src/Pure/term.ML
author wenzelm
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permissions -rw-r--r--
add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons, add_term_consts, map_typ, map_term: moved from sign.ML to term.ML;
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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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(* 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$u;
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(** Equality, membership and insertion of indexnames (string*ints) **)
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(*optimized equality test for indexnames.  Yields a huge gain under Poly/ML*)
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fun eq_ix ((a, i):indexname, (a',i'):indexname) = (a=a') andalso i=i';
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(*membership in a list, optimized version for indexnames*)
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fun mem_ix (_, []) = false
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  | mem_ix (x, y :: ys) = eq_ix(x,y) orelse mem_ix (x, ys);
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(*insertion into list, optimized version for indexnames*)
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fun ins_ix (x,xs) = if mem_ix (x, xs) then xs else x :: xs;
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(*Tests whether 2 terms are alpha-convertible and have same type.
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  Note that constants and Vars may have more than one type.*)
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fun (Const(a,T)) aconv (Const(b,U)) = a=b  andalso  T=U
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  | (Free(a,T))  aconv (Free(b,U))  = a=b  andalso  T=U
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  | (Var(v,T))   aconv (Var(w,U))   = eq_ix(v,w)  andalso  T=U
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  | (Bound i)    aconv (Bound j)    = i=j
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  | (Abs(_,T,t)) aconv (Abs(_,U,u)) = t aconv u  andalso  T=U
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  | (f$t)        aconv (g$u)        = (f aconv g) andalso (t aconv u)
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  | _ aconv _  =  false;
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(** Membership, insertion, union for terms **)
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   343
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fun mem_term (_, []) = false
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   345
  | mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts);
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   346
2182
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   347
fun subset_term ([], ys) = true
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   348
  | subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys);
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   349
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   350
fun eq_set_term (xs, ys) =
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   351
    xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs));
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   352
2176
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   353
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts;
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   354
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   355
fun union_term (xs, []) = xs
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   356
  | union_term ([], ys) = ys
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   357
  | union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys));
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   358
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   359
(** Equality, membership and insertion of sorts (string lists) **)
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   360
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   361
fun eq_sort ([]:sort, []) = true
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   362
  | eq_sort ((s::ss), (t::ts)) = s=t andalso eq_sort(ss,ts)
43e5c20a593c Changed some mem and ins calls to be monomorphic
paulson
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   363
  | eq_sort (_, _) = false;
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paulson
parents: 2146
diff changeset
   364
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paulson
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   365
fun mem_sort (_:sort, []) = false
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   366
  | mem_sort (S, S'::Ss) = eq_sort (S, S') orelse mem_sort(S,Ss);
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   367
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   368
fun ins_sort(S,Ss) = if mem_sort(S,Ss) then Ss else S :: Ss;
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paulson
parents: 2146
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   369
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paulson
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   370
fun union_sort (xs, []) = xs
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   371
  | union_sort ([], ys) = ys
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parents: 2146
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   372
  | union_sort ((x :: xs), ys) = union_sort (xs, ins_sort (x, ys));
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   373
2182
29e56f003599 Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
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   374
fun subset_sort ([], ys) = true
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paulson
parents: 2176
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   375
  | subset_sort (x :: xs, ys) = mem_sort (x, ys) andalso subset_sort(xs, ys);
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parents: 2176
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   376
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   377
fun eq_set_sort (xs, ys) =
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paulson
parents: 2176
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   378
    xs = ys orelse (subset_sort (xs, ys) andalso subset_sort (ys, xs));
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paulson
parents: 2176
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   379
0
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clasohm
parents:
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   380
(*are two term lists alpha-convertible in corresponding elements?*)
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clasohm
parents:
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   381
fun aconvs ([],[]) = true
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clasohm
parents:
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   382
  | aconvs (t::ts, u::us) = t aconv u andalso aconvs(ts,us)
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clasohm
parents:
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   383
  | aconvs _ = false;
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clasohm
parents:
diff changeset
   384
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clasohm
parents:
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   385
(*A fast unification filter: true unless the two terms cannot be unified. 
