src/Pure/term.ML
author clasohm
Mon Jan 29 14:16:13 1996 +0100 (1996-01-29)
changeset 1460 5a6f2aabd538
parent 1458 fd510875fb71
child 2138 056dead45ae8
permissions -rw-r--r--
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(*  Title: 	Pure/term.ML
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    ID:         $Id$
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    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   Cambridge University 1992
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Simply typed lambda-calculus: types, terms, and basic operations
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*)
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infix 9  $;
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infixr 5 -->;
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infixr   --->;
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infix    aconv;
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structure Term =
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struct
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(*Indexnames can be quickly renamed by adding an offset to the integer part,
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  for resolution.*)
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type indexname = string*int;
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(* Types are classified by classes. *)
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type class = string;
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type sort  = class list;
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(* The sorts attached to TFrees and TVars specify the sort of that variable *)
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datatype typ = Type  of string * typ list
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             | TFree of string * sort
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	     | TVar  of indexname * sort;
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fun S --> T = Type("fun",[S,T]);
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(*handy for multiple args: [T1,...,Tn]--->T  gives  T1-->(T2--> ... -->T)*)
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val op ---> = foldr (op -->);
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(*terms.  Bound variables are indicated by depth number.
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  Free variables, (scheme) variables and constants have names.
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  An term is "closed" if there every bound variable of level "lev"
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  is enclosed by at least "lev" abstractions. 
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  It is possible to create meaningless terms containing loose bound vars
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  or type mismatches.  But such terms are not allowed in rules. *)
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datatype term = 
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    Const of string * typ
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  | Free  of string * typ 
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  | Var   of indexname * typ
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  | Bound of int
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  | Abs   of string*typ*term
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  | op $  of term*term;
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(*For errors involving type mismatches*)
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exception TYPE of string * typ list * term list;
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fun raise_type msg tys ts = raise TYPE (msg, tys, ts);
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(*For system errors involving terms*)
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exception TERM of string * term list;
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fun raise_term msg ts = raise TERM (msg, ts);
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(*Note variable naming conventions!
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    a,b,c: string
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    f,g,h: functions (including terms of function type)
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    i,j,m,n: int
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    t,u: term
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    v,w: indexnames
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    x,y: any
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    A,B,C: term (denoting formulae)
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    T,U: typ
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*)
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(** Discriminators **)
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fun is_Const (Const _) = true
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  | is_Const _ = false;
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fun is_Free (Free _) = true
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  | is_Free _ = false;
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fun is_Var (Var _) = true
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  | is_Var _ = false;
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fun is_TVar (TVar _) = true
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  | is_TVar _ = false;
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(** Destructors **)
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fun dest_Const (Const x) =  x
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  | dest_Const t = raise TERM("dest_Const", [t]);
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fun dest_Free (Free x) =  x
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  | dest_Free t = raise TERM("dest_Free", [t]);
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fun dest_Var (Var x) =  x
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  | dest_Var t = raise TERM("dest_Var", [t]);
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(* maps  [T1,...,Tn]--->T  to the list  [T1,T2,...,Tn]*)
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fun binder_types (Type("fun",[S,T])) = S :: binder_types T
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  | binder_types _   =  [];
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(* maps  [T1,...,Tn]--->T  to T*)
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fun body_type (Type("fun",[S,T])) = body_type T
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  | body_type T   =  T;
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(* maps  [T1,...,Tn]--->T  to   ([T1,T2,...,Tn], T)  *)
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fun strip_type T : typ list * typ =
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  (binder_types T, body_type T);
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(*Compute the type of the term, checking that combinations are well-typed
