prod_ord hd_ord int_ord (hd_depth (t, 0), hd_depth (u, 0)) of
wenzelm@16943
   606
              EQUAL => args_ord (t, u) | ord => ord)
wenzelm@16537
   607
        | ord => ord))
wenzelm@16537
   608
and hd_ord (f, g) =
wenzelm@16537
   609
  prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd f, dest_hd g)
wenzelm@16667
   610
and args_ord (f $ t, g $ u) =
wenzelm@16667
   611
      (case args_ord (f, g) of EQUAL => term_ord (t, u) | ord => ord)
wenzelm@16667
   612
  | args_ord _ = EQUAL;
wenzelm@16537
   613
wenzelm@16537
   614
fun termless tu = (term_ord tu = LESS);
wenzelm@16537
   615
wenzelm@16667
   616
end;
wenzelm@16667
   617
wenzelm@16667
   618
wenzelm@16667
   619
(** Lexicographic path order on terms **)
wenzelm@16667
   620
wenzelm@16667
   621
(*
nipkow@16570
   622
  See Baader & Nipkow, Term rewriting, CUP 1998.
nipkow@16570
   623
  Without variables.  Const, Var, Bound, Free and Abs are treated all as
nipkow@16570
   624
  constants.
nipkow@16570
   625
ballarin@20129
   626
  f_ord maps terms to integers and serves two purposes:
nipkow@16570
   627
  - Predicate on constant symbols.  Those that are not recognised by f_ord
nipkow@16570
   628
    must be mapped to ~1.
nipkow@16570
   629
  - Order on the recognised symbols.  These must be mapped to distinct
nipkow@16570
   630
    integers >= 0.
ballarin@20129
   631
  The argument of f_ord is never an application.
wenzelm@16667
   632
*)
nipkow@16570
   633
nipkow@16570
   634
local
ballarin@20129
   635
ballarin@20129
   636
fun unrecognized (Const (a, T)) = ((1, ((a, 0), T)), 0)
ballarin@20129
   637
  | unrecognized (Free (a, T)) = ((1, ((a, 0), T)), 0)
ballarin@20129
   638
  | unrecognized (Var v) = ((1, v), 1)
ballarin@20129
   639
  | unrecognized (Bound i) = ((1, (("", i), dummyT)), 2)
ballarin@20129
   640
  | unrecognized (Abs (_, T, _)) = ((1, (("", 0), T)), 3);
ballarin@20129
   641
ballarin@20129
   642
fun dest_hd f_ord t =
ballarin@20129
   643
      let val ord = f_ord t in
ballarin@20129
   644
        if ord = ~1 then unrecognized t else ((0, (("", ord), fastype_of t)), 0)
nipkow@16570
   645
      end
nipkow@16570
   646
nipkow@16570
   647
fun term_lpo f_ord (s, t) =
nipkow@16570
   648
  let val (f, ss) = strip_comb s and (g, ts) = strip_comb t in
nipkow@16570
   649
    if forall (fn si => term_lpo f_ord (si, t) = LESS) ss
nipkow@16570
   650
    then case hd_ord f_ord (f, g) of
wenzelm@16667
   651
        GREATER =>
wenzelm@16667
   652
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   653
          then GREATER else LESS
nipkow@16570
   654
      | EQUAL =>
wenzelm@16667
   655
          if forall (fn ti => term_lpo f_ord (s, ti) = GREATER) ts
wenzelm@16667
   656
          then list_ord (term_lpo f_ord) (ss, ts)
wenzelm@16667
   657
          else LESS
nipkow@16570
   658
      | LESS => LESS
nipkow@16570
   659
    else GREATER
nipkow@16570
   660
  end
nipkow@16570
   661
and hd_ord f_ord (f, g) = case (f, g) of
nipkow@16570
   662
    (Abs (_, T, t), Abs (_, U, u)) =>
nipkow@16570
   663
      (case term_lpo f_ord (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
nipkow@16570
   664
  | (_, _) => prod_ord (prod_ord int_ord
nipkow@16570
   665
                  (prod_ord indexname_ord typ_ord)) int_ord
nipkow@16570
   666
                (dest_hd f_ord f, dest_hd f_ord g)
nipkow@16570
   667
in
nipkow@16570
   668
val term_lpo = term_lpo
nipkow@16570
   669
end;
nipkow@16570
   670
wenzelm@16537
   671
clasohm@0
   672
(** Connectives of higher order logic **)
clasohm@0
   673
wenzelm@19394
   674
fun aT S = TFree ("'a", S);
wenzelm@19394
   675
wenzelm@375
   676
fun itselfT ty = Type ("itself", [ty]);
wenzelm@14854
   677
val a_itselfT = itselfT (TFree ("'a", []));
wenzelm@375
   678
clasohm@0
   679
val propT : typ = Type("prop",[]);
clasohm@0
   680
clasohm@0
   681
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   682
clasohm@0
   683
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   684
clasohm@0
   685
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   686