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clasohm
parents:
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   386
  Terms must be NORMAL.  Treats all Vars as distinct. *)
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clasohm
parents:
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   387
fun could_unify (t,u) =
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clasohm
parents:
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   388
  let fun matchrands (f$t, g$u) = could_unify(t,u) andalso  matchrands(f,g)
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parents: 1458
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   389
	| matchrands _ = true
0
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clasohm
parents:
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   390
  in case (head_of t , head_of u) of
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   391
	(_, Var _) => true
0
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clasohm
parents:
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   392
      | (Var _, _) => true
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clasohm
parents:
diff changeset
   393
      | (Const(a,_), Const(b,_)) =>  a=b andalso matchrands(t,u)
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clasohm
parents:
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   394
      | (Free(a,_), Free(b,_)) =>  a=b andalso matchrands(t,u)
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clasohm
parents:
diff changeset
   395
      | (Bound i, Bound j) =>  i=j andalso matchrands(t,u)
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clasohm
parents:
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   396
      | (Abs _, _) =>  true   (*because of possible eta equality*)
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clasohm
parents:
diff changeset
   397
      | (_, Abs _) =>  true
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clasohm
parents:
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   398
      | _ => false
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clasohm
parents:
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   399
  end;
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clasohm
parents:
diff changeset
   400
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clasohm
parents:
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   401
(*Substitute new for free occurrences of old in a term*)
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clasohm
parents:
diff changeset
   402
fun subst_free [] = (fn t=>t)
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clasohm
parents:
diff changeset
   403
  | subst_free pairs =
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clasohm
parents:
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   404
      let fun substf u = 
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clasohm
parents: 1458
diff changeset
   405
	    case gen_assoc (op aconv) (pairs, u) of
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clasohm
parents: 1458
diff changeset
   406
		Some u' => u'
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clasohm
parents: 1458
diff changeset
   407
	      | None => (case u of Abs(a,T,t) => Abs(a, T, substf t)
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clasohm
parents: 1458
diff changeset
   408
				 | t$u' => substf t $ substf u'
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clasohm
parents: 1458
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   409
				 | _ => u)
0
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clasohm
parents:
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   410
      in  substf  end;
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clasohm
parents:
diff changeset
   411
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clasohm
parents:
diff changeset
   412
(*a total, irreflexive ordering on index names*)
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clasohm
parents:
diff changeset
   413
fun xless ((a,i), (b,j): indexname) = i<j  orelse  (i=j andalso a<b);
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clasohm
parents:
diff changeset
   414
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clasohm
parents:
diff changeset
   415
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clasohm
parents:
diff changeset
   416
(*Abstraction of the term "body" over its occurrences of v, 
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clasohm
parents:
diff changeset
   417
    which must contain no loose bound variables.
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clasohm
parents:
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   418
  The resulting term is ready to become the body of an Abs.*)
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clasohm
parents:
diff changeset
   419
fun abstract_over (v,body) =
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clasohm
parents:
diff changeset
   420
  let fun abst (lev,u) = if (v aconv u) then (Bound lev) else
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clasohm
parents:
diff changeset
   421
      (case u of
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clasohm
parents:
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   422
          Abs(a,T,t) => Abs(a, T, abst(lev+1, t))
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clasohm
parents: 1458
diff changeset
   423
	| f$rand => abst(lev,f) $ abst(lev,rand)
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clasohm
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   424
	| _ => u)
0
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clasohm
parents:
diff changeset
   425
  in  abst(0,body)  end;
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clasohm
parents:
diff changeset
   426
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clasohm
parents:
diff changeset
   427
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clasohm
parents:
diff changeset
   428
(*Form an abstraction over a free variable.*)
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clasohm
parents:
diff changeset
   429
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body));
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clasohm
parents:
diff changeset
   430
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clasohm
parents:
diff changeset
   431
(*Abstraction over a list of free variables*)
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clasohm
parents:
diff changeset
   432
fun list_abs_free ([ ] ,     t) = t
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clasohm
parents:
diff changeset
   433
  | list_abs_free ((a,T)::vars, t) = 
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clasohm
parents:
diff changeset
   434
      absfree(a, T, list_abs_free(vars,t));
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clasohm
parents:
diff changeset
   435
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clasohm
parents:
diff changeset
   436
(*Quantification over a list of free variables*)
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clasohm
parents:
diff changeset
   437
fun list_all_free ([], t: term) = t
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clasohm
parents:
diff changeset
   438
  | list_all_free ((a,T)::vars, t) = 
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clasohm
parents:
diff changeset
   439
        (all T) $ (absfree(a, T, list_all_free(vars,t)));
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clasohm
parents:
diff changeset
   440
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clasohm
parents:
diff changeset
   441
(*Quantification over a list of variables (already bound in body) *)
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clasohm
parents:
diff changeset
   442
fun list_all ([], t) = t
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clasohm
parents:
diff changeset
   443
  | list_all ((a,T)::vars, t) = 
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clasohm
parents:
diff changeset
   444
        (all T) $ (Abs(a, T, list_all(vars,t)));
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clasohm
parents:
diff changeset
   445
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clasohm
parents:
diff changeset
   446
(*Replace the ATOMIC term ti by ui;    instl = [(t1,u1), ..., (tn,un)]. 