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  Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*)
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fun type_of1 (Ts, Const (_,T)) = T
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  | type_of1 (Ts, Free  (_,T)) = T
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  | type_of1 (Ts, Bound i) = (nth_elem (i,Ts)  
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  	handle LIST _ => raise TYPE("type_of: bound variable", [], [Bound i]))
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  | type_of1 (Ts, Var (_,T)) = T
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  | type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body)
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  | type_of1 (Ts, f$u) = 
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      let val U = type_of1(Ts,u)
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          and T = type_of1(Ts,f)
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      in case T of
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	    Type("fun",[T1,T2]) =>
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	      if T1=U then T2  else raise TYPE
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	            ("type_of: type mismatch in application", [T1,U], [f$u])
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	  | _ => raise TYPE 
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		    ("type_of: function type is expected in application",
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		     [T,U], [f$u])
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      end;
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fun type_of t : typ = type_of1 ([],t);
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(*Determines the type of a term, with minimal checking*)
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fun fastype_of1 (Ts, f$u) = 
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    (case fastype_of1 (Ts,f) of
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	Type("fun",[_,T]) => T
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	| _ => raise TERM("fastype_of: expected function type", [f$u]))
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  | fastype_of1 (_, Const (_,T)) = T
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  | fastype_of1 (_, Free (_,T)) = T
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  | fastype_of1 (Ts, Bound i) = (nth_elem(i,Ts)
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  	 handle LIST _ => raise TERM("fastype_of: Bound", [Bound i]))
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  | fastype_of1 (_, Var (_,T)) = T 
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  | fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u);
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fun fastype_of t : typ = fastype_of1 ([],t);
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(* maps  (x1,...,xn)t   to   t  *)
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fun strip_abs_body (Abs(_,_,t))  =  strip_abs_body t  
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  | strip_abs_body u  =  u;
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(* maps  (x1,...,xn)t   to   [x1, ..., xn]  *)
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fun strip_abs_vars (Abs(a,T,t))  =  (a,T) :: strip_abs_vars t 
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  | strip_abs_vars u  =  [] : (string*typ) list;
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fun strip_qnt_body qnt =
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let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm
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      | strip t = t
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in strip end;
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fun strip_qnt_vars qnt =
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let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else []
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      | strip t  =  [] : (string*typ) list
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in strip end;
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(* maps   (f, [t1,...,tn])  to  f(t1,...,tn) *)
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val list_comb : term * term list -> term = foldl (op $);
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(* maps   f(t1,...,tn)  to  (f, [t1,...,tn]) ; naturally tail-recursive*)
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fun strip_comb u : term * term list = 
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    let fun stripc (f$t, ts) = stripc (f, t::ts)
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        |   stripc  x =  x 
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    in  stripc(u,[])  end;
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(* maps   f(t1,...,tn)  to  f , which is never a combination *)
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fun head_of (f$t) = head_of f
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  | head_of u = u;
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(*Number of atoms and abstractions in a term*)
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fun size_of_term (Abs (_,_,body)) = 1 + size_of_term body
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  | size_of_term (f$t) = size_of_term f  +  size_of_term t
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  | size_of_term _ = 1;
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fun map_type_tvar f (Type(a,Ts)) = Type(a, map (map_type_tvar f) Ts)
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  | map_type_tvar f (T as TFree _) = T
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  | map_type_tvar f (TVar x) = f x;
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fun map_type_tfree f (Type(a,Ts)) = Type(a, map (map_type_tfree f) Ts)
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  | map_type_tfree f (TFree x) = f x
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  | map_type_tfree f (T as TVar _) = T;
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(* apply a function to all types in a term *)
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fun map_term_types f =
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let fun map(Const(a,T)) = Const(a, f T)
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      | map(Free(a,T)) = Free(a, f T)
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      | map(Var(v,T)) = Var(v, f T)
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      | map(t as Bound _)  = t
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      | map(Abs(a,T,t)) = Abs(a, f T, map t)
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      | map(f$t) = map f $ map t;
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in map end;
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(* iterate a function over all types in a term *)
