src/Pure/unify.ML
changeset 0 a5a9c433f639
child 646 7928c9760667
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Pure/unify.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,680 @@
+(*  Title: 	unify
+    ID:         $Id$
+    Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
+    Copyright   Cambridge University 1992
+
+Higher-Order Unification
+
+Potential problem: type of Vars is often ignored, so two Vars with same
+indexname but different types can cause errors!
+*)
+
+
+signature UNIFY = 
+sig
+  structure Sign: SIGN
+  structure Envir : ENVIR
+  structure Sequence : SEQUENCE
+  (*references for control and tracing*)
+  val trace_bound: int ref
+  val trace_simp: bool ref
+  val trace_types: bool ref
+  val search_bound: int ref
+  (*other exports*)
+  val combound : (term*int*int) -> term
+  val rlist_abs: (string*typ)list * term -> term   
+  val smash_unifiers : Sign.sg * Envir.env * (term*term)list
+	-> (Envir.env Sequence.seq)
+  val unifiers: Sign.sg * Envir.env * ((term*term)list)
+	-> (Envir.env * (term * term)list) Sequence.seq
+end;
+
+functor UnifyFun (structure Sign: SIGN and Envir: ENVIR and Sequence: SEQUENCE
+                  and Pattern:PATTERN
+                  sharing type Sign.sg = Pattern.sg
+                  and     type Envir.env = Pattern.env)
+	: UNIFY = 
+struct
+
+structure Sign = Sign;
+structure Envir = Envir;
+structure Sequence = Sequence;
+structure Pretty = Sign.Syntax.Pretty;
+
+(*Unification options*)
+
+val trace_bound = ref 10	(*tracing starts above this depth, 0 for full*)
+and search_bound = ref 20	(*unification quits above this depth*)
+and trace_simp = ref false	(*print dpairs before calling SIMPL*)
+and trace_types = ref false	(*announce potential incompleteness
+				  of type unification*)
+
+val sgr = ref(Sign.pure);
+
+type binderlist = (string*typ) list;
+
+type dpair = binderlist * term * term;
+
+fun body_type(Envir.Envir{iTs,...}) = 
+let fun bT(Type("fun",[_,T])) = bT T
+      | bT(T as TVar(ixn,_)) = (case assoc(iTs,ixn) of
+		None => T | Some(T') => bT T')
+      | bT T = T
+in bT end;
+
+fun binder_types(Envir.Envir{iTs,...}) = 
+let fun bTs(Type("fun",[T,U])) = T :: bTs U
+      | bTs(T as TVar(ixn,_)) = (case assoc(iTs,ixn) of
+		None => [] | Some(T') => bTs T')
+      | bTs _ = []
+in bTs end;
+
+fun strip_type env T = (binder_types env T, body_type env T);
+
+
+(*Put a term into head normal form for unification.
+  Operands need not be in normal form.  Does eta-expansions on the head,
+  which involves renumbering (thus copying) the args.  To avoid this 
+  inefficiency, avoid partial application:  if an atom is applied to
+  any arguments at all, apply it to its full number of arguments.
+  For
+    rbinder = [(x1,T),...,(xm,Tm)]		(user's var names preserved!)
+    args  =   [arg1,...,argn]
+  the value of 
+      (xm,...,x1)(head(arg1,...,argn))  remains invariant.