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clasohm
parents:
diff changeset
   447
  A simultaneous substitution:  [ (a,b), (b,a) ] swaps a and b.  *)
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clasohm
parents:
diff changeset
   448
fun subst_atomic [] t = t : term
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clasohm
parents:
diff changeset
   449
  | subst_atomic (instl: (term*term) list) t =
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clasohm
parents:
diff changeset
   450
      let fun subst (Abs(a,T,body)) = Abs(a, T, subst body)
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clasohm
parents: 1458
diff changeset
   451
	    | subst (f$t') = subst f $ subst t'
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clasohm
parents: 1458
diff changeset
   452
	    | subst t = (case assoc(instl,t) of
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clasohm
parents: 1458
diff changeset
   453
		           Some u => u  |  None => t)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   454
      in  subst t  end;
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clasohm
parents:
diff changeset
   455
728
9a973c3ba350 Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents: 375
diff changeset
   456
(*Substitute for type Vars in a type*)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   457
fun typ_subst_TVars iTs T = if null iTs then T else
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clasohm
parents:
diff changeset
   458
  let fun subst(Type(a,Ts)) = Type(a, map subst Ts)
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clasohm
parents: 1458
diff changeset
   459
	| subst(T as TFree _) = T
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clasohm
parents: 1458
diff changeset
   460
	| subst(T as TVar(ixn,_)) =
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   461
            (case assoc(iTs,ixn) of None => T | Some(U) => U)
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clasohm
parents:
diff changeset
   462
  in subst T end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   463
728
9a973c3ba350 Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents: 375
diff changeset
   464
(*Substitute for type Vars in a term*)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   465
val subst_TVars = map_term_types o typ_subst_TVars;
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clasohm
parents:
diff changeset
   466
728
9a973c3ba350 Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents: 375
diff changeset
   467
(*Substitute for Vars in a term; see also envir/norm_term*)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   468
fun subst_Vars itms t = if null itms then t else
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clasohm
parents:
diff changeset
   469
  let fun subst(v as Var(ixn,_)) =
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clasohm
parents:
diff changeset
   470
            (case assoc(itms,ixn) of None => v | Some t => t)
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clasohm
parents:
diff changeset
   471
        | subst(Abs(a,T,t)) = Abs(a,T,subst t)
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clasohm
parents:
diff changeset
   472
        | subst(f$t) = subst f $ subst t
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   473
        | subst(t) = t
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clasohm
parents:
diff changeset
   474
  in subst t end;
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clasohm
parents:
diff changeset
   475
728
9a973c3ba350 Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents: 375
diff changeset
   476
(*Substitute for type/term Vars in a term; see also envir/norm_term*)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   477
fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else
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clasohm
parents:
diff changeset
   478
  let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T)
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clasohm
parents:
diff changeset
   479
        | subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   480
        | subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of
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clasohm
parents:
diff changeset
   481
            None   => Var(ixn,typ_subst_TVars iTs T)
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clasohm
parents:
diff changeset
   482
          | Some t => t)
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clasohm
parents:
diff changeset
   483
        | subst(b as Bound _) = b
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   484
        | subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   485
        | subst(f$t) = subst f $ subst t
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   486
  in subst end;
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clasohm
parents:
diff changeset
   487
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   488
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   489
(*Computing the maximum index of a typ*)
2146
6854b692f1fe maxidx_of_typs replaces max o map maxidx_of_typ
paulson
parents: 2138
diff changeset
   490
fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   491
  | maxidx_of_typ(TFree _) = ~1
2146
6854b692f1fe maxidx_of_typs replaces max o map maxidx_of_typ
paulson
parents: 2138
diff changeset
   492
  | maxidx_of_typ(TVar((_,i),_)) = i
6854b692f1fe maxidx_of_typs replaces max o map maxidx_of_typ
paulson
parents: 2138
diff changeset
   493
and maxidx_of_typs [] = ~1
6854b692f1fe maxidx_of_typs replaces max o map maxidx_of_typ
paulson
parents: 2138
diff changeset
   494
  | maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts);
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   495
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   496
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   497
(*Computing the maximum index of a term*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   498
fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T
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clasohm
parents:
diff changeset
   499
  | maxidx_of_term (Bound _) = ~1
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clasohm
parents:
diff changeset
   500
  | maxidx_of_term (Free(_,T)) = maxidx_of_typ T
2146
6854b692f1fe maxidx_of_typs replaces max o map maxidx_of_typ
paulson
parents: 2138
diff changeset
