src/Pure/term.ML
author wenzelm
Wed Nov 26 16:37:17 1997 +0100 (1997-11-26)
changeset 4286 a09e3e6da2de
parent 4188 1025a27b08f9
child 4444 fa05a79b3e97
permissions -rw-r--r--
added foldl_atyps: ('a * typ -> 'a) -> 'a * typ -> 'a;
added foldl_aterms: ('a * term -> 'a) -> 'a * term -> 'a;
added foldl_types: ('a * typ -> 'a) -> 'a * term -> 'a;
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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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(*For system errors involving terms*)
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exception TERM of string * term list;
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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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fun domain_type (Type("fun", [T,_])) = 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_int 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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fun loose_bvar1(Bound i,k) = i = k
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  | loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k)
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  | loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1)
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  | loose_bvar1 _ = false;
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(*Substitute arguments for loose bound variables.
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  Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi).
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  Note that for ((x,y)c)(a,b), the bound vars in c are x=1 and y=0
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	and the appropriate call is  subst_bounds([b,a], c) .
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  Loose bound variables >=n are reduced by "n" to
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     compensate for the disappearance of lambdas.
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*)
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fun subst_bounds (args: term list, t) : term = 
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  let val n = length args;
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      fun subst (t as Bound i, lev) =
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 	   (if i<lev then  t    (*var is locally bound*)
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	    else  incr_boundvars lev (List.nth(args, i-lev))
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		    handle Subscript => Bound(i-n)  (*loose: change it*))
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	| subst (Abs(a,T,body), lev) = Abs(a, T,  subst(body,lev+1))
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	| subst (f$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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(*Special case: one argument*)
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fun subst_bound (arg, t) : term = 
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  let 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  if i=lev then incr_boundvars lev arg
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		           else Bound(i-1)  (*loose: change it*)
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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  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_bound (u,t)
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  | betapply (f,u) = f$u;
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(** Equality, membership and insertion of indexnames (string*ints) **)
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(*optimized equality test for indexnames.  Yields a huge gain under Poly/ML*)
wenzelm@2959
   325
fun eq_ix ((a, i):indexname, (a',i'):indexname) = (a=a') andalso i=i';
paulson@2192
   326
paulson@2192
   327
(*membership in a list, optimized version for indexnames*)
wenzelm@2959
   328
fun mem_ix (_, []) = false
paulson@2192
   329
  | mem_ix (x, y :: ys) = eq_ix(x,y) orelse mem_ix (x, ys);
paulson@2192
   330
paulson@2192
   331
(*insertion into list, optimized version for indexnames*)
paulson@2192
   332
fun ins_ix (x,xs) = if mem_ix (x, xs) then xs else x :: xs;
paulson@2192
   333
clasohm@0
   334
(*Tests whether 2 terms are alpha-convertible and have same type.