clasohm@0
   687
(* maps  !!x1...xn. t   to   t  *)
wenzelm@13000
   688
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t
clasohm@0
   689
  | strip_all_body t  =  t;
clasohm@0
   690
clasohm@0
   691
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   692
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
wenzelm@13000
   693
                (a,T) :: strip_all_vars t
clasohm@0
   694
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   695
clasohm@0
   696
(*increments a term's non-local bound variables
clasohm@0
   697
  required when moving a term within abstractions
clasohm@0
   698
     inc is  increment for bound variables
clasohm@0
   699
     lev is  level at which a bound variable is considered 'loose'*)
wenzelm@13000
   700
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u
clasohm@0
   701
  | incr_bv (inc, lev, Abs(a,T,body)) =
wenzelm@9536
   702
        Abs(a, T, incr_bv(inc,lev+1,body))
wenzelm@13000
   703
  | incr_bv (inc, lev, f$t) =
clasohm@0
   704
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   705
  | incr_bv (inc, lev, u) = u;
clasohm@0
   706
clasohm@0
   707
fun incr_boundvars  0  t = t
clasohm@0
   708
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   709
wenzelm@12981
   710
(*Scan a pair of terms; while they are similar,
wenzelm@12981
   711
  accumulate corresponding bound vars in "al"*)
wenzelm@12981
   712
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) =
wenzelm@12981
   713
      match_bvs(s, t, if x="" orelse y="" then al
wenzelm@12981
   714
                                          else (x,y)::al)
wenzelm@12981
   715
  | match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
wenzelm@12981
   716
  | match_bvs(_,_,al) = al;
wenzelm@12981
   717
wenzelm@12981
   718
(* strip abstractions created by parameters *)
wenzelm@12981
   719
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
wenzelm@12981
   720
wenzelm@12981
   721
fun rename_abs pat obj t =
wenzelm@12981
   722
  let
wenzelm@12981
   723
    val ren = match_bvs (pat, obj, []);
wenzelm@12981
   724
    fun ren_abs (Abs (x, T, b)) =
wenzelm@18942
   725
          Abs (the_default x (AList.lookup (op =) ren x), T, ren_abs b)
wenzelm@12981
   726
      | ren_abs (f $ t) = ren_abs f $ ren_abs t
wenzelm@12981
   727
      | ren_abs t = t
skalberg@15531
   728
  in if null ren then NONE else SOME (ren_abs t) end;
clasohm@0
   729
clasohm@0
   730
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   731
   (Bound 0) is loose at level 0 *)
wenzelm@13000
   732
fun add_loose_bnos (Bound i, lev, js) =
haftmann@20854
   733
        if i<lev then js else insert (op =) (i - lev) js
clasohm@0
   734
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   735
  | add_loose_bnos (f$t, lev, js) =
wenzelm@13000
   736
        add_loose_bnos (f, lev, add_loose_bnos (t, lev, js))
clasohm@0
   737
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   738
clasohm@0
   739
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   740
clasohm@0
   741
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   742
   level k or beyond. *)
clasohm@0
   743
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   744
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   745
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   746
  | loose_bvar _ = false;
clasohm@0
   747
nipkow@2792
   748
fun loose_bvar1(Bound i,k) = i = k
nipkow@2792
   749
  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
nipkow@2792
   750
  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
nipkow@2792
   751
  | loose_bvar1 _ = false;
clasohm@0
   752
clasohm@0
   753
(*Substitute arguments for loose bound variables.
clasohm@0
   754
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
wenzelm@4626
   755
  Note that for ((%x y. c) a b), the bound vars in c are x=1 and y=0
wenzelm@9536
   756
        and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   757
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   758
     compensate for the disappearance of lambdas.