   501
  | maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T)
6854b692f1fe maxidx_of_typs replaces max o map maxidx_of_typ
paulson
parents: 2138
diff changeset
   502
  | maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T)
6854b692f1fe maxidx_of_typs replaces max o map maxidx_of_typ
paulson
parents: 2138
diff changeset
   503
  | maxidx_of_term (f$t) = Int.max(maxidx_of_term f,  maxidx_of_term t);
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   504
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   505
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   506
(* Increment the index of all Poly's in T by k *)
949
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   507
fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S));
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   508
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   509
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   510
(**** Syntax-related declarations ****)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   511
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   512
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   513
(*Dummy type for parsing.  Will be replaced during type inference. *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   514
val dummyT = Type("dummy",[]);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   515
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   516
(*scan a numeral of the given radix, normally 10*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   517
fun scan_radixint (radix: int, cs) : int * string list =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   518
  let val zero = ord"0"
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   519
      val limit = zero+radix
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   520
      fun scan (num,[]) = (num,[])
1460
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   521
	| scan (num, c::cs) =
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   522
	      if  zero <= ord c  andalso  ord c < limit
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   523
	      then scan(radix*num + ord c - zero, cs)
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   524
	      else (num, c::cs)
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   525
  in  scan(0,cs)  end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   526
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   527
fun scan_int cs = scan_radixint(10,cs);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   528
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   529
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   530
(*** Printing ***)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   531
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   532
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   533
(*Makes a variant of the name c distinct from the names in bs.
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   534
  First attaches the suffix "a" and then increments this. *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   535
fun variant bs c : string =
2138
056dead45ae8 Changed some mem calls to mem_string for greater efficiency (not that it could matter)
paulson
parents: 1460
diff changeset
   536
  let fun vary2 c = if (c mem_string bs) then  vary2 (bump_string c)  else  c
056dead45ae8 Changed some mem calls to mem_string for greater efficiency (not that it could matter)
paulson
parents: 1460
diff changeset
   537
      fun vary1 c = if (c mem_string bs) then  vary2 (c ^ "a")  else  c
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   538
  in  vary1 (if c="" then "u" else c)  end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   539
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   540
(*Create variants of the list of names, with priority to the first ones*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   541
fun variantlist ([], used) = []
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   542
  | variantlist(b::bs, used) = 
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   543
      let val b' = variant used b
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   544
      in  b' :: variantlist (bs, b'::used)  end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   545
4017
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   546
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   547
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   548
(** Consts etc. **)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   549
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   550
fun add_typ_classes (Type (_, Ts), cs) = foldr add_typ_classes (Ts, cs)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   551
  | add_typ_classes (TFree (_, S), cs) = S union cs
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   552
  | add_typ_classes (TVar (_, S), cs) = S union cs;
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   553
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   554
fun add_typ_tycons (Type (c, Ts), cs) = foldr add_typ_tycons (Ts, c ins cs)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   555
  | add_typ_tycons (_, cs) = cs;
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   556
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   557
val add_term_classes = it_term_types add_typ_classes;
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   558
val add_term_tycons = it_term_types add_typ_tycons;
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   559
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   560
fun add_term_consts (Const (c, _), cs) = c ins cs
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   561
  | add_term_consts (t $ u, cs) = add_term_consts (t, add_term_consts (u, cs))
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   562
  | add_term_consts (Abs (_, _, t), cs) = add_term_consts (t, cs)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   563
  | add_term_consts (_, cs) = cs;
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   564
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   565
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   566
(*map classes, tycons*)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   567
fun map_typ f g (Type (c, Ts)) = Type (g c, map (map_typ f g) Ts)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   568
