src/Pure/term.ML
author paulson
Mon Nov 18 16:28:40 1996 +0100 (1996-11-18)
changeset 2192 3bf092b5310b
parent 2182 29e56f003599
child 2580 e3f680709487
permissions -rw-r--r--
Optimizations: removal of polymorphic equality; one-argument case
for subst_bounds
clasohm@1460
     1
(*  Title: 	Pure/term.ML
clasohm@0
     2
    ID:         $Id$
clasohm@1460
     3
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
clasohm@0
     4
    Copyright   Cambridge University 1992
clasohm@1364
     5
clasohm@1364
     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 -->;
clasohm@1364
    11
infixr   --->;
clasohm@1364
    12
infix    aconv;
clasohm@1364
    13
clasohm@0
    14
clasohm@1364
    15
structure Term =
clasohm@1364
    16
struct
clasohm@0
    17
clasohm@0
    18
(*Indexnames can be quickly renamed by adding an offset to the integer part,
clasohm@0
    19
  for resolution.*)
clasohm@0
    20
type indexname = string*int;
clasohm@0
    21
clasohm@0
    22
(* Types are classified by classes. *)
clasohm@0
    23
type class = string;
clasohm@0
    24
type sort  = class list;
clasohm@0
    25
clasohm@0
    26
(* The sorts attached to TFrees and TVars specify the sort of that variable *)
clasohm@0
    27
datatype typ = Type  of string * typ list
clasohm@0
    28
             | TFree of string * sort
clasohm@1460
    29
	     | TVar  of indexname * sort;
clasohm@0
    30
clasohm@0
    31
fun S --> T = Type("fun",[S,T]);
clasohm@0
    32
clasohm@0
    33
(*handy for multiple args: [T1,...,Tn]--->T  gives  T1-->(T2--> ... -->T)*)
clasohm@0
    34
val op ---> = foldr (op -->);
clasohm@0
    35
clasohm@0
    36
clasohm@0
    37
(*terms.  Bound variables are indicated by depth number.
clasohm@0
    38
  Free variables, (scheme) variables and constants have names.
clasohm@0
    39
  An term is "closed" if there every bound variable of level "lev"
clasohm@0
    40
  is enclosed by at least "lev" abstractions. 
clasohm@0
    41
clasohm@0
    42
  It is possible to create meaningless terms containing loose bound vars
clasohm@0
    43
  or type mismatches.  But such terms are not allowed in rules. *)
clasohm@0
    44
clasohm@0
    45
clasohm@0
    46
clasohm@0
    47
datatype term = 
clasohm@0
    48
    Const of string * typ
clasohm@0
    49
  | Free  of string * typ 
clasohm@0
    50
  | Var   of indexname * typ
clasohm@0
    51
  | Bound of int
clasohm@0
    52
  | Abs   of string*typ*term
clasohm@0
    53
  | op $  of term*term;
clasohm@0
    54
clasohm@0
    55
clasohm@0
    56
(*For errors involving type mismatches*)
clasohm@0
    57
exception TYPE of string * typ list * term list;
clasohm@0
    58
wenzelm@40
    59
fun raise_type msg tys ts = raise TYPE (msg, tys, ts);
wenzelm@40
    60
clasohm@0
    61
(*For system errors involving terms*)
clasohm@0
    62
exception TERM of string * term list;
clasohm@0
    63
wenzelm@40
    64
fun raise_term msg ts = raise TERM (msg, ts);
wenzelm@40
    65
clasohm@0
    66
clasohm@0
    67
(*Note variable naming conventions!
clasohm@0
    68
    a,b,c: string
clasohm@0
    69
    f,g,h: functions (including terms of function type)
clasohm@0
    70
    i,j,m,n: int
clasohm@0
    71
    t,u: term
clasohm@0
    72
    v,w: indexnames
clasohm@0
    73
    x,y: any
clasohm@0
    74
    A,B,C: term (denoting formulae)
clasohm@0
    75
    T,U: typ
clasohm@0
    76
*)
clasohm@0
    77
clasohm@0
    78
clasohm@0
    79
(** Discriminators **)
clasohm@0
    80
clasohm@0
    81
fun is_Const (Const _) = true
clasohm@0
    82
  | is_Const _ = false;
clasohm@0
    83
clasohm@0
    84
fun is_Free (Free _) = true
clasohm@0
    85
  | is_Free _ = false;
clasohm@0
    86
clasohm@0
    87
fun is_Var (Var _) = true
clasohm@0
    88
  | is_Var _ = false;
clasohm@0
    89
clasohm@0
    90
fun is_TVar (TVar _) = true
clasohm@0
    91
  | is_TVar _ = false;
clasohm@0
    92
clasohm@0
    93
(** Destructors **)
clasohm@0
    94
clasohm@0
    95
fun dest_Const (Const x) =  x
clasohm@0
    96
  | dest_Const t = raise TERM("dest_Const", [t]);
clasohm@0
    97
clasohm@0
    98
fun dest_Free (Free x) =  x
clasohm@0
    99
  | dest_Free t = raise TERM("dest_Free", [t]);
clasohm@0
   100
clasohm@0
   101
fun dest_Var (Var x) =  x
clasohm@0
   102
  | dest_Var t = raise TERM("dest_Var", [t]);
clasohm@0
   103
clasohm@0
   104
clasohm@0
   105
(* maps  [T1,...,Tn]--->T  to the list  [T1,T2,...,Tn]*)
clasohm@0
   106