clasohm@0
   335
  Note that constants and Vars may have more than one type.*)
clasohm@0
   336
fun (Const(a,T)) aconv (Const(b,U)) = a=b  andalso  T=U
paulson@2752
   337
  | (Free(a,T))  aconv (Free(b,U))  = a=b  andalso  T=U
paulson@2752
   338
  | (Var(v,T))   aconv (Var(w,U))   = eq_ix(v,w)  andalso  T=U
paulson@2752
   339
  | (Bound i)    aconv (Bound j)    = i=j
clasohm@0
   340
  | (Abs(_,T,t)) aconv (Abs(_,U,u)) = t aconv u  andalso  T=U
paulson@2752
   341
  | (f$t)        aconv (g$u)        = (f aconv g) andalso (t aconv u)
clasohm@0
   342
  | _ aconv _  =  false;
clasohm@0
   343
paulson@2176
   344
(** Membership, insertion, union for terms **)
paulson@2176
   345
paulson@2176
   346
fun mem_term (_, []) = false
paulson@2176
   347
  | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);
paulson@2176
   348
paulson@2182
   349
fun subset_term ([], ys) = true
paulson@2182
   350
  | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);
paulson@2182
   351
paulson@2182
   352
fun eq_set_term (xs, ys) =
paulson@2182
   353
    xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
paulson@2182
   354
paulson@2176
   355
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts;
paulson@2176
   356
paulson@2176
   357
fun union_term (xs, []) = xs
paulson@2176
   358
  | union_term ([], ys) = ys
paulson@2176
   359
  | union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys));
paulson@2176
   360
paulson@2176
   361
(** Equality, membership and insertion of sorts (string lists) **)
paulson@2176
   362
paulson@2176
   363
fun eq_sort ([]:sort, []) = true
paulson@2176
   364
  | eq_sort ((s::ss), (t::ts)) = s=t andalso eq_sort(ss,ts)
paulson@2176
   365
  | eq_sort (_, _) = false;
paulson@2176
   366
paulson@2176
   367
fun mem_sort (_:sort, []) = false
paulson@2176
   368
  | mem_sort (S, S'::Ss) = eq_sort (S, S') orelse mem_sort(S,Ss);
paulson@2176
   369
paulson@2176
   370
fun ins_sort(S,Ss) = if mem_sort(S,Ss) then Ss else S :: Ss;
paulson@2176
   371
paulson@2176
   372
fun union_sort (xs, []) = xs
paulson@2176
   373
  | union_sort ([], ys) = ys
paulson@2176
   374
  | union_sort ((x :: xs), ys) = union_sort (xs, ins_sort (x, ys));
paulson@2176
   375
paulson@2182
   376
fun subset_sort ([], ys) = true
paulson@2182
   377
  | subset_sort (x :: xs, ys) = mem_sort (x, ys) andalso subset_sort(xs, ys);
paulson@2182
   378
paulson@2182
   379
fun eq_set_sort (xs, ys) =
paulson@2182
   380
    xs = ys orelse (subset_sort (xs, ys) andalso subset_sort (ys, xs));
paulson@2182
   381
clasohm@0
   382
(*are two term lists alpha-convertible in corresponding elements?*)
clasohm@0
   383
fun aconvs ([],[]) = true
clasohm@0
   384
  | aconvs (t::ts, u::us) = t aconv u andalso aconvs(ts,us)
clasohm@0
   385
  | aconvs _ = false;
clasohm@0
   386
clasohm@0
   387
(*A fast unification filter: true unless the two terms cannot be unified. 
clasohm@0
   388
  Terms must be NORMAL.  Treats all Vars as distinct. *)
clasohm@0
   389
fun could_unify (t,u) =
clasohm@0
   390
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
clasohm@1460
   391
	| matchrands _ = true
clasohm@0
   392
  in case (head_of t , head_of u) of
clasohm@1460
   393
	(_, Var _) => true
clasohm@0
   394
      | (Var _, _) => true
clasohm@0
   395
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   396
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
clasohm@0
   397
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
clasohm@0
   398
      | (Abs _, _) =>  true   (*because of possible eta equality*)
clasohm@0
   399
      | (_, Abs _) =>  true
clasohm@0
   400
      | _ => false
clasohm@0
   401
  end;
clasohm@0
   402
clasohm@0
   403
(*Substitute new for free occurrences of old in a term*)
clasohm@0
   404
fun subst_free [] = (fn t=>t)
clasohm@0
   405
  | subst_free pairs =
clasohm@0
   406
      let fun substf u = 
clasohm@1460
   407
	    case gen_assoc (op aconv) (pairs, u) of
clasohm@1460
   408
		Some u' => u'
clasohm@1460
   409
	      | None => (case u of Abs(a,T,t) => Abs(a, T, substf t)
clasohm@1460
   410
				 | t$u' => substf t $ substf u'
clasohm@1460
   411
				 | _ => u)
clasohm@0
   412
      in  substf  end;
clasohm@0
   413
clasohm@0
   414
(*a total, irreflexive ordering on index names*)
clasohm@0
   415
fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);
clasohm@0
   416
clasohm@0
   417
clasohm@0
   418
(*Abstraction of the term "body" over its occurrences of v, 
clasohm@0
   419
    which must contain no loose bound variables.