  | map_typ f _ (TFree (x, S)) = TFree (x, map f S)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   569
  | map_typ f _ (TVar (xi, S)) = TVar (xi, map f S);
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   570
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   571
(*map classes, tycons, consts*)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   572
fun map_term f g h (Const (c, T)) = Const (h c, map_typ f g T)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   573
  | map_term f g _ (Free (x, T)) = Free (x, map_typ f g T)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   574
  | map_term f g _ (Var (xi, T)) = Var (xi, map_typ f g T)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   575
  | map_term _ _ _ (t as Bound _) = t
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   576
  | map_term f g h (Abs (x, T, t)) = Abs (x, map_typ f g T, map_term f g h t)
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   577
  | map_term f g h (t $ u) = map_term f g h t $ map_term f g h u;
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   578
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   579
63878e2587a7 add_typ_classes, add_typ_tycons, add_term_classes, add_term_tycons,
wenzelm
parents: 3965
diff changeset
   580
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   581
(** TFrees and TVars **)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   582
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   583
(*maps  (bs,v)  to   v'::bs    this reverses the identifiers bs*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   584
fun add_new_id (bs, c) : string list =  variant bs c  ::  bs;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   585
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   586
(*Accumulates the names in the term, suppressing duplicates.
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   587
  Includes Frees and Consts.  For choosing unambiguous bound var names.*)
2176
43e5c20a593c Changed some mem and ins calls to be monomorphic
paulson
parents: 2146
diff changeset
   588
fun add_term_names (Const(a,_), bs) = a ins_string bs
43e5c20a593c Changed some mem and ins calls to be monomorphic
paulson
parents: 2146
diff changeset
   589
  | add_term_names (Free(a,_), bs) = a ins_string bs
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   590
  | add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs))
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   591
  | add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   592
  | add_term_names (_, bs) = bs;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   593
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   594
(*Accumulates the TVars in a type, suppressing duplicates. *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   595
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars (Ts,vs)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   596
  | add_typ_tvars(TFree(_),vs) = vs
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   597
  | add_typ_tvars(TVar(v),vs) = v ins vs;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   598
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   599
(*Accumulates the TFrees in a type, suppressing duplicates. *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   600
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names (Ts,fs)
2176
43e5c20a593c Changed some mem and ins calls to be monomorphic
paulson
parents: 2146
diff changeset
   601
  | add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   602
  | add_typ_tfree_names(TVar(_),fs) = fs;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   603
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   604
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees (Ts,fs)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   605
  | add_typ_tfrees(TFree(f),fs) = f ins fs
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   606
  | add_typ_tfrees(TVar(_),fs) = fs;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   607
949
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   608
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames (Ts,nms)
2176
43e5c20a593c Changed some mem and ins calls to be monomorphic
paulson
parents: 2146
diff changeset
   609
  | add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms
43e5c20a593c Changed some mem and ins calls to be monomorphic
paulson
parents: 2146
diff changeset
   610
  | add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms;
949
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   611
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   612
(*Accumulates the TVars in a term, suppressing duplicates. *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   613
val add_term_tvars = it_term_types add_typ_tvars;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   614
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   615
(*Accumulates the TFrees in a term, suppressing duplicates. *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   616
val add_term_tfrees = it_term_types add_typ_tfrees;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   617
val add_term_tfree_names = it_term_types add_typ_tfree_names;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   618
949
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   619
val add_term_tvarnames = it_term_types add_typ_varnames;
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   620
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   621
(*Non-list versions*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   622
fun typ_tfrees T = add_typ_tfrees(T,[]);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   623
fun typ_tvars T = add_typ_tvars(T,[]);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   624
fun term_tfrees t = add_term_tfrees(t,[]);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   625
fun term_tvars t = add_term_tvars(t,[]);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   626
949
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   627
(*special code to enforce left-to-right collection of TVar-indexnames*)
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   628
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   629
fun add_typ_ixns(ixns,Type(_,Ts)) = foldl add_typ_ixns (ixns,Ts)
2176
43e5c20a593c Changed some mem and ins calls to be monomorphic
paulson
parents: 2146
diff changeset
   630
  | add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns 