fun binder_types (Type("fun",[S,T])) = S :: binder_types T
clasohm@0
   107
  | binder_types _   =  [];
clasohm@0
   108
clasohm@0
   109
(* maps  [T1,...,Tn]--->T  to T*)
clasohm@0
   110
fun body_type (Type("fun",[S,T])) = body_type T
clasohm@0
   111
  | body_type T   =  T;
clasohm@0
   112
clasohm@0
   113
(* maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T)  *)
clasohm@0
   114
fun strip_type T : typ list * typ =
clasohm@0
   115
  (binder_types T, body_type T);
clasohm@0
   116
clasohm@0
   117
clasohm@0
   118
(*Compute the type of the term, checking that combinations are well-typed
clasohm@0
   119
  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
clasohm@0
   120
fun type_of1 (Ts, Const (_,T)) = T
clasohm@0
   121
  | type_of1 (Ts, Free  (_,T)) = T
clasohm@0
   122
  | type_of1 (Ts, Bound i) = (nth_elem (i,Ts)  
clasohm@1460
   123
  	handle LIST _ => raise TYPE("type_of: bound variable", [], [Bound i]))
clasohm@0
   124
  | type_of1 (Ts, Var (_,T)) = T
clasohm@0
   125
  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
clasohm@0
   126
  | type_of1 (Ts, f$u) = 
clasohm@0
   127
      let val U = type_of1(Ts,u)
clasohm@0
   128
          and T = type_of1(Ts,f)
clasohm@0
   129
      in case T of
clasohm@1460
   130
	    Type("fun",[T1,T2]) =>
clasohm@1460
   131
	      if T1=U then T2  else raise TYPE
clasohm@1460
   132
	            ("type_of: type mismatch in application", [T1,U], [f$u])
clasohm@1460
   133
	  | _ => raise TYPE 
clasohm@1460
   134
		    ("type_of: function type is expected in application",
clasohm@1460
   135
		     [T,U], [f$u])
clasohm@0
   136
      end;
clasohm@0
   137
clasohm@0
   138
fun type_of t : typ = type_of1 ([],t);
clasohm@0
   139
clasohm@0
   140
(*Determines the type of a term, with minimal checking*)
lcp@61
   141
fun fastype_of1 (Ts, f$u) = 
lcp@61
   142
    (case fastype_of1 (Ts,f) of
clasohm@1460
   143
	Type("fun",[_,T]) => T
clasohm@1460
   144
	| _ => raise TERM("fastype_of: expected function type", [f$u]))
lcp@61
   145
  | fastype_of1 (_, Const (_,T)) = T
lcp@61
   146
  | fastype_of1 (_, Free (_,T)) = T
lcp@61
   147
  | fastype_of1 (Ts, Bound i) = (nth_elem(i,Ts)
clasohm@1460
   148
  	 handle LIST _ => raise TERM("fastype_of: Bound", [Bound i]))
lcp@61
   149
  | fastype_of1 (_, Var (_,T)) = T 
lcp@61
   150
  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
lcp@61
   151
lcp@61
   152
fun fastype_of t : typ = fastype_of1 ([],t);
clasohm@0
   153
clasohm@0
   154
clasohm@0
   155
(* maps  (x1,...,xn)t   to   t  *)
clasohm@0
   156
fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t  
clasohm@0
   157
  | strip_abs_body u  =  u;
clasohm@0
   158
clasohm@0
   159
clasohm@0
   160
(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
clasohm@0
   161
fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t 
clasohm@0
   162
  | strip_abs_vars u  =  [] : (string*typ) list;
clasohm@0
   163
clasohm@0
   164
clasohm@0
   165
fun strip_qnt_body qnt =
clasohm@0
   166
let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
clasohm@0
   167
      | strip t = t
clasohm@0
   168
in strip end;
clasohm@0
   169
clasohm@0
   170
fun strip_qnt_vars qnt =
clasohm@0
   171
let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
clasohm@0
   172
      | strip t  =  [] : (string*typ) list
clasohm@0
   173
in strip end;
clasohm@0
   174
clasohm@0
   175
clasohm@0
   176
(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
clasohm@0
   177
val list_comb : term * term list -> term = foldl (op $);
clasohm@0
   178
clasohm@0
   179
clasohm@0
   180
(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
clasohm@0
   181
fun strip_comb u : term * term list = 
clasohm@0
   182
    let fun stripc (f$t, ts) = stripc (f, t::ts)
clasohm@0
   183
        |   stripc  x =  x 
clasohm@0
   184
    in  stripc(u,[])  end;
clasohm@0
   185
clasohm@0
   186
clasohm@0
   187
(* maps   f(t1,...,tn)  to  f , which is never a combination *)
clasohm@0
   188
fun head_of (f$t) = head_of f
clasohm@0
   189
  | head_of u = u;
clasohm@0
   190
clasohm@0
   191
clasohm@0
   192
(*Number of atoms and abstractions in a term*)
clasohm@0
   193
fun size_of_term (Abs (_,_,body)) = 1 + size_of_term body
clasohm@0
   194
  | size_of_term (f$t) = size_of_term f  +  size_of_term t
clasohm@0
   195
  | size_of_term _ = 1;
clasohm@0
   196
nipkow@949
   197
fun map_type_tvar f (Type(a,Ts)) = Type(a, map (map_type_tvar f) Ts)