clasohm@0
   420
  The resulting term is ready to become the body of an Abs.*)
clasohm@0
   421
fun abstract_over (v,body) =
clasohm@0
   422
  let fun abst (lev,u) = if (v aconv u) then (Bound lev) else
clasohm@0
   423
      (case u of
clasohm@0
   424
          Abs(a,T,t) => Abs(a, T, abst(lev+1, t))
clasohm@1460
   425
	| f$rand => abst(lev,f) $ abst(lev,rand)
clasohm@1460
   426
	| _ => u)
clasohm@0
   427
  in  abst(0,body)  end;
clasohm@0
   428
clasohm@0
   429
clasohm@0
   430
(*Form an abstraction over a free variable.*)
clasohm@0
   431
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
clasohm@0
   432
clasohm@0
   433
(*Abstraction over a list of free variables*)
clasohm@0
   434
fun list_abs_free ([ ] ,     t) = t
clasohm@0
   435
  | list_abs_free ((a,T)::vars, t) = 
clasohm@0
   436
      absfree(a, T, list_abs_free(vars,t));
clasohm@0
   437
clasohm@0
   438
(*Quantification over a list of free variables*)
clasohm@0
   439
fun list_all_free ([], t: term) = t
clasohm@0
   440
  | list_all_free ((a,T)::vars, t) = 
clasohm@0
   441
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
clasohm@0
   442
clasohm@0
   443
(*Quantification over a list of variables (already bound in body) *)
clasohm@0
   444
fun list_all ([], t) = t
clasohm@0
   445
  | list_all ((a,T)::vars, t) = 
clasohm@0
   446
        (all T) $ (Abs(a, T, list_all(vars,t)));
clasohm@0
   447
clasohm@0
   448
(*Replace the ATOMIC term ti by ui;    instl = [(t1,u1), ..., (tn,un)]. 
clasohm@0
   449
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
clasohm@0
   450
fun subst_atomic [] t = t : term
clasohm@0
   451
  | subst_atomic (instl: (term*term) list) t =
clasohm@0
   452
      let fun subst (Abs(a,T,body)) = Abs(a, T, subst body)
clasohm@1460
   453
	    | subst (f$t') = subst f $ subst t'
clasohm@1460
   454
	    | subst t = (case assoc(instl,t) of
clasohm@1460
   455
		           Some u => u  |  None => t)
clasohm@0
   456
      in  subst t  end;
clasohm@0
   457
lcp@728
   458
(*Substitute for type Vars in a type*)
clasohm@0
   459
fun typ_subst_TVars iTs T = if null iTs then T else
clasohm@0
   460
  let fun subst(Type(a,Ts)) = Type(a, map subst Ts)
clasohm@1460
   461
	| subst(T as TFree _) = T
clasohm@1460
   462
	| subst(T as TVar(ixn,_)) =
clasohm@0
   463
            (case assoc(iTs,ixn) of None => T | Some(U) => U)
clasohm@0
   464
  in subst T end;
clasohm@0
   465
lcp@728
   466
(*Substitute for type Vars in a term*)
clasohm@0
   467
val subst_TVars = map_term_types o typ_subst_TVars;
clasohm@0
   468
lcp@728
   469
(*Substitute for Vars in a term; see also envir/norm_term*)
clasohm@0
   470
fun subst_Vars itms t = if null itms then t else
clasohm@0
   471
  let fun subst(v as Var(ixn,_)) =
clasohm@0
   472
            (case assoc(itms,ixn) of None => v | Some t => t)
clasohm@0
   473
        | subst(Abs(a,T,t)) = Abs(a,T,subst t)
clasohm@0
   474
        | subst(f$t) = subst f $ subst t
clasohm@0
   475
        | subst(t) = t
clasohm@0