+*)
+
+local exception SAME
+in
+  fun head_norm (env,t) : term =
+    let fun hnorm (Var (v,T)) = 
+	      (case Envir.lookup (env,v) of
+		  Some u => head_norm (env, u)
+		| None   => raise SAME)
+	  | hnorm (Abs(a,T,body)) =  Abs(a, T, hnorm body)
+	  | hnorm (Abs(_,_,body) $ t) =
+	      head_norm (env, subst_bounds([t], body))
+	  | hnorm (f $ t) =
+	      (case hnorm f of
+		 Abs(_,_,body) =>
+		   head_norm (env, subst_bounds([t], body))
+	       | nf => nf $ t)
+	  | hnorm _ =  raise SAME
+    in  hnorm t  handle SAME=> t  end
+end;
+
+
+(*finds type of term without checking that combinations are consistent
+  rbinder holds types of bound variables*)
+fun fastype (Envir.Envir{iTs,...}) =
+let val funerr = "fastype: expected function type";
+    fun fast(rbinder, f$u) =
+	(case (fast (rbinder, f)) of
+	   Type("fun",[_,T]) => T
+	 | TVar(ixn,_) =>
+		(case assoc(iTs,ixn) of
+		   Some(Type("fun",[_,T])) => T
+		 | _ => raise TERM(funerr, [f$u]))
+	 | _ => raise TERM(funerr, [f$u]))
+      | fast (rbinder, Const (_,T)) = T
+      | fast (rbinder, Free (_,T)) = T
+      | fast (rbinder, Bound i) =
+	(#2 (nth_elem (i,rbinder))
+  	 handle LIST _=> raise TERM("fastype: Bound", [Bound i]))
+      | fast (rbinder, Var (_,T)) = T 
+      | fast (rbinder, Abs (_,T,u)) =  T --> fast (("",T) :: rbinder, u)
+in fast end;
+
+
+(*Eta normal form*)
+fun eta_norm(env as Envir.Envir{iTs,...}) =
+  let fun etif (Type("fun",[T,U]), t) =
+	    Abs("", T, etif(U, incr_boundvars 1 t $ Bound 0))
+	| etif (TVar(ixn,_),t) = 
+	    (case assoc(iTs,ixn) of
+		  None => t | Some(T) => etif(T,t))
+	| etif (_,t) = t;
+      fun eta_nm (rbinder, Abs(a,T,body)) =
+	    Abs(a, T, eta_nm ((a,T)::rbinder, body))
+	| eta_nm (rbinder, t) = etif(fastype env (rbinder,t), t)
+  in eta_nm end;
+
+
+(*OCCURS CHECK
+  Does the uvar occur in the term t?  
+  two forms of search, for whether there is a rigid path to the current term.
+  "seen" is list of variables passed thru, is a memo variable for sharing.
+  This version searches for nonrigid occurrence, returns true if found. *)
+fun occurs_terms (seen: (indexname list) ref,
+ 		  env: Envir.env, v: indexname, ts: term list): bool =
+  let fun occurs [] = false
+	| occurs (t::ts) =  occur t  orelse  occurs ts
+      and occur (Const _)  = false
+	| occur (Bound _)  = false
+	| occur (Free _)  = false
+	| occur (Var (w,_))  = 
+	    if w mem !seen then false
+	    else if v=w then true
+	      (*no need to lookup: v has no assignment*)
+	    else (seen := w:: !seen;  
+	          case  Envir.lookup(env,w)  of
+		      None    => false
+		    | Some t => occur t)
+	| occur (Abs(_,_,body)) = occur body
+	| occur (f$t) = occur t  orelse   occur f
+  in  occurs ts  end;
+
+
+
+(* f(a1,...,an)  ---->   (f,  [a1,...,an])  using the assignments*)
+fun head_of_in (env,t) : term = case t of
+    f$_ => head_of_in(env,f)
+  | Var (v,_) => (case  Envir.lookup(env,v)  of  
+			Some u => head_of_in(env,u)  |  None   => t)
+  | _ => t;
+
+
+datatype occ = NoOcc | Nonrigid | Rigid;
+
+(* Rigid occur check
+Returns Rigid    if it finds a rigid occurrence of the variable,
+        Nonrigid if it finds a nonrigid path to the variable.
+        NoOcc    otherwise.
+  Continues searching for a rigid occurrence even if it finds a nonrigid one.
+
+Condition for detecting non-unifable terms: [ section 5.3 of Huet (1975) ]
+   a rigid path to the variable, appearing with no arguments.
+Here completeness is sacrificed in order to reduce danger of divergence:
+   reject ALL rigid paths to the variable.
+Could check for rigid paths to bound variables that are out of scope.  
+Not necessary because the assignment test looks at variable's ENTIRE rbinder.
+
+Treatment of head(arg1,...,argn):
+If head is a variable then no rigid path, switch to nonrigid search
+for arg1,...,argn. 
+If head is an abstraction then possibly no rigid path (head could be a 
+   constant function) so again use nonrigid search.  Happens only if
+   term is not in normal form. 