nipkow@949
   198
  | map_type_tvar f (T as TFree _) = T
nipkow@949
   199
  | map_type_tvar f (TVar x) = f x;
nipkow@949
   200
nipkow@949
   201
fun map_type_tfree f (Type(a,Ts)) = Type(a, map (map_type_tfree f) Ts)
nipkow@949
   202
  | map_type_tfree f (TFree x) = f x
nipkow@949
   203
  | map_type_tfree f (T as TVar _) = T;
nipkow@949
   204
clasohm@0
   205
(* apply a function to all types in a term *)
clasohm@0
   206
fun map_term_types f =
clasohm@0
   207
let fun map(Const(a,T)) = Const(a, f T)
clasohm@0
   208
      | map(Free(a,T)) = Free(a, f T)
clasohm@0
   209
      | map(Var(v,T)) = Var(v, f T)
clasohm@0
   210
      | map(t as Bound _)  = t
clasohm@0
   211
      | map(Abs(a,T,t)) = Abs(a, f T, map t)
clasohm@0
   212
      | map(f$t) = map f $ map t;
clasohm@0
   213
in map end;
clasohm@0
   214
clasohm@0
   215
(* iterate a function over all types in a term *)
clasohm@0
   216
fun it_term_types f =
clasohm@0
   217
let fun iter(Const(_,T), a) = f(T,a)
clasohm@0
   218
      | iter(Free(_,T), a) = f(T,a)
clasohm@0
   219
      | iter(Var(_,T), a) = f(T,a)
clasohm@0
   220
      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
clasohm@0
   221
      | iter(f$u, a) = iter(f, iter(u, a))
clasohm@0
   222
      | iter(Bound _, a) = a
clasohm@0
   223
in iter end
clasohm@0
   224
clasohm@0
   225
clasohm@0
   226
(** Connectives of higher order logic **)
clasohm@0
   227
wenzelm@375
   228
val logicC: class = "logic";
wenzelm@375
   229
val logicS: sort = [logicC];
wenzelm@375
   230
wenzelm@375
   231
fun itselfT ty = Type ("itself", [ty]);
wenzelm@375
   232
val a_itselfT = itselfT (TFree ("'a", logicS));
wenzelm@375
   233
clasohm@0
   234
val propT : typ = Type("prop",[]);
clasohm@0
   235
clasohm@0
   236
val implies = Const("==>", propT-->propT-->propT);
clasohm@0
   237
clasohm@0
   238
fun all T = Const("all", (T-->propT)-->propT);
clasohm@0
   239
clasohm@0
   240
fun equals T = Const("==", T-->T-->propT);
clasohm@0
   241
clasohm@0
   242
fun flexpair T = Const("=?=", T-->T-->propT);
clasohm@0
   243
clasohm@0
   244
(* maps  !!x1...xn. t   to   t  *)
clasohm@0
   245
fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t  
clasohm@0
   246
  | strip_all_body t  =  t;
clasohm@0
   247
clasohm@0
   248
(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
clasohm@0
   249
fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
clasohm@1460
   250
		(a,T) :: strip_all_vars t 
clasohm@0
   251
  | strip_all_vars t  =  [] : (string*typ) list;
clasohm@0
   252
clasohm@0
   253
(*increments a term's non-local bound variables
clasohm@0
   254
  required when moving a term within abstractions
clasohm@0
   255
     inc is  increment for bound variables
clasohm@0
   256
     lev is  level at which a bound variable is considered 'loose'*)
clasohm@0
   257
fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u 
clasohm@0
   258
  | incr_bv (inc, lev, Abs(a,T,body)) =
clasohm@1460
   259
	Abs(a, T, incr_bv(inc,lev+1,body))
clasohm@0
   260
  | incr_bv (inc, lev, f$t) = 
clasohm@0
   261
      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
clasohm@0
   262
  | incr_bv (inc, lev, u) = u;
clasohm@0
   263
clasohm@0
   264
fun incr_boundvars  0  t = t
clasohm@0
   265
  | incr_boundvars inc t = incr_bv(inc,0,t);
clasohm@0
   266
clasohm@0
   267
clasohm@0
   268
(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
clasohm@0
   269
   (Bound 0) is loose at level 0 *)
clasohm@0
   270
fun add_loose_bnos (Bound i, lev, js) = 
paulson@2176
   271
	if i<lev then js  else  (i-lev) ins_int js
clasohm@0
   272
  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
clasohm@0
   273
  | add_loose_bnos (f$t, lev, js) =
clasohm@1460
   274
	add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) 
clasohm@0
   275
  | add_loose_bnos (_, _, js) = js;
clasohm@0
   276
clasohm@0
   277
fun loose_bnos t = add_loose_bnos (t, 0, []);
clasohm@0
   278
clasohm@0
   279
(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
clasohm@0
   280
   level k or beyond. *)
clasohm@0
   281
fun loose_bvar(Bound i,k) = i >= k
clasohm@0
   282
  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
clasohm@0
   283
  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
clasohm@0
   284
  | loose_bvar _ = false;
clasohm@0
   285
clasohm@0
   286
clasohm@0
   287
(*Substitute arguments for loose bound variables.