   476
  in subst t end;
clasohm@0
   477
lcp@728
   478
(*Substitute for type/term Vars in a term; see also envir/norm_term*)
clasohm@0
   479
fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else
clasohm@0
   480
  let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T)
clasohm@0
   481
        | subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T)
clasohm@0
   482
        | subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of
clasohm@0
   483
            None   => Var(ixn,typ_subst_TVars iTs T)
clasohm@0
   484
          | Some t => t)
clasohm@0
   485
        | subst(b as Bound _) = b
clasohm@0
   486
        | subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t)
clasohm@0
   487
        | subst(f$t) = subst f $ subst t
clasohm@0
   488
  in subst end;
clasohm@0
   489
clasohm@0
   490
clasohm@0
   491
(*Computing the maximum index of a typ*)
paulson@2146
   492
fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts
clasohm@0
   493
  | maxidx_of_typ(TFree _) = ~1
paulson@2146
   494
  | maxidx_of_typ(TVar((_,i),_)) = i
paulson@2146
   495
and maxidx_of_typs [] = ~1
paulson@2146
   496
  | maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts);
clasohm@0
   497
clasohm@0
   498
clasohm@0
   499
(*Computing the maximum index of a term*)
clasohm@0
   500
fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T
clasohm@0
   501
  | maxidx_of_term (Bound _) = ~1
clasohm@0
   502
  | maxidx_of_term (Free(_,T)) = maxidx_of_typ T
paulson@2146
   503
  | maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T)
paulson@2146
   504
  | maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T)
paulson@2146
   505
  | maxidx_of_term (f$t) = Int.max(maxidx_of_term f,  maxidx_of_term t);
clasohm@0
   506
clasohm@0
   507
clasohm@0
   508
(* Increment the index of all Poly's in T by k *)
nipkow@949
   509
fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S));
clasohm@0
   510
clasohm@0
   511
clasohm@0
   512
(**** Syntax-related declarations ****)
clasohm@0
   513
clasohm@0
   514
clasohm@0
   515
(*Dummy type for parsing.  Will be replaced during type inference. *)
clasohm@0
   516
val dummyT = Type("dummy",[]);
clasohm@0
   517
clasohm@0
   518
(*scan a numeral of the given radix, normally 10*)
clasohm@0
   519
fun scan_radixint (radix: int, cs) : int * string list =
clasohm@0
   520
  let val zero = ord"0"
clasohm@0
   521
      val limit = zero+radix
clasohm@0
   522
      fun scan (num,[]) = (num,[])
clasohm@1460
   523
	| scan (num, c::cs) =
clasohm@1460
   524
	      if  zero <= ord c  andalso  ord c < limit
clasohm@1460
   525
	      then scan(radix*num + ord c - zero, cs)
clasohm@1460
   526
	      else (num, c::cs)
clasohm@0
   527
  in  scan(0,cs)  end;
clasohm@0
   528
clasohm@0
   529
fun scan_int cs = scan_radixint(10,cs);
clasohm@0
   530
clasohm@0
   531
clasohm@0
   532
(*** Printing ***)
clasohm@0
   533
clasohm@0
   534
clasohm@0
   535
(*Makes a variant of the name c distinct from the names in bs.