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fun it_term_types f =
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let fun iter(Const(_,T), a) = f(T,a)
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      | iter(Free(_,T), a) = f(T,a)
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      | iter(Var(_,T), a) = f(T,a)
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      | iter(Abs(_,T,t), a) = iter(t,f(T,a))
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      | iter(f$u, a) = iter(f, iter(u, a))
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      | iter(Bound _, a) = a
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in iter end
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(** Connectives of higher order logic **)
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val logicC: class = "logic";
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val logicS: sort = [logicC];
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fun itselfT ty = Type ("itself", [ty]);
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val a_itselfT = itselfT (TFree ("'a", logicS));
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val propT : typ = Type("prop",[]);
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val implies = Const("==>", propT-->propT-->propT);
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fun all T = Const("all", (T-->propT)-->propT);
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fun equals T = Const("==", T-->T-->propT);
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fun flexpair T = Const("=?=", T-->T-->propT);
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(* maps  !!x1...xn. t   to   t  *)
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fun strip_all_body (Const("all",_)$Abs(_,_,t))  =  strip_all_body t  
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  | strip_all_body t  =  t;
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(* maps  !!x1...xn. t   to   [x1, ..., xn]  *)
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fun strip_all_vars (Const("all",_)$Abs(a,T,t))  =
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		(a,T) :: strip_all_vars t 
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  | strip_all_vars t  =  [] : (string*typ) list;
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(*increments a term's non-local bound variables
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  required when moving a term within abstractions
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     inc is  increment for bound variables
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     lev is  level at which a bound variable is considered 'loose'*)
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fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u 
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  | incr_bv (inc, lev, Abs(a,T,body)) =
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	Abs(a, T, incr_bv(inc,lev+1,body))
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  | incr_bv (inc, lev, f$t) = 
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      incr_bv(inc,lev,f) $ incr_bv(inc,lev,t)
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  | incr_bv (inc, lev, u) = u;
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fun incr_boundvars  0  t = t
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  | incr_boundvars inc t = incr_bv(inc,0,t);
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(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond.
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   (Bound 0) is loose at level 0 *)
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fun add_loose_bnos (Bound i, lev, js) = 
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	if i<lev then js  else  (i-lev) ins js
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  | add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js)
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  | add_loose_bnos (f$t, lev, js) =
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	add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) 
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  | add_loose_bnos (_, _, js) = js;
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fun loose_bnos t = add_loose_bnos (t, 0, []);
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(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to
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   level k or beyond. *)
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fun loose_bvar(Bound i,k) = i >= k
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  | loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k)
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  | loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1)
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  | loose_bvar _ = false;
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(*Substitute arguments for loose bound variables.
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  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
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  Note that for ((x,y)c)(a,b), the bound vars in c are x=1 and y=0
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	and the appropriate call is  subst_bounds([b,a], c) .
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  Loose bound variables >=n are reduced by "n" to
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     compensate for the disappearance of lambdas.
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*)
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fun subst_bounds (args: term list, t) : term = 
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  let val n = length args;
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      fun subst (t as Bound i, lev) =
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 	    if i<lev then  t    (*var is locally bound*)
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	    else  (case (drop (i-lev,args)) of
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		  []     => Bound(i-n)  (*loose: change it*)
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	        | arg::_ => incr_boundvars lev arg)
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	| subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
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	| subst (f$t, lev) =  subst(f,lev)  $  subst(t,lev)
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	| subst (t,lev) = t
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  in   case args of [] => t  | _ => subst (t,0)  end;
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(*beta-reduce if possible, else form application*)
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fun betapply (Abs(_,_,t), u) = subst_bounds([u],t)
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  | betapply (f,u) = f$u;
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(*Tests whether 2 terms are alpha-convertible and have same type.