clasohm@0
   759
*)
wenzelm@13000
   760
fun subst_bounds (args: term list, t) : term =
wenzelm@19065
   761
  let
wenzelm@19065
   762
    exception SAME;
wenzelm@19065
   763
    val n = length args;
wenzelm@19065
   764
    fun subst (t as Bound i, lev) =
wenzelm@19065
   765
         (if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   766
          else incr_boundvars lev (List.nth (args, i - lev))
wenzelm@19065
   767
            handle Subscript => Bound (i - n))  (*loose: change it*)
wenzelm@19065
   768
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   769
      | subst (f $ t, lev) =
wenzelm@19065
   770
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   771
      | subst _ = raise SAME;
wenzelm@19065
   772
  in case args of [] => t | _ => (subst (t, 0) handle SAME => t) end;
clasohm@0
   773
paulson@2192
   774
(*Special case: one argument*)
wenzelm@13000
   775
fun subst_bound (arg, t) : term =
wenzelm@19065
   776
  let
wenzelm@19065
   777
    exception SAME;
wenzelm@19065
   778
    fun subst (Bound i, lev) =
wenzelm@19065
   779
          if i < lev then raise SAME   (*var is locally bound*)
wenzelm@19065
   780
          else if i = lev then incr_boundvars lev arg
wenzelm@19065
   781
          else Bound (i - 1)   (*loose: change it*)
wenzelm@19065
   782
      | subst (Abs (a, T, body), lev) = Abs (a, T, subst (body, lev + 1))
wenzelm@19065
   783
      | subst (f $ t, lev) =
wenzelm@19065
   784
          (subst (f, lev) $ (subst (t, lev) handle SAME => t) handle SAME => f $ subst (t, lev))
wenzelm@19065
   785
      | subst _ = raise SAME;
wenzelm@19065
   786
  in subst (t, 0) handle SAME => t end;
paulson@2192
   787
clasohm@0
   788
(*beta-reduce if possible, else form application*)
paulson@2192
   789
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   790
  | betapply (f,u) = f$u;
clasohm@0
   791
wenzelm@18183
   792
val betapplys = Library.foldl betapply;
wenzelm@18183
   793
wenzelm@14786
   794
haftmann@20109
   795
(*unfolding abstractions with substitution
haftmann@20109
   796
  of bound variables and implicit eta-expansion*)
haftmann@20109
   797
fun strip_abs_eta k t =
haftmann@20109
   798
  let
wenzelm@20122
   799
    val used = fold_aterms (fn Free (v, _) => Name.declare v | _ => I) t Name.context;
haftmann@20109
   800
    fun strip_abs t (0, used) = (([], t), (0, used))
haftmann@20109
   801
      | strip_abs (Abs (v, T, t)) (k, used) =
haftmann@20109
   802
          let
wenzelm@20122
   803
            val ([v'], used') = Name.variants [v] used;
haftmann@21013
   804
            val t' = subst_bound (Free (v', T), t);
wenzelm@20122
   805
            val ((vs, t''), (k', used'')) = strip_abs t' (k - 1, used');
wenzelm@20122
   806
          in (((v', T) :: vs, t''), (k', used'')) end
haftmann@20109
   807
      | strip_abs t (k, used) = (([], t), (k, used));
haftmann@20109
   808
    fun expand_eta [] t _ = ([], t)
haftmann@20109
   809
      | expand_eta (T::Ts) t used =
haftmann@20109
   810
          let
wenzelm@20122
   811
            val ([v], used') = Name.variants [""] used;
wenzelm@20122
   812
            val (vs, t') = expand_eta Ts (t $ Free (v, T)) used';
haftmann@20109
   813
          in ((v, T) :: vs, t') end;
haftmann@20109
   814
    val ((vs1, t'), (k', used')) = strip_abs t (k, used);
haftmann@20109
   815
    val Ts = (fst o chop k' o fst o strip_type o fastype_of) t';
haftmann@20109
   816
    val (vs2, t'') = expand_eta Ts t' used';
haftmann@20109
   817
  in (vs1 @ vs2, t'') end;
haftmann@20109
   818
haftmann@20109
   819
wenzelm@20199
   820
(* comparing variables *)
wenzelm@16882
   821
wenzelm@16724
   822
fun eq_ix ((x, i): indexname, (y, j)) = i = j andalso x = y;
paulson@2192
   823
wenzelm@16943
   824
fun eq_tvar ((xi, S: sort), (xi', S')) = eq_ix (xi, xi') andalso S = S';
wenzelm@16943
   825
fun eq_var ((xi, T: typ), (xi', T')) = eq_ix (xi, xi') andalso T = T';
wenzelm@16943
   826
wenzelm@16943
   827
val tvar_ord = prod_ord indexname_ord sort_ord;
wenzelm@16943
   828
val var_ord = prod_ord indexname_ord typ_ord;
wenzelm@16882
   829
wenzelm@16882
   830
wenzelm@13000
   831
(*A fast unification filter: true unless the two terms cannot be unified.