clasohm@0
   536
  First attaches the suffix "a" and then increments this. *)
clasohm@0
   537
fun variant bs c : string =
paulson@2138
   538
  let fun vary2 c = if (c mem_string bs) then  vary2 (bump_string c)  else  c
paulson@2138
   539
      fun vary1 c = if (c mem_string bs) then  vary2 (c ^ "a")  else  c
clasohm@0
   540
  in  vary1 (if c="" then "u" else c)  end;
clasohm@0
   541
clasohm@0
   542
(*Create variants of the list of names, with priority to the first ones*)
clasohm@0
   543
fun variantlist ([], used) = []
clasohm@0
   544
  | variantlist(b::bs, used) = 
clasohm@0
   545
      let val b' = variant used b
clasohm@0
   546
      in  b' :: variantlist (bs, b'::used)  end;
clasohm@0
   547
wenzelm@4017
   548
wenzelm@4017
   549
wenzelm@4017
   550
(** Consts etc. **)
wenzelm@4017
   551
wenzelm@4017
   552
fun add_typ_classes (Type (_, Ts), cs) = foldr add_typ_classes (Ts, cs)
wenzelm@4017
   553
  | add_typ_classes (TFree (_, S), cs) = S union cs
wenzelm@4017
   554
  | add_typ_classes (TVar (_, S), cs) = S union cs;
wenzelm@4017
   555
wenzelm@4017
   556
fun add_typ_tycons (Type (c, Ts), cs) = foldr add_typ_tycons (Ts, c ins cs)
wenzelm@4017
   557
  | add_typ_tycons (_, cs) = cs;
wenzelm@4017
   558
wenzelm@4017
   559
val add_term_classes = it_term_types add_typ_classes;
wenzelm@4017
   560
val add_term_tycons = it_term_types add_typ_tycons;
wenzelm@4017
   561
wenzelm@4017
   562
fun add_term_consts (Const (c, _), cs) = c ins cs
wenzelm@4017
   563
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
wenzelm@4017
   564
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
wenzelm@4017
   565
  | add_term_consts (_, cs) = cs;
wenzelm@4017
   566
oheimb@4185
   567
fun exists_Const P t = let
oheimb@4185
   568
	fun ex (Const c      ) = P c
oheimb@4185
   569
	|   ex (t $ u        ) = ex t orelse ex u
oheimb@4185
   570
	|   ex (Abs (_, _, t)) = ex t
oheimb@4185
   571
	|   ex _               = false
oheimb@4185
   572
    in ex t end;
wenzelm@4017
   573
wenzelm@4017
   574
(*map classes, tycons*)
wenzelm@4017
   575
fun map_typ f g (Type (c, Ts)) = Type (g c, map (map_typ f g) Ts)
wenzelm@4017
   576
  | map_typ f _ (TFree (x, S)) = TFree (x, map f S)
wenzelm@4017
   577
  | map_typ f _ (TVar (xi, S)) = TVar (xi, map f S);
wenzelm@4017
   578
wenzelm@4017
   579
(*map classes, tycons, consts*)
wenzelm@4017
   580
fun map_term f g h (Const (c, T)) = Const (h c, map_typ f g T)
wenzelm@4017
   581
  | map_term f g _ (Free (x, T)) = Free (x, map_typ f g T)
wenzelm@4017
   582
  | map_term f g _ (Var (xi, T)) = Var (xi, map_typ f g T)
wenzelm@4017
   583
  | map_term _ _ _ (t as Bound _) = t
wenzelm@4017
   584
  | map_term f g h (Abs (x, T, t)) = Abs (x, map_typ f g T, map_term f g h t)
wenzelm@4017
   585
  | map_term f g h (t $ u) = map_term f g h t $ map_term f g h u;
wenzelm@4017
   586
wenzelm@4017
   587
wenzelm@4017
   588
clasohm@0
   589
(** TFrees and TVars **)
clasohm@0
   590
clasohm@0
   591
(*maps  (bs,v)  to   v'::bs    this reverses the identifiers bs*)
clasohm@0
   592
fun add_new_id (bs, c) : string list =  variant bs c  ::  bs;
clasohm@0
   593
clasohm@0
   594
(*Accumulates the names in the term, suppressing duplicates.