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  Note that constants and Vars may have more than one type.*)
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fun (Const(a,T)) aconv (Const(b,U)) = a=b  andalso  T=U
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  | (Free(a,T)) aconv (Free(b,U)) = a=b  andalso  T=U
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  | (Var(v,T)) aconv (Var(w,U)) =   v=w  andalso  T=U
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  | (Bound i) aconv (Bound j)  =   i=j
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  | (Abs(_,T,t)) aconv (Abs(_,U,u)) = t aconv u  andalso  T=U
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  | (f$t) aconv (g$u) = (f aconv g) andalso (t aconv u)
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  | _ aconv _  =  false;
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(*are two term lists alpha-convertible in corresponding elements?*)
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fun aconvs ([],[]) = true
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  | aconvs (t::ts, u::us) = t aconv u andalso aconvs(ts,us)
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  | aconvs _ = false;
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(*A fast unification filter: true unless the two terms cannot be unified. 
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  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   327
fun could_unify (t,u) =
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   328
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
clasohm@1460
   329
	| matchrands _ = true
clasohm@0
   330
  in case (head_of t , head_of u) of
clasohm@1460
   331
	(_, Var _) => true
clasohm@0
   332
      | (Var _, _) => true
clasohm@0
   333
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   334
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   335
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   336
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   337
      | (_, Abs _) =>  true
clasohm@0
   338
      | _ => false
clasohm@0
   339
  end;
clasohm@0
   340
clasohm@0
   341
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   342
fun subst_free [] = (fn t=>t)
clasohm@0
   343
  | subst_free pairs =
clasohm@0
   344
      let fun substf u = 
clasohm@1460
   345
	    case gen_assoc (op aconv) (pairs, u) of
clasohm@1460
   346
		Some u' => u'
clasohm@1460
   347
	      | None => (case u of Abs(a,T,t) => Abs(a, T, substf t)
clasohm@1460
   348
				 | t$u' => substf t $ substf u'
clasohm@1460
   349
				 | _ => u)
clasohm@0
   350
      in  substf  end;
clasohm@0
   351
clasohm@0
   352
(*a total, irreflexive ordering on index names*)
clasohm@0
   353
fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);
clasohm@0
   354
clasohm@0
   355
clasohm@0
   356
(*Abstraction of the term "body" over its occurrences of v, 
clasohm@0
   357
    which must contain no loose bound variables.
clasohm@0
   358
  The resulting term is ready to become the body of an Abs.*)
clasohm@0
   359
fun abstract_over (v,body) =
clasohm@0
   360
  let fun abst (lev,u) = if (v aconv u) then (Bound lev) else
clasohm@0
   361
      (case u of
clasohm@0
   362
          Abs(a,T,t) => Abs(a, T, abst(lev+1, t))
clasohm@1460
   363
	| f$rand => abst(lev,f) $ abst(lev,rand)
clasohm@1460
   364
	| _ => u)
clasohm@0
   365
  in  abst(0,body)  end;
clasohm@0
   366
clasohm@0
   367
clasohm@0
   368
(*Form an abstraction over a free variable.*)
clasohm@0
   369
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
clasohm@0
   370
clasohm@0
   371
(*Abstraction over a list of free variables*)
clasohm@0
   372
fun list_abs_free ([ ] ,     t) = t
clasohm@0
   373
  | list_abs_free ((a,T)::vars, t) = 
clasohm@0
   374
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   375
clasohm@0
   376
(*Quantification over a list of free variables*)
clasohm@0
   377
fun list_all_free ([], t: term) = t
clasohm@0
   378
  | list_all_free ((a,T)::vars, t) = 
clasohm@0
   379
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   380
clasohm@0
   381
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   382
fun list_all ([], t) = t
clasohm@0
   383
  | list_all ((a,T)::vars, t) = 
clasohm@0
   384
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   385
clasohm@0
   386
(*Replace the ATOMIC term ti by ui;    instl = [(t1,u1), ..., (tn,un)]. 