clasohm@0
   288
  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
clasohm@0
   289
  Note that for ((x,y)c)(a,b), the bound vars in c are x=1 and y=0
clasohm@1460
   290
	and the appropriate call is  subst_bounds([b,a], c) .
clasohm@0
   291
  Loose bound variables >=n are reduced by "n" to
clasohm@0
   292
     compensate for the disappearance of lambdas.
clasohm@0
   293
*)
clasohm@0
   294
fun subst_bounds (args: term list, t) : term = 
clasohm@0
   295
  let val n = length args;
clasohm@0
   296
      fun subst (t as Bound i, lev) =
clasohm@1460
   297
 	    if i<lev then  t    (*var is locally bound*)
clasohm@1460
   298
	    else  (case (drop (i-lev,args)) of
clasohm@1460
   299
		  []     => Bound(i-n)  (*loose: change it*)
clasohm@1460
   300
	        | arg::_ => incr_boundvars lev arg)
clasohm@1460
   301
	| subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
clasohm@1460
   302
	| subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
clasohm@1460
   303
	| subst (t,lev) = t
clasohm@0
   304
  in   case args of [] => t  | _ => subst (t,0)  end;
clasohm@0
   305
paulson@2192
   306
(*Special case: one argument*)
paulson@2192
   307
fun subst_bound (arg, t) : term = 
paulson@2192
   308
  let fun subst (t as Bound i, lev) =
paulson@2192
   309
 	    if i<lev then  t    (*var is locally bound*)
paulson@2192
   310
	    else  if i=lev then incr_boundvars lev arg
paulson@2192
   311
		           else Bound(i-1)  (*loose: change it*)
paulson@2192
   312
	| subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
paulson@2192
   313
	| subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
paulson@2192
   314
	| subst (t,lev) = t
paulson@2192
   315
  in  subst (t,0)  end;
paulson@2192
   316
clasohm@0
   317
(*beta-reduce if possible, else form application*)
paulson@2192
   318
fun betapply (Abs(_,_,t), u) = subst_bound (u,t)
clasohm@0
   319
  | betapply (f,u) = f$u;
clasohm@0
   320
paulson@2192
   321
(** Equality, membership and insertion of indexnames (string*ints) **)
paulson@2192
   322
paulson@2192
   323
(*optimized equality test for indexnames.  Yields a huge gain under Poly/ML*)
paulson@2192
   324
fun eq_ix ((a:string, i:int), (a',i')) = (a=a') andalso i=i';
paulson@2192
   325
paulson@2192
   326
(*membership in a list, optimized version for indexnames*)
paulson@2192
   327
fun mem_ix (x:string*int, []) = false
paulson@2192
   328
  | mem_ix (x, y :: ys) = eq_ix(x,y) orelse mem_ix (x, ys);
paulson@2192
   329
paulson@2192
   330
(*insertion into list, optimized version for indexnames*)
paulson@2192
   331
fun ins_ix (x,xs) = if mem_ix (x, xs) then xs else x :: xs;
paulson@2192
   332
clasohm@0
   333
(*Tests whether 2 terms are alpha-convertible and have same type.