clasohm@0
   595
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
paulson@2176
   596
fun add_term_names (Const(a,_), bs) = a ins_string bs
paulson@2176
   597
  | add_term_names (Free(a,_), bs) = a ins_string bs
clasohm@0
   598
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
clasohm@0
   599
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
clasohm@0
   600
  | add_term_names (_, bs) = bs;
clasohm@0
   601
clasohm@0
   602
(*Accumulates the TVars in a type, suppressing duplicates. *)
clasohm@0
   603
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars (Ts,vs)
clasohm@0
   604
  | add_typ_tvars(TFree(_),vs) = vs
clasohm@0
   605
  | add_typ_tvars(TVar(v),vs) = v ins vs;
clasohm@0
   606
clasohm@0
   607
(*Accumulates the TFrees in a type, suppressing duplicates. *)
clasohm@0
   608
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names (Ts,fs)
paulson@2176
   609
  | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
clasohm@0
   610
  | add_typ_tfree_names(TVar(_),fs) = fs;
clasohm@0
   611
clasohm@0
   612
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees (Ts,fs)
clasohm@0
   613
  | add_typ_tfrees(TFree(f),fs) = f ins fs
clasohm@0
   614
  | add_typ_tfrees(TVar(_),fs) = fs;
clasohm@0
   615
nipkow@949
   616
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames (Ts,nms)
paulson@2176
   617
  | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
paulson@2176
   618
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
nipkow@949
   619
clasohm@0
   620
(*Accumulates the TVars in a term, suppressing duplicates. *)
clasohm@0
   621
val add_term_tvars = it_term_types add_typ_tvars;
clasohm@0
   622
clasohm@0
   623
(*Accumulates the TFrees in a term, suppressing duplicates. *)
clasohm@0
   624
val add_term_tfrees = it_term_types add_typ_tfrees;
clasohm@0
   625
val add_term_tfree_names = it_term_types add_typ_tfree_names;
clasohm@0
   626
nipkow@949
   627
val add_term_tvarnames = it_term_types add_typ_varnames;
nipkow@949
   628
clasohm@0
   629
(*Non-list versions*)
clasohm@0
   630
fun typ_tfrees T = add_typ_tfrees(T,[]);
clasohm@0
   631
fun typ_tvars T = add_typ_tvars(T,[]);
clasohm@0
   632
fun term_tfrees t = add_term_tfrees(t,[]);
clasohm@0
   633
fun term_tvars t = add_term_tvars(t,[]);
clasohm@0
   634
nipkow@949
   635
(*special code to enforce left-to-right collection of TVar-indexnames*)
nipkow@949
   636
nipkow@949
   637
fun add_typ_ixns(ixns,Type(_,Ts)) = foldl add_typ_ixns (ixns,Ts)
paulson@2176
   638
  | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns 
paulson@2176
   639
				     else ixns@[ixn]
nipkow@949
   640
  | add_typ_ixns(ixns,TFree(_)) = ixns;
nipkow@949
   641
nipkow@949
   642
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   643
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   644
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
nipkow@949
   645
  | add_term_tvar_ixns(Bound _,ixns) = ixns
nipkow@949
   646
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
nipkow@949
   647
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
nipkow@949
   648
  | add_term_tvar_ixns(f$t,ixns) =
nipkow@949
   649
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
nipkow@949
   650
clasohm@0
   651
(** Frees and Vars **)
clasohm@0
   652
clasohm@0
   653
(*a partial ordering (not reflexive) for atomic terms*)
clasohm@0
   654
fun atless (Const (a,_), Const (b,_))  =  a<b
clasohm@0
   655
  | atless (Free (a,_), Free (b,_)) =  a<b
clasohm@0
   656