+
+Warning: finds a rigid occurrence of ?f in ?f(t).
+  Should NOT be called in this case: there is a flex-flex unifier
+*)
+fun rigid_occurs_term (seen: (indexname list)ref, env, v: indexname, t) = 
+  let fun nonrigid t = if occurs_terms(seen,env,v,[t]) then Nonrigid 
+		       else NoOcc
+      fun occurs [] = NoOcc
+	| occurs (t::ts) =
+            (case occur t of
+               Rigid => Rigid
+             | oc =>  (case occurs ts of NoOcc => oc  |  oc2 => oc2))
+      and occomb (f$t) =
+            (case occur t of
+               Rigid => Rigid
+             | oc =>  (case occomb f of NoOcc => oc  |  oc2 => oc2))
+        | occomb t = occur t
+      and occur (Const _)  = NoOcc
+	| occur (Bound _)  = NoOcc
+	| occur (Free _)  = NoOcc
+	| occur (Var (w,_))  = 
+	    if w mem !seen then NoOcc
+	    else if v=w then Rigid
+	    else (seen := w:: !seen;  
+	          case  Envir.lookup(env,w)  of
+		      None    => NoOcc
+		    | Some t => occur t)
+	| occur (Abs(_,_,body)) = occur body
+	| occur (t as f$_) =  (*switch to nonrigid search?*)
+	   (case head_of_in (env,f) of
+	      Var (w,_) => (*w is not assigned*)
+		if v=w then Rigid  
+		else  nonrigid t
+	    | Abs(_,_,body) => nonrigid t (*not in normal form*)
+	    | _ => occomb t)
+  in  occur t  end;
+
+
+exception CANTUNIFY;	(*Signals non-unifiability.  Does not signal errors!*)
+exception ASSIGN;	(*Raised if not an assignment*)
+
+
+fun unify_types(T,U, env as Envir.Envir{asol,iTs,maxidx}) =
+	if T=U then env else
+	let val iTs' = Sign.Type.unify (#tsig(Sign.rep_sg (!sgr))) ((U,T),iTs)
+	in Envir.Envir{asol=asol,maxidx=maxidx,iTs=iTs'}
+	end handle Sign.Type.TUNIFY => raise CANTUNIFY;
+
+fun test_unify_types(args as (T,U,_)) =
+let val sot = Sign.string_of_typ (!sgr);
+    fun warn() = writeln("Potential loss of completeness: "^sot U^" = "^sot T);
+    val env' = unify_types(args)
+in if is_TVar(T) orelse is_TVar(U) then warn() else ();
+   env'
+end;
+
+(*Is the term eta-convertible to a single variable with the given rbinder?
+  Examples: ?a   ?f(B.0)   ?g(B.1,B.0)
+  Result is var a for use in SIMPL. *)
+fun get_eta_var ([], _, Var vT)  =  vT
+  | get_eta_var (_::rbinder, n, f $ Bound i) =
+	if  n=i  then  get_eta_var (rbinder, n+1, f) 
+		 else  raise ASSIGN
+  | get_eta_var _ = raise ASSIGN;
+
+
+(* ([xn,...,x1], t)   ======>   (x1,...,xn)t *)
+fun rlist_abs ([], body) = body
+  | rlist_abs ((a,T)::pairs, body) = rlist_abs(pairs, Abs(a, T, body));
+
+
+(*Solve v=u by assignment -- "fixedpoint" to Huet -- if v not in u.
+  If v occurs rigidly then nonunifiable.
+  If v occurs nonrigidly then must use full algorithm. *)
+fun assignment (env, rbinder, t, u) =
+    let val (v,T) = get_eta_var(rbinder,0,t)
+    in  case rigid_occurs_term (ref[], env, v, u) of
+	      NoOcc => let val env = unify_types(body_type env T,
+						 fastype env (rbinder,u),env)
+		in Envir.update ((v, rlist_abs(rbinder,u)), env) end
+	    | Nonrigid =>  raise ASSIGN
+	    | Rigid =>  raise CANTUNIFY
+    end;
+
+
+(*Extends an rbinder with a new disagreement pair, if both are abstractions.