clasohm@0
   334
  Note that constants and Vars may have more than one type.*)
clasohm@0
   335
fun (Const(a,T)) aconv (Const(b,U)) = a=b  andalso  T=U
clasohm@0
   336
  | (Free(a,T)) aconv (Free(b,U)) = a=b  andalso  T=U
paulson@2192
   337
  | (Var(v,T)) aconv (Var(w,U)) =   eq_ix(v,w)  andalso  T=U
clasohm@0
   338
  | (Bound i) aconv (Bound j)  =   i=j
clasohm@0
   339
  | (Abs(_,T,t)) aconv (Abs(_,U,u)) = t aconv u  andalso  T=U
clasohm@0
   340
  | (f$t) aconv (g$u) = (f aconv g) andalso (t aconv u)
clasohm@0
   341
  | _ aconv _  =  false;
clasohm@0
   342
paulson@2176
   343
(** Membership, insertion, union for terms **)
paulson@2176
   344
paulson@2176
   345
fun mem_term (_, []) = false
paulson@2176
   346
  | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);
paulson@2176
   347
paulson@2182
   348
fun subset_term ([], ys) = true
paulson@2182
   349
  | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);
paulson@2182
   350
paulson@2182
   351
fun eq_set_term (xs, ys) =
paulson@2182
   352
    xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
paulson@2182
   353
paulson@2176
   354
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts;
paulson@2176
   355
paulson@2176
   356
fun union_term (xs, []) = xs
paulson@2176
   357
  | union_term ([], ys) = ys
paulson@2176
   358
  | union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys));
paulson@2176
   359
paulson@2176
   360
(** Equality, membership and insertion of sorts (string lists) **)
paulson@2176
   361
paulson@2176
   362
fun eq_sort ([]:sort, []) = true
paulson@2176
   363
  | eq_sort ((s::ss), (t::ts)) = s=t andalso eq_sort(ss,ts)
paulson@2176
   364
  | eq_sort (_, _) = false;
paulson@2176
   365
paulson@2176
   366
fun mem_sort (_:sort, []) = false
paulson@2176
   367
  | mem_sort (S, S'::Ss) = eq_sort (S, S') orelse mem_sort(S,Ss);
paulson@2176
   368
paulson@2176
   369
fun ins_sort(S,Ss) = if mem_sort(S,Ss) then Ss else S :: Ss;
paulson@2176
   370
paulson@2176
   371
fun union_sort (xs, []) = xs
paulson@2176
   372
  | union_sort ([], ys) = ys
paulson@2176
   373
  | union_sort ((x :: xs), ys) = union_sort (xs, ins_sort (x, ys));
paulson@2176
   374
paulson@2182
   375
fun subset_sort ([], ys) = true
paulson@2182
   376
  | subset_sort (x :: xs, ys) = mem_sort (x, ys) andalso subset_sort(xs, ys);
paulson@2182
   377
paulson@2182
   378
fun eq_set_sort (xs, ys) =
paulson@2182
   379
    xs = ys orelse (subset_sort (xs, ys) andalso subset_sort (ys, xs));
paulson@2182
   380
clasohm@0
   381
(*are two term lists alpha-convertible in corresponding elements?*)
clasohm@0
   382
fun aconvs ([],[]) = true
clasohm@0
   383
  | aconvs (t::ts, u::us) = t aconv u andalso aconvs(ts,us)
clasohm@0
   384
  | aconvs _ = false;
clasohm@0
   385
clasohm@0
   386
(*A fast unification filter: true unless the two terms cannot be unified. 
clasohm@0
   387
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   388
fun could_unify (t,u) =
clasohm@0
   389
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
clasohm@1460
   390
	| matchrands _ = true
clasohm@0
   391
  in case (head_of t , head_of u) of
clasohm@1460
   392
	(_, Var _) => true
clasohm@0
   393
      | (Var _, _) => true
clasohm@0
   394
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   395
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   396
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   397
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   398
      | (_, Abs _) =>  true
clasohm@0
   399
      | _ => false
clasohm@0
   400
  end;
clasohm@0
   401
clasohm@0
   402
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   403
fun subst_free [] = (fn t=>t)
clasohm@0
   404
  | subst_free pairs =
clasohm@0
   405
      let fun substf u = 
clasohm@1460
   406
	    case gen_assoc (op aconv) (pairs, u) of
clasohm@1460
   407
		Some u' => u'
clasohm@1460
   408
	      | None => (case u of Abs(a,T,t) => Abs(a, T, substf t)
clasohm@1460
   409
				 | t$u' => substf t $ substf u'
clasohm@1460
   410
				 | _ => u)
clasohm@0
   411
      in  substf  end;
clasohm@0
   412
clasohm@0
   413
(*a total, irreflexive ordering on index names*)
clasohm@0
   414
fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);
clasohm@0
   415
clasohm@0
   416
clasohm@0
   417
(*Abstraction of the term "body" over its occurrences of v, 
clasohm@0
   418
    which must contain no loose bound variables.
clasohm@0
   419
  The resulting term is ready to become the body of an Abs.*)
clasohm@0
   420
fun abstract_over (v,body) =
clasohm@0
   421
  let fun abst (lev,u) = if (v aconv u) then (Bound lev) else
clasohm@0
   422
      (case u of
clasohm@0
   423
          Abs(a,T,t) => Abs(a, T, abst(lev+1, t))
clasohm@1460
   424
	| f$rand => abst(lev,f) $ abst(lev,rand)
clasohm@1460
   425
	| _ => u)
clasohm@0
   426
  in  abst(0,body)  end;
clasohm@0
   427
clasohm@0
   428
clasohm@0
   429
(*Form an abstraction over a free variable.*)
clasohm@0
   430
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
clasohm@0
   431
clasohm@0
   432
(*Abstraction over a list of free variables*)
clasohm@0
   433
fun list_abs_free ([ ] ,     t) = t
clasohm@0
   434
  | list_abs_free ((a,T)::vars, t) = 
clasohm@0
   435
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   436
clasohm@0
   437
(*Quantification over a list of free variables*)
clasohm@0
   438
fun list_all_free ([], t: term) = t
clasohm@0
   439
  | list_all_free ((a,T)::vars, t) = 
clasohm@0
   440
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   441
clasohm@0
   442
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   443
fun list_all ([], t) = t
clasohm@0
   444
  | list_all ((a,T)::vars, t) = 
clasohm@0
   445
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   446
clasohm@0
   447
(*Replace the ATOMIC term ti by ui;    instl = [(t1,u1), ..., (tn,un)]. 