43e5c20a593c Changed some mem and ins calls to be monomorphic
paulson
parents: 2146
diff changeset
   631
				     else ixns@[ixn]
949
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   632
  | add_typ_ixns(ixns,TFree(_)) = ixns;
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   633
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   634
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T)
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   635
  | add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T)
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   636
  | add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T)
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   637
  | add_term_tvar_ixns(Bound _,ixns) = ixns
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   638
  | add_term_tvar_ixns(Abs(_,T,t),ixns) =
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   639
      add_term_tvar_ixns(t,add_typ_ixns(ixns,T))
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   640
  | add_term_tvar_ixns(f$t,ixns) =
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   641
      add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns));
83c588d6fee9 Changed treatment of during type inference internally generated type
nipkow
parents: 728
diff changeset
   642
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   643
(** Frees and Vars **)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   644
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   645
(*a partial ordering (not reflexive) for atomic terms*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   646
fun atless (Const (a,_), Const (b,_))  =  a<b
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   647
  | atless (Free (a,_), Free (b,_)) =  a<b
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   648
  | atless (Var(v,_), Var(w,_))  =  xless(v,w)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   649
  | atless (Bound i, Bound j)  =   i<j
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   650
  | atless _  =  false;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   651
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   652
(*insert atomic term into partially sorted list, suppressing duplicates (?)*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   653
fun insert_aterm (t,us) =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   654
  let fun inserta [] = [t]
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   655
        | inserta (us as u::us') = 
1460
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   656
	      if atless(t,u) then t::us
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   657
	      else if t=u then us (*duplicate*)
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   658
	      else u :: inserta(us')
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   659
  in  inserta us  end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   660
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   661
(*Accumulates the Vars in the term, suppressing duplicates*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   662
fun add_term_vars (t, vars: term list) = case t of
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   663
    Var   _ => insert_aterm(t,vars)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   664
  | Abs (_,_,body) => add_term_vars(body,vars)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   665
  | f$t =>  add_term_vars (f, add_term_vars(t, vars))
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   666
  | _ => vars;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   667
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   668
fun term_vars t = add_term_vars(t,[]);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   669
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   670
(*Accumulates the Frees in the term, suppressing duplicates*)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   671
fun add_term_frees (t, frees: term list) = case t of
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   672
    Free   _ => insert_aterm(t,frees)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   673
  | Abs (_,_,body) => add_term_frees(body,frees)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   674
  | f$t =>  add_term_frees (f, add_term_frees(t, frees))
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   675
  | _ => frees;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   676
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   677
fun term_frees t = add_term_frees(t,[]);
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   678
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   679
(*Given an abstraction over P, replaces the bound variable by a Free variable
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   680
  having a unique name. *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   681
fun variant_abs (a,T,P) =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   682
  let val b = variant (add_term_names(P,[])) a
2192
3bf092b5310b Optimizations: removal of polymorphic equality; one-argument case
paulson
parents: 2182
diff changeset
   683
  in  (b,  subst_bound (Free(b,T), P))  end;
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   684
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   685
(* renames and reverses the strings in vars away from names *)
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   686
fun rename_aTs names vars : (string*typ)list =
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   687
  let fun rename_aT (vars,(a,T)) =
1460
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   688
		(variant (map #1 vars @ names) a, T) :: vars
0
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   689
  in foldl rename_aT ([],vars) end;
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   690
a5a9c433f639 Initial revision
clasohm
parents:
diff changeset
   691
fun rename_wrt_term t = rename_aTs (add_term_names(t,[]));
1364
8ea1a962ad72 files now define a structure to allow SML/NJ to optimize the code
clasohm
parents: 1029
diff changeset
   692
1417
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   693
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   694
1426
c60e9e1a1a23 Updated comments for compression functions
paulson
parents: 1417
diff changeset
   695
(*** Compression of terms and types by sharing common subtrees.  