+  Tries to unify types of the bound variables!
+  Checks that binders have same length, since terms should be eta-normal;
+    if not, raises TERM, probably indicating type mismatch.
+  Uses variable a (unless the null string) to preserve user's naming.*) 
+fun new_dpair (rbinder, Abs(a,T,body1), Abs(b,U,body2), env) =
+	let val env' = unify_types(T,U,env)
+	    val c = if a="" then b else a
+	in new_dpair((c,T) :: rbinder, body1, body2, env') end
+    | new_dpair (_, Abs _, _, _) = raise TERM ("new_dpair", [])
+    | new_dpair (_, _, Abs _, _) = raise TERM ("new_dpair", [])
+    | new_dpair (rbinder, t1, t2, env) = ((rbinder, t1, t2), env);
+
+
+fun head_norm_dpair (env, (rbinder,t,u)) : dpair * Envir.env =
+     new_dpair (rbinder,
+		eta_norm env (rbinder, head_norm(env,t)),
+	  	eta_norm env (rbinder, head_norm(env,u)), env);
+
+
+
+(*flexflex: the flex-flex pairs,  flexrigid: the flex-rigid pairs
+  Does not perform assignments for flex-flex pairs:
+    may create nonrigid paths, which prevent other assignments*)
+fun SIMPL0 (dp0, (env,flexflex,flexrigid))
+	: Envir.env * dpair list * dpair list =
+    let val (dp as (rbinder,t,u), env) = head_norm_dpair(env,dp0);
+	    fun SIMRANDS(f$t, g$u, env) =
+			SIMPL0((rbinder,t,u), SIMRANDS(f,g,env))
+	      | SIMRANDS (t as _$_, _, _) =
+		raise TERM ("SIMPL: operands mismatch", [t,u])
+	      | SIMRANDS (t, u as _$_, _) =
+		raise TERM ("SIMPL: operands mismatch", [t,u])
+	      | SIMRANDS(_,_,env) = (env,flexflex,flexrigid);
+    in case (head_of t, head_of u) of
+       (Var(_,T), Var(_,U)) =>
+	    let val T' = body_type env T and U' = body_type env U;
+		val env = unify_types(T',U',env)
+	    in (env, dp::flexflex, flexrigid) end
+     | (Var _, _) =>
+	    ((assignment (env,rbinder,t,u), flexflex, flexrigid)
+	     handle ASSIGN => (env, flexflex, dp::flexrigid))
+     | (_, Var _) =>
+	    ((assignment (env,rbinder,u,t), flexflex, flexrigid)
+	     handle ASSIGN => (env, flexflex, (rbinder,u,t)::flexrigid))
+     | (Const(a,T), Const(b,U)) =>
+	    if a=b then SIMRANDS(t,u, unify_types(T,U,env))
+	    else raise CANTUNIFY
+     | (Bound i,    Bound j)    =>
+	    if i=j  then SIMRANDS(t,u,env) else raise CANTUNIFY
+     | (Free(a,T),  Free(b,U))  =>
+	    if a=b then SIMRANDS(t,u, unify_types(T,U,env))
+	    else raise CANTUNIFY
+     | _ => raise CANTUNIFY
+    end;
+
+
+(* changed(env,t) checks whether the head of t is a variable assigned in env*)
+fun changed (env, f$_) = changed (env,f)
+  | changed (env, Var (v,_)) =
+      (case Envir.lookup(env,v) of None=>false  |  _ => true)
+  | changed _ = false;
+
+
+(*Recursion needed if any of the 'head variables' have been updated
+  Clever would be to re-do just the affected dpairs*)
+fun SIMPL (env,dpairs) : Envir.env * dpair list * dpair list =
+    let val all as (env',flexflex,flexrigid) =
+	    foldr SIMPL0 (dpairs, (env,[],[]));
+	val dps = flexrigid@flexflex
+    in if exists (fn ((_,t,u)) => changed(env',t) orelse changed(env',u)) dps
+       then SIMPL(env',dps) else all
+    end;
+
+
+(*computes t(Bound(n+k-1),...,Bound(n))  *)
+fun combound (t, n, k) = 
+    if  k>0  then  combound (t,n+1,k-1) $ (Bound n)  else  t;
+
+
+(*Makes the terms E1,...,Em,    where Ts = [T...Tm]. 