clasohm@0
   448
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
clasohm@0
   449
fun subst_atomic [] t = t : term
clasohm@0
   450
  | subst_atomic (instl: (term*term) list) t =
clasohm@0
   451
      let fun subst (Abs(a,T,body)) = Abs(a, T, subst body)
clasohm@1460
   452
	    | subst (f$t') = subst f $ subst t'
clasohm@1460
   453
	    | subst t = (case assoc(instl,t) of
clasohm@1460
   454
		           Some u => u  |  None => t)
clasohm@0
   455
      in  subst t  end;
clasohm@0
   456
lcp@728
   457
(*Substitute for type Vars in a type*)
clasohm@0
   458
fun typ_subst_TVars iTs T = if null iTs then T else
clasohm@0
   459
  let fun subst(Type(a,Ts)) = Type(a, map subst Ts)
clasohm@1460
   460
	| subst(T as TFree _) = T
clasohm@1460
   461
	| subst(T as TVar(ixn,_)) =
clasohm@0
   462
            (case assoc(iTs,ixn) of None => T | Some(U) => U)
clasohm@0
   463
  in subst T end;
clasohm@0
   464
lcp@728
   465
(*Substitute for type Vars in a term*)
clasohm@0
   466
val subst_TVars = map_term_types o typ_subst_TVars;
clasohm@0
   467
lcp@728
   468
(*Substitute for Vars in a term; see also envir/norm_term*)
clasohm@0
   469
fun subst_Vars itms t = if null itms then t else
clasohm@0
   470
  let fun subst(v as Var(ixn,_)) =
clasohm@0
   471
            (case assoc(itms,ixn) of None => v | Some t => t)
clasohm@0
   472
        | subst(Abs(a,T,t)) = Abs(a,T,subst t)
clasohm@0
   473
        | subst(f$t) = subst f $ subst t
clasohm@0
   474
        | subst(t) = t
clasohm@0
   475
  in subst t end;
clasohm@0
   476
lcp@728
   477
(*Substitute for type/term Vars in a term; see also envir/norm_term*)
clasohm@0
   478
fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else
clasohm@0
   479
  let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T)
clasohm@0
   480
        | subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T)
clasohm@0
   481
        | subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of
clasohm@0
   482
            None   => Var(ixn,typ_subst_TVars iTs T)
clasohm@0
   483
          | Some t => t)
clasohm@0
   484
        | subst(b as Bound _) = b
clasohm@0
   485
        | subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t)
clasohm@0
   486
        | subst(f$t) = subst f $ subst t
clasohm@0
   487
  in subst end;
clasohm@0
   488
clasohm@0
   489
clasohm@0
   490
(*Computing the maximum index of a typ*)
paulson@2146
   491
fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts
clasohm@0
   492
  | maxidx_of_typ(TFree _) = ~1
paulson@2146
   493
  | maxidx_of_typ(TVar((_,i),_)) = i
paulson@2146
   494
and maxidx_of_typs [] = ~1
paulson@2146
   495
  | maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts);
clasohm@0
   496
clasohm@0
   497
clasohm@0
   498
(*Computing the maximum index of a term*)
clasohm@0
   499
fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T
clasohm@0
   500
  | maxidx_of_term (Bound _) = ~1
clasohm@0
   501
  | maxidx_of_term (Free(_,T)) = maxidx_of_typ T
paulson@2146
   502
  | maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T)
paulson@2146
   503
  | maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T)
paulson@2146
   504
  | maxidx_of_term (f$t) = Int.max(maxidx_of_term f,  maxidx_of_term t);
clasohm@0
   505
clasohm@0
   506
clasohm@0
   507
(* Increment the index of all Poly's in T by k *)
nipkow@949
   508
fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S));
clasohm@0
   509
clasohm@0
   510
clasohm@0
   511
(**** Syntax-related declarations ****)
clasohm@0
   512
clasohm@0
   513
clasohm@0
   514
(*Dummy type for parsing.  Will be replaced during type inference. *)
clasohm@0
   515
val dummyT = Type("dummy",[]);
clasohm@0
   516
clasohm@0
   517
(*scan a numeral of the given radix, normally 10*)
clasohm@0
   518
fun scan_radixint (radix: int, cs) : int * string list =
clasohm@0
   519
  let val zero = ord"0"
clasohm@0
   520
      val limit = zero+radix
clasohm@0
   521
      fun scan (num,[]) = (num,[])
clasohm@1460
   522
	| scan (num, c::cs) =
clasohm@1460
   523
	      if  zero <= ord c  andalso  ord c < limit
clasohm@1460
   524
	      then scan(radix*num + ord c - zero, cs)
clasohm@1460
   525
	      else (num, c::cs)
clasohm@0
   526
  in  scan(0,cs)  end;
clasohm@0
   527
clasohm@0
   528
fun scan_int cs = scan_radixint(10,cs);
clasohm@0
   529
clasohm@0
   530
clasohm@0
   531
(*** Printing ***)
clasohm@0
   532
clasohm@0
   533
clasohm@0
   534
(*Makes a variant of the name c distinct from the names in bs.