clasohm@0
   832
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   833
fun could_unify (t,u) =
clasohm@0
   834
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
wenzelm@9536
   835
        | matchrands _ = true
clasohm@0
   836
  in case (head_of t , head_of u) of
wenzelm@9536
   837
        (_, Var _) => true
clasohm@0
   838
      | (Var _, _) => true
clasohm@0
   839
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   840
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   841
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   842
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   843
      | (_, Abs _) =>  true
clasohm@0
   844
      | _ => false
clasohm@0
   845
  end;
clasohm@0
   846
clasohm@0
   847
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   848
fun subst_free [] = (fn t=>t)
clasohm@0
   849
  | subst_free pairs =
wenzelm@13000
   850
      let fun substf u =
haftmann@17314
   851
            case AList.lookup (op aconv) pairs u of
skalberg@15531
   852
                SOME u' => u'
skalberg@15531
   853
              | NONE => (case u of Abs(a,T,t) => Abs(a, T, substf t)
wenzelm@9536
   854
                                 | t$u' => substf t $ substf u'
wenzelm@9536
   855
                                 | _ => u)
clasohm@0
   856
      in  substf  end;
clasohm@0
   857
wenzelm@13000
   858
(*Abstraction of the term "body" over its occurrences of v,
clasohm@0
   859
    which must contain no loose bound variables.
clasohm@0
   860
  The resulting term is ready to become the body of an Abs.*)
wenzelm@16882
   861
fun abstract_over (v, body) =
wenzelm@16882
   862
  let
wenzelm@16990
   863
    exception SAME;
wenzelm@16990
   864
    fun abs lev tm =
wenzelm@16990
   865
      if v aconv tm then Bound lev
wenzelm@16882
   866
      else
wenzelm@16990
   867
        (case tm of
wenzelm@16990
   868
          Abs (a, T, t) => Abs (a, T, abs (lev + 1) t)
wenzelm@16990
   869
        | t $ u => (abs lev t $ (abs lev u handle SAME => u) handle SAME => t $ abs lev u)
wenzelm@16990
   870
        | _ => raise SAME);
wenzelm@16990
   871
  in abs 0 body handle SAME => body end;
clasohm@0
   872
wenzelm@18975
   873
fun lambda (v as Const (x, T)) t = Abs (NameSpace.base x, T, abstract_over (v, t))
wenzelm@18942
   874
  | lambda (v as Free (x, T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   875
  | lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t))
berghofe@13665
   876
  | lambda v t = raise TERM ("lambda", [v, t]);
clasohm@0
   877
clasohm@0
   878
(*Form an abstraction over a free variable.*)
clasohm@0
   879
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
wenzelm@17786
   880
fun absdummy (T, body) = Abs ("uu", T, body);
clasohm@0
   881
clasohm@0
   882
(*Abstraction over a list of free variables*)
clasohm@0
   883
fun list_abs_free ([ ] ,     t) = t
wenzelm@13000
   884
  | list_abs_free ((a,T)::vars, t) =
clasohm@0
   885
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   886
clasohm@0
   887
(*Quantification over a list of free variables*)
clasohm@0
   888
fun list_all_free ([], t: term) = t
wenzelm@13000
   889
  | list_all_free ((a,T)::vars, t) =
clasohm@0
   890
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   891
clasohm@0
   892
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   893
fun list_all ([], t) = t
wenzelm@13000
   894
  | list_all ((a,T)::vars, t) =
clasohm@0
   895
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   896
wenzelm@16678
   897
(*Replace the ATOMIC term ti by ui;    inst = [(t1,u1), ..., (tn,un)].
clasohm@0
   898
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
wenzelm@16678
   899
fun subst_atomic [] tm = tm
wenzelm@16678
   900
  | subst_atomic inst tm =
wenzelm@16678
   901
      let
wenzelm@16678
   902
        fun subst (Abs (a, T, body)) = Abs (a, T, subst body)
wenzelm@16678
   903
          | subst (t $ u) = subst t $ subst u
wenzelm@18942
   904
          | subst t = the_default t (AList.lookup (op aconv) inst t);
wenzelm@16678
   905
      in subst tm end;
clasohm@0
   906
wenzelm@16678
   907
(*Replace the ATOMIC type Ti by Ui;    inst = [(T1,U1), ..., (Tn,Un)].*)
wenzelm@16678
