src/Pure/envir.ML

MAJOR INTERNAL CHANGE: extend and merge operations of syntax tables
now much leaner (eliminated gramgraph, all data except tables of old
parser are shared); simplified the internal interfaces for syntax
extension;

(*  Title: 	envir
    ID:         $Id$
    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1988  University of Cambridge
*)

(*Environments
  Should take account that typ is part of variable name,
    otherwise two variables with same name and different types
    will cause errors!
*)


signature ENVIR = 
sig
  type 'a xolist
  exception ENVIR of string * indexname;
  datatype env = Envir of {asol: term xolist,
			   iTs: (indexname * typ) list,
			   maxidx: int}
  val alist_of : env -> (indexname * term) list
  val alist_of_olist : 'a xolist -> (indexname * 'a) list
  val empty : int->env
  val genvar  : string -> env * typ -> env * term
  val genvars : string -> env * typ list -> env * term list
  val lookup : env * indexname -> term option
  val norm_term : env -> term -> term
  val null_olist : 'a xolist
  val olist_of_alist: (indexname * 'a) list -> 'a xolist
  val update : (indexname * term) * env -> env
  val vupdate : (indexname * term) * env -> env
end;

functor EnvirFun () : ENVIR = 
struct


(*association lists with keys in ascending order, no repeated keys*)
datatype 'a xolist = Olist of (indexname * 'a) list;


exception ENVIR of string * indexname;
 
(*look up key in ordered list*)  
fun xsearch (Olist[], key) = None
  | xsearch (Olist ((keyi,xi)::pairs), key) =
      if xless(keyi,key) then xsearch (Olist pairs, key)
      else if key=keyi then Some xi  
      else None;

(*insert pair in ordered list, reject if key already present*)
fun xinsert_new (newpr as (key, x), Olist al) =
  let fun insert [] = [newpr]
	| insert ((pair as (keyi,xi)) :: pairs) =
	    if xless(keyi,key) then pair :: insert pairs
	    else if key=keyi then
		raise ENVIR("xinsert_new: already present",key)
	    else newpr::pair::pairs
  in  Olist (insert al)  end;

(*insert pair in ordered list, overwrite if key already present*)
fun xinsert (newpr as (key, x), Olist al) =
  let fun insert [] = [newpr]
	| insert ((pair as (keyi,xi)) :: pairs) =
	    if xless(keyi,key) then pair :: insert pairs
	    else if key=keyi then newpr::pairs
	    else newpr::pair::pairs
  in  Olist (insert al)  end;

(*apply function to the contents part of each pair*)   
fun xmap f (Olist pairs) =
  let fun xmp [] = []
	| xmp ((key,x)::pairs) = (key, f x) :: xmp pairs
  in Olist (xmp pairs)  end;

(*allows redefinition of a key by "join"ing the contents parts*)
fun xmerge_olists join (Olist pairsa, Olist pairsb) =
  let fun xmrg ([],pairsb) = pairsb
	| xmrg (pairsa,[]) = pairsa
	| xmrg ((keya,x)::pairsa, (keyb,y)::pairsb) =
	    if xless(keya,keyb) then 
		(keya,x) :: xmrg (pairsa, (keyb,y)::pairsb)
	    else if xless(keyb,keya) then
		(keyb,y) :: xmrg ((keya,x)::pairsa, pairsb)
	    else (*equal*)  (keya, join(x,y)) :: xmrg (pairsa, pairsb)
  in  Olist (xmrg (pairsa,pairsb))  end;

val null_olist = Olist[];

fun alist_of_olist (Olist pairs) = pairs;

fun olist_of_alist pairs = foldr xinsert (pairs, Olist[]);



(*updating can destroy environment in 2 ways!!
   (1) variables out of range   (2) circular assignments
*)
datatype env = Envir of
    {maxidx: int, 		(*maximum index of vars*)
     asol: term xolist,  	(*table of assignments to Vars*)
     iTs: (indexname*typ)list}	(*table of assignments to TVars*)