clasohm@0
   535
  First attaches the suffix "a" and then increments this. *)
clasohm@0
   536
fun variant bs c : string =
paulson@2138
   537
  let fun vary2 c = if (c mem_string bs) then  vary2 (bump_string c)  else  c
paulson@2138
   538
      fun vary1 c = if (c mem_string bs) then  vary2 (c ^ "a")  else  c
clasohm@0
   539
  in  vary1 (if c="" then "u" else c)  end;
clasohm@0
   540
clasohm@0
   541
(*Create variants of the list of names, with priority to the first ones*)
clasohm@0
   542
fun variantlist ([], used) = []
clasohm@0
   543
  | variantlist(b::bs, used) = 
clasohm@0
   544
      let val b' = variant used b
clasohm@0
   545
      in  b' :: variantlist (bs, b'::used)  end;
clasohm@0
   546
clasohm@0
   547
(** TFrees and TVars **)
clasohm@0
   548
clasohm@0
   549
(*maps  (bs,v)  to   v'::bs    this reverses the identifiers bs*)
clasohm@0
   550
fun add_new_id (bs, c) : string list =  variant bs c  ::  bs;
clasohm@0
   551
clasohm@0
   552
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
   553
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
paulson@2176
   554
fun add_term_names (Const(a,_), bs) = a ins_string bs
paulson@2176
   555
  | add_term_names (Free(a,_), bs) = a ins_string bs
clasohm@0
   556
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
   557
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
   558
  | add_term_names (_, bs) = bs;
clasohm@0
   559
clasohm@0
   560
(*Accumulates the TVars in a type, suppressing duplicates. *)
clasohm@0
   561
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars (Ts,vs)
clasohm@0
   562
  | add_typ_tvars(TFree(_),vs) = vs
clasohm@0
   563
  | add_typ_tvars(TVar(v),vs) = v ins vs;
clasohm@0
   564
clasohm@0
   565
(*Accumulates the TFrees in a type, suppressing duplicates. *)
clasohm@0
   566
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names (Ts,fs)
paulson@2176
   567
  | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
clasohm@0
   568
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
   569
clasohm@0
   570
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees (Ts,fs)
clasohm@0
   571
  | add_typ_tfrees(TFree(f),fs) = f ins fs
clasohm@0
   572
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
   573
nipkow@949
   574
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames (Ts,nms)
paulson@2176
   575
  | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
paulson@2176
   576
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
nipkow@949
   577
clasohm@0
   578
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
   579
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
   580
clasohm@0
   581
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
   582
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
   583
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
   584
nipkow@949
   585
val add_term_tvarnames = it_term_types add_typ_varnames;
nipkow@949
   586
clasohm@0
   587
(*Non-list versions*)
clasohm@0
   588
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
   589
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
   590
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
   591
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
   592
nipkow@949
   593
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
   594
nipkow@949
   595
fun add_typ_ixns(ixns,Type(_,Ts)) = foldl add_typ_ixns (ixns,Ts)
paulson@2176
   596
  | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns 
paulson@2176
   597
				     else ixns@[ixn]
nipkow@949
   598
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
   599
nipkow@949
   600
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   601
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   602
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   603
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
   604
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
   605
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
   606
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
   607
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
   608
clasohm@0
   609
(** Frees and Vars **)
clasohm@0
   610
clasohm@0
   611
(*a partial ordering (not reflexive) for atomic terms*)
clasohm@0
   612
fun atless (Const (a,_), Const (b,_))  =  a<b
clasohm@0
   613
  | atless (Free (a,_), Free (b,_)) =  a<b
clasohm@0
   614
  | atless (Var(v,_), Var(w,_))  =  xless(v,w)
clasohm@0
   615
  | atless (Bound i, Bound j)  =   i<j
clasohm@0
   616
  | atless _  =  false;
clasohm@0
   617
clasohm@0
   618
(*insert atomic term into partially sorted list, suppressing duplicates (?)*)
clasohm@0
   619
fun insert_aterm (t,us) =
clasohm@0
   620
  let fun inserta [] = [t]
clasohm@0
   621
        | inserta (us as u::us') = 
clasohm@1460
   622
	      if atless(t,u) then t::us
clasohm@1460
   623
	      else if t=u then us (*duplicate*)
clasohm@1460
   624
	      else u :: inserta(us')
clasohm@0
   625
  in  inserta us  end;
clasohm@0
   626
clasohm@0
   627
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
   628
fun add_term_vars (t, vars: term list) = case t of
clasohm@0
   629
    Var   _ => insert_aterm(t,vars)
clasohm@0
   630
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
   631
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
   632
  | _ => vars;
clasohm@0
   633
clasohm@0
   634
fun term_vars t = add_term_vars(t,[]);
clasohm@0
   635
clasohm@0
   636
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
   637
fun add_term_frees (t, frees: term list) = case t of
clasohm@0
   638
    Free   _ => insert_aterm(t,frees)
clasohm@0
   639
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
   640
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
   641
  | _ => frees;
clasohm@0
   642
clasohm@0
   643
fun term_frees t = add_term_frees(t,[]);
clasohm@0
   644
clasohm@0
   645
(*Given an abstraction over P, replaces the bound variable by a Free variable
clasohm@0
   646
  having a unique name. *)
clasohm@0
   647
fun variant_abs (a,T,P) =
clasohm@0
   648
  let val b = variant (add_term_names(P,[])) a
paulson@2192
   649
  in  (b,  subst_bound (Free(b,T), P))  end;
clasohm@0
   650
clasohm@0
   651
(* renames and reverses the strings in vars away from names *)
clasohm@0
   652
fun rename_aTs names vars : (string*typ)list =
clasohm@0
   653
  let fun rename_aT (vars,(a,T)) =
clasohm@1460
   654
		(variant (map #1 vars @ names) a, T) :: vars
clasohm@0
   655
  in foldl rename_aT ([],vars) end;
clasohm@0
   656
clasohm@0
   657
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
clasohm@1364
   658
paulson@1417
   659
paulson@1417
   660
paulson@1426
   661
(*** Compression of terms and types by sharing common subtrees.  