   908
fun typ_subst_atomic [] ty = ty
wenzelm@16678
   909
  | typ_subst_atomic inst ty =
wenzelm@16678
   910
      let
wenzelm@16678
   911
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   912
          | subst T = the_default T (AList.lookup (op = : typ * typ -> bool) inst T);
wenzelm@16678
   913
      in subst ty end;
berghofe@15797
   914
wenzelm@16678
   915
fun subst_atomic_types [] tm = tm
wenzelm@20548
   916
  | subst_atomic_types inst tm = map_types (typ_subst_atomic inst) tm;
wenzelm@16678
   917
wenzelm@16678
   918
fun typ_subst_TVars [] ty = ty
wenzelm@16678
   919
  | typ_subst_TVars inst ty =
wenzelm@16678
   920
      let
wenzelm@16678
   921
        fun subst (Type (a, Ts)) = Type (a, map subst Ts)
wenzelm@18942
   922
          | subst (T as TVar (xi, _)) = the_default T (AList.lookup (op =) inst xi)
wenzelm@16678
   923
          | subst T = T;
wenzelm@16678
   924
      in subst ty end;
clasohm@0
   925
wenzelm@16678
   926
fun subst_TVars [] tm = tm
wenzelm@20548
   927
  | subst_TVars inst tm = map_types (typ_subst_TVars inst) tm;
clasohm@0
   928
wenzelm@16678
   929
fun subst_Vars [] tm = tm
wenzelm@16678
   930
  | subst_Vars inst tm =
wenzelm@16678
   931
      let
wenzelm@18942
   932
        fun subst (t as Var (xi, _)) = the_default t (AList.lookup (op =) inst xi)
wenzelm@16678
   933
          | subst (Abs (a, T, t)) = Abs (a, T, subst t)
wenzelm@16678
   934
          | subst (t $ u) = subst t $ subst u
wenzelm@16678
   935
          | subst t = t;
wenzelm@16678
   936
      in subst tm end;
clasohm@0
   937
wenzelm@16678
   938
fun subst_vars ([], []) tm = tm
wenzelm@16678
   939
  | subst_vars ([], inst) tm = subst_Vars inst tm
wenzelm@16678
   940
  | subst_vars (instT, inst) tm =
wenzelm@16678
   941
      let
wenzelm@16678
   942
        fun subst (Const (a, T)) = Const (a, typ_subst_TVars instT T)
wenzelm@16678
   943
          | subst (Free (a, T)) = Free (a, typ_subst_TVars instT T)
wenzelm@16678
   944
          | subst (t as Var (xi, T)) =
haftmann@17271
   945
              (case AList.lookup (op =) inst xi of
wenzelm@16678
   946
                NONE => Var (xi, typ_subst_TVars instT T)
wenzelm@16678
   947
              | SOME t => t)
wenzelm@16678
   948
          | subst (t as Bound _) = t
wenzelm@16678
   949
          | subst (Abs (a, T, t)) = Abs (a, typ_subst_TVars instT T, subst t)
wenzelm@16678
   950
          | subst (t $ u) = subst t $ subst u;
wenzelm@16678
   951
      in subst tm end;
clasohm@0
   952
clasohm@0
   953
paulson@15573
   954
(** Identifying first-order terms **)
paulson@15573
   955
wenzelm@20199
   956
(*Differs from proofterm/is_fun in its treatment of TVar*)
wenzelm@20199
   957
fun is_funtype (Type("fun",[_,_])) = true
wenzelm@20199
   958
  | is_funtype _ = false;
wenzelm@20199
   959
paulson@15573
   960
(*Argument Ts is a reverse list of binder types, needed if term t contains Bound vars*)
paulson@15573
   961
fun has_not_funtype Ts t = not (is_funtype (fastype_of1 (Ts,t)));
paulson@15573
   962
wenzelm@16537
   963
(*First order means in all terms of the form f(t1,...,tn) no argument has a
paulson@16589
   964
  function type. The supplied quantifiers are excluded: their argument always
paulson@16589
   965
  has a function type through a recursive call into its body.*)
wenzelm@16667
   966
fun is_first_order quants =
paulson@16589
   967
  let fun first_order1 Ts (Abs (_,T,body)) = first_order1 (T::Ts) body
wenzelm@16667
   968
        | first_order1 Ts (Const(q,_) $ Abs(a,T,body)) =
wenzelm@20664
   969
            member (op =) quants q  andalso   (*it is a known quantifier*)
paulson@16589
   970
            not (is_funtype T)   andalso first_order1 (T::Ts) body
wenzelm@16667
   971
        | first_order1 Ts t =
wenzelm@16667
   972
            case strip_comb t of
wenzelm@16667
   973
                 (Var _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   974
               | (Free _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   975
               | (Const _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   976
               | (Bound _, ts) => forall (first_order1 Ts andf has_not_funtype Ts) ts