clasohm@0
   387
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
clasohm@0
   388
fun subst_atomic [] t = t : term
clasohm@0
   389
  | subst_atomic (instl: (term*term) list) t =
clasohm@0
   390
      let fun subst (Abs(a,T,body)) = Abs(a, T, subst body)
clasohm@1460
   391
	    | subst (f$t') = subst f $ subst t'
clasohm@1460
   392
	    | subst t = (case assoc(instl,t) of
clasohm@1460
   393
		           Some u => u  |  None => t)
clasohm@0
   394
      in  subst t  end;
clasohm@0
   395
lcp@728
   396
(*Substitute for type Vars in a type*)
clasohm@0
   397
fun typ_subst_TVars iTs T = if null iTs then T else
clasohm@0
   398
  let fun subst(Type(a,Ts)) = Type(a, map subst Ts)
clasohm@1460
   399
	| subst(T as TFree _) = T
clasohm@1460
   400
	| subst(T as TVar(ixn,_)) =
clasohm@0
   401
            (case assoc(iTs,ixn) of None => T | Some(U) => U)
clasohm@0
   402
  in subst T end;
clasohm@0
   403
lcp@728
   404
(*Substitute for type Vars in a term*)
clasohm@0
   405
val subst_TVars = map_term_types o typ_subst_TVars;
clasohm@0
   406
lcp@728
   407
(*Substitute for Vars in a term; see also envir/norm_term*)
clasohm@0
   408
fun subst_Vars itms t = if null itms then t else
clasohm@0
   409
  let fun subst(v as Var(ixn,_)) =
clasohm@0
   410
            (case assoc(itms,ixn) of None => v | Some t => t)
clasohm@0
   411
        | subst(Abs(a,T,t)) = Abs(a,T,subst t)
clasohm@0
   412
        | subst(f$t) = subst f $ subst t
clasohm@0
   413
        | subst(t) = t
clasohm@0
   414
  in subst t end;
clasohm@0
   415
lcp@728
   416
(*Substitute for type/term Vars in a term; see also envir/norm_term*)
clasohm@0
   417
fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else
clasohm@0
   418
  let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T)
clasohm@0
   419
        | subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T)
clasohm@0
   420
        | subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of
clasohm@0
   421
            None   => Var(ixn,typ_subst_TVars iTs T)
clasohm@0
   422
          | Some t => t)
clasohm@0
   423
        | subst(b as Bound _) = b
clasohm@0
   424
        | subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t)
clasohm@0
   425
        | subst(f$t) = subst f $ subst t
clasohm@0
   426
  in subst end;
clasohm@0
   427
clasohm@0
   428
clasohm@0
   429
(*Computing the maximum index of a typ*)
clasohm@0
   430
fun maxidx_of_typ(Type(_,Ts)) =
clasohm@1460
   431
	if Ts=[] then ~1 else max(map maxidx_of_typ Ts)
clasohm@0
   432
  | maxidx_of_typ(TFree _) = ~1
clasohm@0
   433
  | maxidx_of_typ(TVar((_,i),_)) = i;
clasohm@0
   434
clasohm@0
   435
clasohm@0
   436
(*Computing the maximum index of a term*)
clasohm@0
   437
fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T
clasohm@0
   438
  | maxidx_of_term (Bound _) = ~1
clasohm@0
   439
  | maxidx_of_term (Free(_,T)) = maxidx_of_typ T
clasohm@0
   440
  | maxidx_of_term (Var ((_,i), T)) = max[i, maxidx_of_typ T]
clasohm@0
   441
  | maxidx_of_term (Abs (_,T,body)) = max[maxidx_of_term body, maxidx_of_typ T]
clasohm@0
   442
  | maxidx_of_term (f$t) = max [maxidx_of_term f,  maxidx_of_term t];
clasohm@0
   443
clasohm@0
   444
clasohm@0
   445
(* Increment the index of all Poly's in T by k *)
nipkow@949
   446
fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S));
clasohm@0
   447
clasohm@0
   448
clasohm@0
   449
(**** Syntax-related declarations ****)
clasohm@0
   450
clasohm@0
   451
clasohm@0
   452
(*Dummy type for parsing.  Will be replaced during type inference. *)
clasohm@0
   453
val dummyT = Type("dummy",[]);
clasohm@0
   454
clasohm@0
   455
(*scan a numeral of the given radix, normally 10*)
clasohm@0