  | atless (Var(v,_), Var(w,_))  =  xless(v,w)
clasohm@0
   657
  | atless (Bound i, Bound j)  =   i<j
clasohm@0
   658
  | atless _  =  false;
clasohm@0
   659
clasohm@0
   660
(*insert atomic term into partially sorted list, suppressing duplicates (?)*)
clasohm@0
   661
fun insert_aterm (t,us) =
clasohm@0
   662
  let fun inserta [] = [t]
clasohm@0
   663
        | inserta (us as u::us') = 
clasohm@1460
   664
	      if atless(t,u) then t::us
clasohm@1460
   665
	      else if t=u then us (*duplicate*)
clasohm@1460
   666
	      else u :: inserta(us')
clasohm@0
   667
  in  inserta us  end;
clasohm@0
   668
clasohm@0
   669
(*Accumulates the Vars in the term, suppressing duplicates*)
clasohm@0
   670
fun add_term_vars (t, vars: term list) = case t of
clasohm@0
   671
    Var   _ => insert_aterm(t,vars)
clasohm@0
   672
  | Abs (_,_,body) => add_term_vars(body,vars)
clasohm@0
   673
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
clasohm@0
   674
  | _ => vars;
clasohm@0
   675
clasohm@0
   676
fun term_vars t = add_term_vars(t,[]);
clasohm@0
   677
clasohm@0
   678
(*Accumulates the Frees in the term, suppressing duplicates*)
clasohm@0
   679
fun add_term_frees (t, frees: term list) = case t of
clasohm@0
   680
    Free   _ => insert_aterm(t,frees)
clasohm@0
   681
  | Abs (_,_,body) => add_term_frees(body,frees)
clasohm@0
   682
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
clasohm@0
   683
  | _ => frees;
clasohm@0
   684
clasohm@0
   685
fun term_frees t = add_term_frees(t,[]);
clasohm@0
   686
clasohm@0
   687
(*Given an abstraction over P, replaces the bound variable by a Free variable
clasohm@0
   688
  having a unique name. *)
clasohm@0
   689
fun variant_abs (a,T,P) =
clasohm@0
   690
  let val b = variant (add_term_names(P,[])) a
paulson@2192
   691
  in  (b,  subst_bound (Free(b,T), P))  end;
clasohm@0
   692
clasohm@0
   693
(* renames and reverses the strings in vars away from names *)
clasohm@0
   694
fun rename_aTs names vars : (string*typ)list =
clasohm@0
   695
  let fun rename_aT (vars,(a,T)) =
clasohm@1460
   696
		(variant (map #1 vars @ names) a, T) :: vars
clasohm@0
   697
  in foldl rename_aT ([],vars) end;
clasohm@0
   698
clasohm@0
   699
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
clasohm@1364
   700
paulson@1417
   701
wenzelm@4286
   702
(* left-ro-right traversal *)
wenzelm@4286
   703
wenzelm@4286
   704
(*foldl atoms of type*)
wenzelm@4286
   705
fun foldl_atyps f (x, Type (_, Ts)) = foldl (foldl_atyps f) (x, Ts)
wenzelm@4286
   706
  | foldl_atyps f x_atom = f x_atom;
wenzelm@4286
   707
wenzelm@4286
   708
(*foldl atoms of term*)
wenzelm@4286
   709
fun foldl_aterms f (x, t $ u) = foldl_aterms f (foldl_aterms f (x, t), u)
wenzelm@4286
   710
  | foldl_aterms f (x, Abs (_, _, t)) = foldl_aterms f (x, t)
wenzelm@4286
   711
  | foldl_aterms f x_atom = f x_atom;
wenzelm@4286
   712
wenzelm@4286
   713
(*foldl types of term*)
wenzelm@4286
   714
fun foldl_types f (x, Const (_, T)) = f (x, T)
wenzelm@4286
   715
  | foldl_types f (x, Free (_, T)) = f (x, T)
wenzelm@4286
   716
  | foldl_types f (x, Var (_, T)) = f (x, T)
wenzelm@4286
   717
  | foldl_types f (x, Bound _) = x
wenzelm@4286
   718
  | foldl_types f (x, Abs (_, T, t)) = foldl_types f (f (x, T), t)
wenzelm@4286
   719
  | foldl_types f (x, t $ u) = foldl_types f (foldl_types f (x, t), u);
wenzelm@4286
   720
wenzelm@4286
   721
paulson@1417
   722
paulson@1426
   723
(*** Compression of terms and types by sharing common subtrees.  