paulson@1426
   662
     Saves 50-75% on storage requirements.  As it is fairly slow, 
paulson@1426
   663
     it is called only for axioms, stored theorems, etc. ***)
paulson@1417
   664
paulson@1417
   665
(** Sharing of types **)
paulson@1417
   666
paulson@1417
   667
fun atomic_tag (Type (a,_)) = if a<>"fun" then a else raise Match
paulson@1417
   668
  | atomic_tag (TFree (a,_)) = a
paulson@1417
   669
  | atomic_tag (TVar ((a,_),_)) = a;
paulson@1417
   670
paulson@1417
   671
fun type_tag (Type("fun",[S,T])) = atomic_tag S ^ type_tag T
paulson@1417
   672
  | type_tag T = atomic_tag T;
paulson@1417
   673
paulson@1417
   674
val memo_types = ref (Symtab.null : typ list Symtab.table);
paulson@1417
   675
paulson@1417
   676
fun find_type (T, []: typ list) = None
paulson@1417
   677
  | find_type (T, T'::Ts) =
paulson@1417
   678
       if T=T' then Some T'
paulson@1417
   679
       else find_type (T, Ts);
paulson@1417
   680
paulson@1417
   681
fun compress_type T =
paulson@1417
   682
  let val tag = type_tag T
paulson@1417
   683
      val tylist = the (Symtab.lookup (!memo_types, tag))
clasohm@1460
   684
	           handle _ => []
paulson@1417
   685
  in  
paulson@1417
   686
      case find_type (T,tylist) of
clasohm@1460
   687
	Some T' => T'
paulson@1417
   688
      | None => 
clasohm@1460
   689
	    let val T' =
clasohm@1460
   690
		case T of
clasohm@1460
   691
		    Type (a,Ts) => Type (a, map compress_type Ts)
clasohm@1460
   692
		  | _ => T
clasohm@1460
   693
	    in  memo_types := Symtab.update ((tag, T'::tylist), !memo_types);
clasohm@1460
   694
		T
clasohm@1460
   695
	    end
paulson@1417
   696
  end
paulson@1417
   697
  handle Match =>
paulson@1417
   698
      let val Type (a,Ts) = T
paulson@1417
   699
      in  Type (a, map compress_type Ts)  end;
paulson@1417
   700
paulson@1417
   701
(** Sharing of atomic terms **)
paulson@1417
   702
paulson@1417
   703
val memo_terms = ref (Symtab.null : term list Symtab.table);
paulson@1417
   704
paulson@1417
   705
fun find_term (t, []: term list) = None
paulson@1417
   706
  | find_term (t, t'::ts) =
paulson@1417
   707
       if t=t' then Some t'
paulson@1417
   708
       else find_term (t, ts);
paulson@1417
   709
paulson@1417
   710
fun const_tag (Const (a,_)) = a
paulson@1417
   711
  | const_tag (Free (a,_))  = a
paulson@1417
   712
  | const_tag (Var ((a,i),_)) = a
paulson@1417
   713
  | const_tag (t as Bound _)  = ".B.";
paulson@1417
   714
paulson@1417
   715
fun share_term (t $ u) = share_term t $ share_term u
paulson@1417
   716
  | share_term (Abs (a,T,u)) = Abs (a, T, share_term u)
paulson@1417
   717
  | share_term t =
paulson@1417
   718
      let val tag = const_tag t
clasohm@1460
   719
	  val ts = the (Symtab.lookup (!memo_terms, tag))
clasohm@1460
   720
	               handle _ => []
paulson@1417
   721
      in 
clasohm@1460
   722
	  case find_term (t,ts) of
clasohm@1460
   723
	      Some t' => t'
clasohm@1460
   724
	    | None => (memo_terms := Symtab.update ((tag, t::ts), !memo_terms);
clasohm@1460
   725
		       t)
paulson@1417
   726
      end;
paulson@1417
   727
paulson@1417
   728
val compress_term = share_term o map_term_types compress_type;
paulson@1417
   729
clasohm@1364
   730
end;
clasohm@1364
   731
clasohm@1364
   732
open Term;