wenzelm@16667
   977
               | (Abs _, ts) => false (*not in beta-normal form*)
wenzelm@16667
   978
               | _ => error "first_order: unexpected case"
paulson@16589
   979
    in  first_order1 []  end;
paulson@15573
   980
wenzelm@16710
   981
wenzelm@16990
   982
(* maximum index of typs and terms *)
clasohm@0
   983
wenzelm@16710
   984
fun maxidx_typ (TVar ((_, j), _)) i = Int.max (i, j)
wenzelm@16710
   985
  | maxidx_typ (Type (_, Ts)) i = maxidx_typs Ts i
wenzelm@16710
   986
  | maxidx_typ (TFree _) i = i
wenzelm@16710
   987
and maxidx_typs [] i = i
wenzelm@16710
   988
  | maxidx_typs (T :: Ts) i = maxidx_typs Ts (maxidx_typ T i);
clasohm@0
   989
wenzelm@16710
   990
fun maxidx_term (Var ((_, j), T)) i = maxidx_typ T (Int.max (i, j))
wenzelm@16710
   991
  | maxidx_term (Const (_, T)) i = maxidx_typ T i
wenzelm@16710
   992
  | maxidx_term (Free (_, T)) i = maxidx_typ T i
wenzelm@16710
   993
  | maxidx_term (Bound _) i = i
wenzelm@16710
   994
  | maxidx_term (Abs (_, T, t)) i = maxidx_term t (maxidx_typ T i)
wenzelm@16710
   995
  | maxidx_term (t $ u) i = maxidx_term u (maxidx_term t i);
clasohm@0
   996
wenzelm@16710
   997
fun maxidx_of_typ T = maxidx_typ T ~1;
wenzelm@16710
   998
fun maxidx_of_typs Ts = maxidx_typs Ts ~1;
wenzelm@16710
   999
fun maxidx_of_term t = maxidx_term t ~1;
berghofe@13665
  1000
clasohm@0
  1001
clasohm@0
  1002
clasohm@0
  1003
(**** Syntax-related declarations ****)
clasohm@0
  1004
wenzelm@19909
  1005
(* substructure *)
wenzelm@4017
  1006
wenzelm@19909
  1007
fun exists_subtype P =
wenzelm@19909
  1008
  let
wenzelm@19909
  1009
    fun ex ty = P ty orelse
wenzelm@19909
  1010
      (case ty of Type (_, Ts) => exists ex Ts | _ => false);
wenzelm@19909
  1011
  in ex end;
nipkow@13646
  1012
wenzelm@20531
  1013
fun exists_type P =
wenzelm@20531
  1014
  let
wenzelm@20531
  1015
    fun ex (Const (_, T)) = P T
wenzelm@20531
  1016
      | ex (Free (_, T)) = P T
wenzelm@20531
  1017
      | ex (Var (_, T)) = P T
wenzelm@20531
  1018
      | ex (Bound _) = false
wenzelm@20531
  1019
      | ex (Abs (_, T, t)) = P T orelse ex t
wenzelm@20531
  1020
      | ex (t $ u) = ex t orelse ex u;
wenzelm@20531
  1021
  in ex end;
wenzelm@20531
  1022
wenzelm@16943
  1023
fun exists_subterm P =
wenzelm@16943
  1024
  let
wenzelm@16943
  1025
    fun ex tm = P tm orelse
wenzelm@16943
  1026
      (case tm of
wenzelm@16943
  1027
        t $ u => ex t orelse ex u
wenzelm@16943
  1028
      | Abs (_, _, t) => ex t
wenzelm@16943
  1029
      | _ => false);
wenzelm@16943
  1030
  in ex end;
obua@16108
  1031
wenzelm@19909
  1032
wenzelm@19909
  1033
(** Consts etc. **)
wenzelm@19909
  1034
wenzelm@19909
  1035
fun add_term_consts (Const (c, _), cs) = insert (op =) c cs
wenzelm@19909
  1036
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@19909
  1037
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@19909
  1038
  | add_term_consts (_, cs) = cs;
wenzelm@19909
  1039
wenzelm@19909
  1040
fun term_consts t = add_term_consts(t,[]);
wenzelm@19909
  1041
wenzelm@16943
  1042
fun exists_Const P = exists_subterm (fn Const c => P c | _ => false);
nipkow@4631
  1043
wenzelm@4017
  1044
clasohm@0
  1045
(** TFrees and TVars **)
clasohm@0
  1046
wenzelm@12802
  1047
(*Accumulates the names of Frees in the term, suppressing duplicates.*)
haftmann@20854
  1048
fun add_term_free_names (Free(a,_), bs) = insert (op =) a bs
wenzelm@12802
  1049
  | add_term_free_names (f$u, bs) = add_term_free_names (f, add_term_free_names(u, bs))
wenzelm@12802
  1050
  | add_term_free_names (Abs(_,_,t), bs) = add_term_free_names(t,bs)
wenzelm@12802
  1051
  | add_term_free_names (_, bs) = bs;
wenzelm@12802
  1052
clasohm@0
  1053
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
  1054
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
haftmann@20854
  1055
fun add_term_names (Const(a,_), bs) = insert (op =) (NameSpace.base a) bs
haftmann@20854
  1056
  | add_term_names (Free(a,_), bs) = insert (op =) a bs
clasohm@0
  1057
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
  1058
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
  1059
  | add_term_names (_, bs) = bs;