   456
fun scan_radixint (radix: int, cs) : int * string list =
clasohm@0
   457
  let val zero = ord"0"
clasohm@0
   458
      val limit = zero+radix
clasohm@0
   459
      fun scan (num,[]) = (num,[])
clasohm@1460
   460
	| scan (num, c::cs) =
clasohm@1460
   461
	      if  zero <= ord c  andalso  ord c < limit
clasohm@1460
   462
	      then scan(radix*num + ord c - zero, cs)
clasohm@1460
   463
	      else (num, c::cs)
clasohm@0
   464
  in  scan(0,cs)  end;
clasohm@0
   465
clasohm@0
   466
fun scan_int cs = scan_radixint(10,cs);
clasohm@0
   467
clasohm@0
   468
clasohm@0
   469
(*** Printing ***)
clasohm@0
   470
clasohm@0
   471
clasohm@0
   472
(*Makes a variant of the name c distinct from the names in bs.
clasohm@0
   473
  First attaches the suffix "a" and then increments this. *)
clasohm@0
   474
fun variant bs c : string =
clasohm@0
   475
  let fun vary2 c = if (c mem bs) then  vary2 (bump_string c)  else  c
clasohm@0
   476
      fun vary1 c = if (c mem bs) then  vary2 (c ^ "a")  else  c
clasohm@0
   477
  in  vary1 (if c="" then "u" else c)  end;
clasohm@0
   478
clasohm@0
   479
(*Create variants of the list of names, with priority to the first ones*)
clasohm@0
   480
fun variantlist ([], used) = []
clasohm@0
   481
  | variantlist(b::bs, used) = 
clasohm@0
   482
      let val b' = variant used b
clasohm@0
   483
      in  b' :: variantlist (bs, b'::used)  end;
clasohm@0
   484
clasohm@0
   485
(** TFrees and TVars **)
clasohm@0
   486
clasohm@0
   487
(*maps  (bs,v)  to   v'::bs    this reverses the identifiers bs*)
clasohm@0
   488
fun add_new_id (bs, c) : string list =  variant bs c  ::  bs;
clasohm@0
   489
clasohm@0
   490
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
   491
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
clasohm@0
   492
fun add_term_names (Const(a,_), bs) = a ins bs
clasohm@0
   493
  | add_term_names (Free(a,_), bs) = a ins bs
clasohm@0
   494
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
   495
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
   496
  | add_term_names (_, bs) = bs;
clasohm@0
   497
clasohm@0
   498
(*Accumulates the TVars in a type, suppressing duplicates. *)
clasohm@0
   499
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars (Ts,vs)
clasohm@0
   500
  | add_typ_tvars(TFree(_),vs) = vs
clasohm@0
   501
  | add_typ_tvars(TVar(v),vs) = v ins vs;
clasohm@0
   502
clasohm@0
   503
(*Accumulates the TFrees in a type, suppressing duplicates. *)
clasohm@0
   504
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names (Ts,fs)
clasohm@0
   505
  | add_typ_tfree_names(TFree(f,_),fs) = f ins fs
clasohm@0
   506
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
   507
clasohm@0
   508
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees (Ts,fs)
clasohm@0
   509
  | add_typ_tfrees(TFree(f),fs) = f ins fs
clasohm@0
   510
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
   511
nipkow@949
   512
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames (Ts,nms)
nipkow@949
   513
  | add_typ_varnames(TFree(nm,_),nms) = nm ins nms
nipkow@949
   514
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins nms;
nipkow@949
   515
clasohm@0
   516
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
   517
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
   518
clasohm@0
   519
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
   520
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
   521
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
   522
nipkow@949
   523
val add_term_tvarnames = it_term_types add_typ_varnames;
nipkow@949
   524
clasohm@0
   525
(*Non-list versions*)
clasohm@0
   526