paulson@1426
   724
     Saves 50-75% on storage requirements.  As it is fairly slow, 
paulson@1426
   725
     it is called only for axioms, stored theorems, etc. ***)
paulson@1417
   726
paulson@1417
   727
(** Sharing of types **)
paulson@1417
   728
paulson@1417
   729
fun atomic_tag (Type (a,_)) = if a<>"fun" then a else raise Match
paulson@1417
   730
  | atomic_tag (TFree (a,_)) = a
paulson@1417
   731
  | atomic_tag (TVar ((a,_),_)) = a;
paulson@1417
   732
paulson@1417
   733
fun type_tag (Type("fun",[S,T])) = atomic_tag S ^ type_tag T
paulson@1417
   734
  | type_tag T = atomic_tag T;
paulson@1417
   735
paulson@1417
   736
val memo_types = ref (Symtab.null : typ list Symtab.table);
paulson@1417
   737
oheimb@4188
   738
(* special case of library/find_first *)
paulson@1417
   739
fun find_type (T, []: typ list) = None
paulson@1417
   740
  | find_type (T, T'::Ts) =
paulson@1417
   741
       if T=T' then Some T'
paulson@1417
   742
       else find_type (T, Ts);
paulson@1417
   743
paulson@1417
   744
fun compress_type T =
paulson@1417
   745
  let val tag = type_tag T
paulson@1417
   746
      val tylist = the (Symtab.lookup (!memo_types, tag))
clasohm@1460
   747
	           handle _ => []
paulson@1417
   748
  in  
paulson@1417
   749
      case find_type (T,tylist) of
clasohm@1460
   750
	Some T' => T'
paulson@1417
   751
      | None => 
clasohm@1460
   752
	    let val T' =
clasohm@1460
   753
		case T of
clasohm@1460
   754
		    Type (a,Ts) => Type (a, map compress_type Ts)
clasohm@1460
   755
		  | _ => T
clasohm@1460
   756
	    in  memo_types := Symtab.update ((tag, T'::tylist), !memo_types);
clasohm@1460
   757
		T
clasohm@1460
   758
	    end
paulson@1417
   759
  end
paulson@1417
   760
  handle Match =>
paulson@1417
   761
      let val Type (a,Ts) = T
paulson@1417
   762
      in  Type (a, map compress_type Ts)  end;
paulson@1417
   763
paulson@1417
   764
(** Sharing of atomic terms **)
paulson@1417
   765
paulson@1417
   766
val memo_terms = ref (Symtab.null : term list Symtab.table);
paulson@1417
   767
oheimb@4188
   768
(* special case of library/find_first *)
paulson@1417
   769
fun find_term (t, []: term list) = None
paulson@1417
   770
  | find_term (t, t'::ts) =
paulson@1417
   771
       if t=t' then Some t'
paulson@1417
   772
       else find_term (t, ts);
paulson@1417
   773
paulson@1417
   774
fun const_tag (Const (a,_)) = a
paulson@1417
   775
  | const_tag (Free (a,_))  = a
paulson@1417
   776
  | const_tag (Var ((a,i),_)) = a
paulson@1417
   777
  | const_tag (t as Bound _)  = ".B.";
paulson@1417
   778
paulson@1417
   779
fun share_term (t $ u) = share_term t $ share_term u
paulson@1417
   780
  | share_term (Abs (a,T,u)) = Abs (a, T, share_term u)
paulson@1417
   781
  | share_term t =
paulson@1417
   782
      let val tag = const_tag t
clasohm@1460
   783
	  val ts = the (Symtab.lookup (!memo_terms, tag))
clasohm@1460
   784
	               handle _ => []
paulson@1417
   785
      in 
clasohm@1460
   786
	  case find_term (t,ts) of
clasohm@1460
   787
	      Some t' => t'
clasohm@1460
   788
	    | None => (memo_terms := Symtab.update ((tag, t::ts), !memo_terms);
clasohm@1460
   789
		       t)
paulson@1417
   790
      end;
paulson@1417
   791
paulson@1417
   792
val compress_term = share_term o map_term_types compress_type;
paulson@1417
   793
clasohm@1364
   794
end;
clasohm@1364
   795
clasohm@1364
   796
open Term;