c60e9e1a1a23 Updated comments for compression functions
paulson
parents: 1417
diff changeset
   696
     Saves 50-75% on storage requirements.  As it is fairly slow, 
c60e9e1a1a23 Updated comments for compression functions
paulson
parents: 1417
diff changeset
   697
     it is called only for axioms, stored theorems, etc. ***)
1417
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   698
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   699
(** Sharing of types **)
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   700
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   701
fun atomic_tag (Type (a,_)) = if a<>"fun" then a else raise Match
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   702
  | atomic_tag (TFree (a,_)) = a
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   703
  | atomic_tag (TVar ((a,_),_)) = a;
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   704
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   705
fun type_tag (Type("fun",[S,T])) = atomic_tag S ^ type_tag T
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   706
  | type_tag T = atomic_tag T;
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   707
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   708
val memo_types = ref (Symtab.null : typ list Symtab.table);
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   709
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   710
fun find_type (T, []: typ list) = None
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   711
  | find_type (T, T'::Ts) =
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   712
       if T=T' then Some T'
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   713
       else find_type (T, Ts);
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   714
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   715
fun compress_type T =
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   716
  let val tag = type_tag T
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   717
      val tylist = the (Symtab.lookup (!memo_types, tag))
1460
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   718
	           handle _ => []
1417
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   719
  in  
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   720
      case find_type (T,tylist) of
1460
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   721
	Some T' => T'
1417
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   722
      | None => 
1460
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   723
	    let val T' =
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   724
		case T of
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   725
		    Type (a,Ts) => Type (a, map compress_type Ts)
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   726
		  | _ => T
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   727
	    in  memo_types := Symtab.update ((tag, T'::tylist), !memo_types);
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   728
		T
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   729
	    end
1417
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   730
  end
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   731
  handle Match =>
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   732
      let val Type (a,Ts) = T
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   733
      in  Type (a, map compress_type Ts)  end;
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   734
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   735
(** Sharing of atomic terms **)
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   736
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   737
val memo_terms = ref (Symtab.null : term list Symtab.table);
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   738
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   739
fun find_term (t, []: term list) = None
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   740
  | find_term (t, t'::ts) =
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   741
       if t=t' then Some t'
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   742
       else find_term (t, ts);
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   743
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   744
fun const_tag (Const (a,_)) = a
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   745
  | const_tag (Free (a,_))  = a
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   746
  | const_tag (Var ((a,i),_)) = a
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   747
  | const_tag (t as Bound _)  = ".B.";
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   748
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   749
fun share_term (t $ u) = share_term t $ share_term u
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   750
  | share_term (Abs (a,T,u)) = Abs (a, T, share_term u)
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   751
  | share_term t =
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   752
      let val tag = const_tag t
1460
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   753
	  val ts = the (Symtab.lookup (!memo_terms, tag))
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   754
	               handle _ => []
1417
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   755
      in 
1460
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   756
	  case find_term (t,ts) of
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   757
	      Some t' => t'
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   758
	    | None => (memo_terms := Symtab.update ((tag, t::ts), !memo_terms);
5a6f2aabd538 inserted tabs again
clasohm
parents: 1458
diff changeset
   759
		       t)
1417
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   760
      end;
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   761
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   762
val compress_term = share_term o map_term_types compress_type;
c0f6a1887518 Addition of compression, that is, sharing.
paulson
parents: 1391
diff changeset
   763
1364
8ea1a962ad72 files now define a structure to allow SML/NJ to optimize the code
clasohm
parents: 1029
diff changeset
   764
end;
8ea1a962ad72 files now define a structure to allow SML/NJ to optimize the code
clasohm
parents: 1029
diff changeset
   765
8ea1a962ad72 files now define a structure to allow SML/NJ to optimize the code
clasohm
parents: 1029
diff changeset
   766
open Term;