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
   527
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
   528
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
   529
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
   530
nipkow@949
   531
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
   532
nipkow@949
   533
fun add_typ_ixns(ixns,Type(_,Ts)) = foldl add_typ_ixns (ixns,Ts)
nipkow@949
   534
  | add_typ_ixns(ixns,TVar(ixn,_)) = if ixn mem ixns then ixns else ixns@[ixn]
nipkow@949
   535
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
   536
nipkow@949
   537
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   538
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   539
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   540
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
   541
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
   542
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
   543
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
   544
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
   545
clasohm@0
   546
(** Frees and Vars **)
clasohm@0
   547
clasohm@0
   548
(*a partial ordering (not reflexive) for atomic terms*)
clasohm@0
   549
fun atless (Const (a,_), Const (b,_))  =  a<b
clasohm@0
   550
  | atless (Free (a,_), Free (b,_)) =  a<b
clasohm@0
   551
  | atless (Var(v,_), Var(w,_))  =  xless(v,w)
clasohm@0
   552
  | atless (Bound i, Bound j)  =   i<j
clasohm@0
   553
  | atless _  =  false;
clasohm@0
   554
clasohm@0
   555
(*insert atomic term into partially sorted list, suppressing duplicates (?)*)
clasohm@0
   556
fun insert_aterm (t,us) =
clasohm@0
   557
  let fun inserta [] = [t]
clasohm@0
   558
        | inserta (us as u::us') = 
clasohm@1460
   559
	      if atless(t,u) then t::us
clasohm@1460
   560
	      else if t=u then us (*duplicate*)
clasohm@1460
   561
	      else u :: inserta(us')
clasohm@0
   562
  in  inserta us  end;
clasohm@0
   563
clasohm@0
   564
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
   565
fun add_term_vars (t, vars: term list) = case t of
clasohm@0
   566
    Var   _ => insert_aterm(t,vars)
clasohm@0
   567
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
   568
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
   569
  | _ => vars;
clasohm@0
   570
clasohm@0
   571
fun term_vars t = add_term_vars(t,[]);
clasohm@0
   572
clasohm@0
   573
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
   574
fun add_term_frees (t, frees: term list) = case t of
clasohm@0
   575
    Free   _ => insert_aterm(t,frees)
clasohm@0
   576
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
   577
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
   578
  | _ => frees;
clasohm@0
   579
clasohm@0
   580
fun term_frees t = add_term_frees(t,[]);
clasohm@0
   581
clasohm@0
   582
(*Given an abstraction over P, replaces the bound variable by a Free variable
clasohm@0
   583
  having a unique name. *)
clasohm@0
   584
fun variant_abs (a,T,P) =
clasohm@0
   585
  let val b = variant (add_term_names(P,[])) a
clasohm@0
   586
  in  (b,  subst_bounds ([Free(b,T)], P))  end;
clasohm@0
   587
clasohm@0
   588
(* renames and reverses the strings in vars away from names *)
clasohm@0
   589
fun rename_aTs names vars : (string*typ)list =
clasohm@0
   590
  let fun rename_aT (vars,(a,T)) =
clasohm@1460
   591
		(variant (map #1 vars @ names) a, T) :: vars
clasohm@0
   592
  in foldl rename_aT ([],vars) end;
clasohm@0
   593
clasohm@0
   594
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
clasohm@1364
   595
paulson@1417
   596
paulson@1417
   597
paulson@1426
   598
(*** Compression of terms and types by sharing common subtrees.  