clasohm@0
  1060
clasohm@0
  1061
(*Accumulates the TVars in a type, suppressing duplicates. *)
skalberg@15574
  1062
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars vs Ts
clasohm@0
  1063
  | add_typ_tvars(TFree(_),vs) = vs
wenzelm@16294
  1064
  | add_typ_tvars(TVar(v),vs) = insert (op =) v vs;
clasohm@0
  1065
clasohm@0
  1066
(*Accumulates the TFrees in a type, suppressing duplicates. *)
skalberg@15574
  1067
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names fs Ts
haftmann@20854
  1068
  | add_typ_tfree_names(TFree(f,_),fs) = insert (op =) f fs
clasohm@0
  1069
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
  1070
skalberg@15574
  1071
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees fs Ts
wenzelm@16294
  1072
  | add_typ_tfrees(TFree(f),fs) = insert (op =) f fs
clasohm@0
  1073
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
  1074
skalberg@15574
  1075
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames nms Ts
haftmann@20854
  1076
  | add_typ_varnames(TFree(nm,_),nms) = insert (op =) nm nms
haftmann@20854
  1077
  | add_typ_varnames(TVar((nm,_),_),nms) = insert (op =) nm nms;
nipkow@949
  1078
clasohm@0
  1079
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
  1080
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
  1081
clasohm@0
  1082
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
  1083
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
  1084
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
  1085
clasohm@0
  1086
(*Non-list versions*)
clasohm@0
  1087
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
  1088
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
  1089
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
  1090
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
  1091
nipkow@949
  1092
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
  1093
skalberg@15570
  1094
fun add_typ_ixns(ixns,Type(_,Ts)) = Library.foldl add_typ_ixns (ixns,Ts)
wenzelm@20082
  1095
  | add_typ_ixns(ixns,TVar(ixn,_)) = if member (op =) ixns ixn then ixns
wenzelm@9536
  1096
                                     else ixns@[ixn]
nipkow@949
  1097
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
  1098
nipkow@949
  1099
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1100
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1101
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
  1102
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
  1103
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
  1104
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
  1105
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
  1106
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
  1107
wenzelm@16537
  1108
clasohm@0
  1109
(** Frees and Vars **)
clasohm@0
  1110
clasohm@0
  1111
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
  1112
fun add_term_vars (t, vars: term list) = case t of
wenzelm@16990
  1113
    Var   _ => OrdList.insert term_ord t vars
clasohm@0
  1114
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
  1115
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
  1116
  | _ => vars;
clasohm@0
  1117
clasohm@0
  1118
fun term_vars t = add_term_vars(t,[]);
clasohm@0
  1119
clasohm@0
  1120
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
  1121
fun add_term_frees (t, frees: term list) = case t of
wenzelm@16990
  1122
    Free   _ => OrdList.insert term_ord t frees
clasohm@0
  1123
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
  1124
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
  1125
  | _ => frees;
clasohm@0
  1126
clasohm@0
  1127
fun term_frees t = add_term_frees(t,[]);
clasohm@0
  1128
wenzelm@20199
  1129
wenzelm@20199
  1130
(* dest abstraction *)
clasohm@0
  1131
wenzelm@16678
  1132
fun dest_abs (x, T, body) =
wenzelm@16678
  1133
  let
wenzelm@16678
  1134
    fun name_clash (Free (y, _)) = (x = y)
wenzelm@16678
  1135
      | name_clash (t $ u) = name_clash t orelse name_clash u
wenzelm@16678
  1136
      | name_clash (Abs (_, _, t)) = name_clash t
wenzelm@16678
  1137
      | name_clash _ = false;
wenzelm@16678
  1138
  in
wenzelm@16678
  1139
    if name_clash body then