(*Generate a list of distinct variables.
  Increments index to make them distinct from ALL present variables. *)
fun genvars name (Envir{maxidx, asol, iTs}, Ts) : env * term list =
  let fun genvs (_, [] : typ list) : term list = []
        | genvs (n, [T]) = [ Var((name, maxidx+1), T) ]
        | genvs (n, T::Ts) =
            Var((name ^ radixstring(26,"a",n), maxidx+1), T) 
            :: genvs(n+1,Ts) 
  in  (Envir{maxidx=maxidx+1, asol=asol, iTs=iTs}, genvs (0,Ts))  end;

(*Generate a variable.*)
fun genvar name (env,T) : env * term =
  let val (env',[v]) = genvars name (env,[T])  
  in  (env',v)  end;

fun lookup (Envir{asol,...}, xname) : term option = xsearch (asol,xname);

fun update ((xname, t), Envir{maxidx, asol, iTs}) =
  Envir{maxidx=maxidx, asol=xinsert_new ((xname,t), asol), iTs=iTs};

(*The empty environment.  New variables will start with the given index.*)
fun empty m = Envir{maxidx=m, asol=null_olist, iTs=[]};

(*Update, checking Var-Var assignments: try to suppress higher indexes*)
fun vupdate((a,t), env) = case t of
      Var(name',T) =>
	if a=name' then env	(*cycle!*)
	else if xless(a, name')  then  
	   (case lookup(env,name') of  (*if already assigned, chase*)
		None => update((name', Var(a,T)), env)
	      | Some u => vupdate((a,u), env))
	else update((a,t), env)
    | _ => update((a,t), env);


(*Convert environment to alist*)
fun alist_of (Envir{maxidx,asol,...}) = alist_of_olist asol;


(*Beta normal form for terms (not eta normal form). 
  Chases variables in env;  Does not exploit sharing of variable bindings
  Does not check types, so could loop. *)
local 
      (*raised when norm has no effect on a term, 
        to encourage sharing instead of copying*)
  exception SAME;

  fun norm_term1 (asol,t) : term =
    let fun norm (Var (w,T)) = 
	      (case xsearch(asol,w) of
		  Some u => normh u
		| None   => raise SAME)
	  | norm (Abs(a,T,body)) =  Abs(a, T, norm body)
	  | norm (Abs(_,_,body) $ t) = normh(subst_bounds([t], body))
	  | norm (f $ t) =
	      ((case norm f of
		 Abs(_,_,body) => normh(subst_bounds([t], body))
	       | nf => nf $ normh t)
	      handle SAME => f $ norm t)
	  | norm _ =  raise SAME
	and normh t = (norm t) handle SAME => t
    in normh t end

  and norm_term2(asol,iTs,t) : term =
    let fun normT(Type(a,Ts)) = Type(a, normTs Ts)
	  | normT(TFree _) = raise SAME
	  | normT(TVar(v,_)) = (case assoc(iTs,v) of
		  Some(U) => normTh U
		| None => raise SAME)
	and normTh T = ((normT T) handle SAME => T)
	and normTs([]) = raise SAME
	  | normTs(T::Ts) = ((normT T :: normTsh Ts)
			     handle SAME => T :: normTs Ts)
	and normTsh Ts = ((normTs Ts) handle SAME => Ts)
	and norm(Const(a,T)) = Const(a, normT T)
	  | norm(Free(a,T)) = Free(a, normT T)
	  | norm(Var (w,T)) = 
	      (case xsearch(asol,w) of
		  Some u => normh u
		| None   => Var(w,normT T))
	  | norm(Abs(a,T,body)) =
		(Abs(a,normT T,normh body) handle SAME => Abs(a, T, norm body))
	  | norm(Abs(_,_,body) $ t) = normh(subst_bounds([t], body))
	  | norm(f $ t) =
	      ((case norm f of
		 Abs(_,_,body) => normh(subst_bounds([t], body))
	       | nf => nf $ normh t)
	      handle SAME => f $ norm t)
	  | norm _ =  raise SAME
	and normh t = (norm t) handle SAME => t
    in normh t end;

in

(*curried version might be slower in recursive calls*)
fun norm_term (env as Envir{asol,iTs,...}) t : term =
	if iTs=[] then norm_term1(asol, t) else norm_term2(asol,iTs, t)

end;

end;