paulson@1426
   599
     Saves 50-75% on storage requirements.  As it is fairly slow, 
paulson@1426
   600
     it is called only for axioms, stored theorems, etc. ***)
paulson@1417
   601
paulson@1417
   602
(** Sharing of types **)
paulson@1417
   603
paulson@1417
   604
fun atomic_tag (Type (a,_)) = if a<>"fun" then a else raise Match
paulson@1417
   605
  | atomic_tag (TFree (a,_)) = a
paulson@1417
   606
  | atomic_tag (TVar ((a,_),_)) = a;
paulson@1417
   607
paulson@1417
   608
fun type_tag (Type("fun",[S,T])) = atomic_tag S ^ type_tag T
paulson@1417
   609
  | type_tag T = atomic_tag T;
paulson@1417
   610
paulson@1417
   611
val memo_types = ref (Symtab.null : typ list Symtab.table);
paulson@1417
   612
paulson@1417
   613
fun find_type (T, []: typ list) = None
paulson@1417
   614
  | find_type (T, T'::Ts) =
paulson@1417
   615
       if T=T' then Some T'
paulson@1417
   616
       else find_type (T, Ts);
paulson@1417
   617
paulson@1417
   618
fun compress_type T =
paulson@1417
   619
  let val tag = type_tag T
paulson@1417
   620
      val tylist = the (Symtab.lookup (!memo_types, tag))
clasohm@1460
   621
	           handle _ => []
paulson@1417
   622
  in  
paulson@1417
   623
      case find_type (T,tylist) of
clasohm@1460
   624
	Some T' => T'
paulson@1417
   625
      | None => 
clasohm@1460
   626
	    let val T' =
clasohm@1460
   627
		case T of
clasohm@1460
   628
		    Type (a,Ts) => Type (a, map compress_type Ts)
clasohm@1460
   629
		  | _ => T
clasohm@1460
   630
	    in  memo_types := Symtab.update ((tag, T'::tylist), !memo_types);
clasohm@1460
   631
		T
clasohm@1460
   632
	    end
paulson@1417
   633
  end
paulson@1417
   634
  handle Match =>
paulson@1417
   635
      let val Type (a,Ts) = T
paulson@1417
   636
      in  Type (a, map compress_type Ts)  end;
paulson@1417
   637
paulson@1417
   638
(** Sharing of atomic terms **)
paulson@1417
   639
paulson@1417
   640
val memo_terms = ref (Symtab.null : term list Symtab.table);
paulson@1417
   641
paulson@1417
   642
fun find_term (t, []: term list) = None
paulson@1417
   643
  | find_term (t, t'::ts) =
paulson@1417
   644
       if t=t' then Some t'
paulson@1417
   645
       else find_term (t, ts);
paulson@1417
   646
paulson@1417
   647
fun const_tag (Const (a,_)) = a
paulson@1417
   648
  | const_tag (Free (a,_))  = a
paulson@1417
   649
  | const_tag (Var ((a,i),_)) = a
paulson@1417
   650
  | const_tag (t as Bound _)  = ".B.";
paulson@1417
   651
paulson@1417
   652
fun share_term (t $ u) = share_term t $ share_term u
paulson@1417
   653
  | share_term (Abs (a,T,u)) = Abs (a, T, share_term u)
paulson@1417
   654
  | share_term t =
paulson@1417
   655
      let val tag = const_tag t
clasohm@1460
   656
	  val ts = the (Symtab.lookup (!memo_terms, tag))
clasohm@1460
   657
	               handle _ => []
paulson@1417
   658
      in 
clasohm@1460
   659
	  case find_term (t,ts) of
clasohm@1460
   660
	      Some t' => t'
clasohm@1460
   661
	    | None => (memo_terms := Symtab.update ((tag, t::ts), !memo_terms);
clasohm@1460
   662
		       t)
paulson@1417
   663
      end;
paulson@1417
   664
paulson@1417
   665
val compress_term = share_term o map_term_types compress_type;
paulson@1417
   666
clasohm@1364
   667
end;
clasohm@1364
   668
clasohm@1364
   669
open Term;