wenzelm@20082
  1140
      dest_abs (Name.variant [x] x, T, body)    (*potentially slow, but rarely happens*)
wenzelm@16678
  1141
    else (x, subst_bound (Free (x, T), body))
wenzelm@16678
  1142
  end;
wenzelm@16678
  1143
wenzelm@20160
  1144
wenzelm@20160
  1145
(* renaming variables *)
clasohm@0
  1146
wenzelm@20239
  1147
fun declare_term_names tm =
wenzelm@20239
  1148
  fold_aterms
wenzelm@20239
  1149
    (fn Const (a, _) => Name.declare (NameSpace.base a)
wenzelm@20239
  1150
      | Free (a, _) => Name.declare a
wenzelm@20239
  1151
      | _ => I) tm #>
wenzelm@20239
  1152
  fold_types (fold_atyps (fn TFree (a, _) => Name.declare a | _ => I)) tm;
wenzelm@20239
  1153
wenzelm@20160
  1154
fun variant_frees t frees =
wenzelm@20160
  1155
  fst (Name.variants (map fst frees) (declare_term_names t Name.context)) ~~ map snd frees;
wenzelm@20160
  1156
wenzelm@20160
  1157
fun rename_wrt_term t frees = rev (variant_frees t frees);  (*reversed result!*)
clasohm@1364
  1158
paulson@1417
  1159
wenzelm@9536
  1160
(* dummy patterns *)
wenzelm@9536
  1161
wenzelm@9536
  1162
val dummy_patternN = "dummy_pattern";
wenzelm@9536
  1163
wenzelm@18253
  1164
fun dummy_pattern T = Const (dummy_patternN, T);
wenzelm@18253
  1165
wenzelm@9536
  1166
fun is_dummy_pattern (Const ("dummy_pattern", _)) = true
wenzelm@9536
  1167
  | is_dummy_pattern _ = false;
wenzelm@9536
  1168
wenzelm@9536
  1169
fun no_dummy_patterns tm =
haftmann@16787
  1170
  if not (fold_aterms (fn t => fn b => b orelse is_dummy_pattern t) tm false) then tm
wenzelm@9536
  1171
  else raise TERM ("Illegal occurrence of '_' dummy pattern", [tm]);
wenzelm@9536
  1172
wenzelm@11903
  1173
fun replace_dummy Ts (i, Const ("dummy_pattern", T)) =
wenzelm@11903
  1174
      (i + 1, list_comb (Var (("_dummy_", i), Ts ---> T), map Bound (0 upto length Ts - 1)))
wenzelm@11903
  1175
  | replace_dummy Ts (i, Abs (x, T, t)) =
wenzelm@11903
  1176
      let val (i', t') = replace_dummy (T :: Ts) (i, t)
wenzelm@11903
  1177
      in (i', Abs (x, T, t')) end
wenzelm@11903
  1178
  | replace_dummy Ts (i, t $ u) =
wenzelm@11903
  1179
      let val (i', t') = replace_dummy Ts (i, t); val (i'', u') = replace_dummy Ts (i', u)
wenzelm@11903
  1180
      in (i'', t' $ u') end
wenzelm@11903
  1181
  | replace_dummy _ (i, a) = (i, a);
wenzelm@11903
  1182
wenzelm@11903
  1183
val replace_dummy_patterns = replace_dummy [];
wenzelm@9536
  1184
wenzelm@10552
  1185
fun is_replaced_dummy_pattern ("_dummy_", _) = true
wenzelm@10552
  1186
  | is_replaced_dummy_pattern _ = false;
wenzelm@9536
  1187
wenzelm@16035
  1188
fun show_dummy_patterns (Var (("_dummy_", _), T)) = Const ("dummy_pattern", T)
wenzelm@16035
  1189
  | show_dummy_patterns (t $ u) = show_dummy_patterns t $ show_dummy_patterns u
wenzelm@16035
  1190
  | show_dummy_patterns (Abs (x, T, t)) = Abs (x, T, show_dummy_patterns t)
wenzelm@16035
  1191
  | show_dummy_patterns a = a;
wenzelm@16035
  1192
wenzelm@13484
  1193
wenzelm@20100
  1194
(* display variables *)
wenzelm@20100
  1195
wenzelm@15986
  1196
val show_question_marks = ref true;
berghofe@15472
  1197
wenzelm@14786
  1198
fun string_of_vname (x, i) =
wenzelm@14786
  1199
  let
wenzelm@15986
  1200
    val question_mark = if ! show_question_marks then "?" else "";
wenzelm@15986
  1201
    val idx = string_of_int i;
wenzelm@15986
  1202
    val dot =
wenzelm@15986
  1203
      (case rev (Symbol.explode x) of
wenzelm@15986
  1204
        _ :: "\\<^isub>" :: _ => false
wenzelm@15986
  1205
      | _ :: "\\<^isup>" :: _ => false
wenzelm@15986
  1206
      | c :: _ => Symbol.is_digit c
wenzelm@15986
  1207
      | _ => true);
wenzelm@14786
  1208
  in
wenzelm@15986
  1209
    if dot then question_mark ^ x ^ "." ^ idx
wenzelm@15986
  1210
    else if i <> 0 then question_mark ^ x ^ idx
wenzelm@15986
  1211
    else question_mark ^ x
wenzelm@14786
  1212
  end;
wenzelm@14786
  1213
wenzelm@14786
  1214
fun string_of_vname' (x, ~1) = x
wenzelm@14786
  1215
  | string_of_vname' xi = string_of_vname xi;
wenzelm@14786
  1216
clasohm@1364
  1217
end;
clasohm@1364
  1218
wenzelm@4444
  1219
structure BasicTerm: BASIC_TERM = Term;
wenzelm@4444
  1220
open BasicTerm;