+  Each Ei is   ?Gi(B.(n-1),...,B.0), and has type Ti
+  The B.j are bound vars of binder.
+  The terms are not made in eta-normal-form, SIMPL does that later.  
+  If done here, eta-expansion must be recursive in the arguments! *)
+fun make_args name (binder: typ list, env, []) = (env, [])   (*frequent case*)
+  | make_args name (binder: typ list, env, Ts) : Envir.env * term list =
+       let fun funtype T = binder--->T;
+	   val (env', vars) = Envir.genvars name (env, map funtype Ts)
+       in  (env',  map (fn var=> combound(var, 0, length binder)) vars)  end;
+
+
+(*Abstraction over a list of types, like list_abs*)
+fun types_abs ([],u) = u
+  | types_abs (T::Ts, u) = Abs("", T, types_abs(Ts,u));
+
+(*Abstraction over the binder of a type*)
+fun type_abs (env,T,t) = types_abs(binder_types env T, t);
+
+
+(*MATCH taking "big steps".
+  Copies u into the Var v, using projection on targs or imitation.
+  A projection is allowed unless SIMPL raises an exception.
+  Allocates new variables in projection on a higher-order argument,
+    or if u is a variable (flex-flex dpair).
+  Returns long sequence of every way of copying u, for backtracking
+  For example, projection in ?b'(?a) may be wrong if other dpairs constrain ?a.
+  The order for trying projections is crucial in ?b'(?a)   
+  NB "vname" is only used in the call to make_args!!   *)
+fun matchcopy vname = let fun mc(rbinder, targs, u, ed as (env,dpairs)) 
+	: (term * (Envir.env * dpair list))Sequence.seq =
+let (*Produce copies of uarg and cons them in front of uargs*)
+    fun copycons uarg (uargs, (env, dpairs)) =
+	Sequence.maps(fn (uarg', ed') => (uarg'::uargs, ed'))
+	    (mc (rbinder, targs,eta_norm env (rbinder,head_norm(env,uarg)),
+		 (env, dpairs)));
+	(*Produce sequence of all possible ways of copying the arg list*)
+    fun copyargs [] = Sequence.cons( ([],ed), Sequence.null)
+      | copyargs (uarg::uargs) =
+	    Sequence.flats (Sequence.maps (copycons uarg) (copyargs uargs));
+    val (uhead,uargs) = strip_comb u;
+    val base = body_type env (fastype env (rbinder,uhead));
+    fun joinargs (uargs',ed') = (list_comb(uhead,uargs'), ed');
+    (*attempt projection on argument with given typ*)
+    val Ts = map (curry (fastype env) rbinder) targs;
+    fun projenv (head, (Us,bary), targ, tail) = 
+	let val env = if !trace_types then test_unify_types(base,bary,env)
+		      else unify_types(base,bary,env)
+	in Sequence.seqof (fn () =>  
+	    let val (env',args) = make_args vname (Ts,env,Us);
+		(*higher-order projection: plug in targs for bound vars*)
+		fun plugin arg = list_comb(head_of arg, targs);
+		val dp = (rbinder, list_comb(targ, map plugin args), u);
+		val (env2,frigid,fflex) = SIMPL (env', dp::dpairs)
+		    (*may raise exception CANTUNIFY*)
+	    in  Some ((list_comb(head,args), (env2, frigid@fflex)),
+			tail)
+	    end  handle CANTUNIFY => Sequence.pull tail)
+	end handle CANTUNIFY => tail;
+    (*make a list of projections*)
+    fun make_projs (T::Ts, targ::targs) =
+	      (Bound(length Ts), T, targ) :: make_projs (Ts,targs)
+      | make_projs ([],[]) = []
+      | make_projs _ = raise TERM ("make_projs", u::targs);
+    (*try projections and imitation*)
+    fun matchfun ((bvar,T,targ)::projs) =
+	       (projenv(bvar, strip_type env T, targ, matchfun projs))
+      | matchfun [] = (*imitation last of all*)
+	      (case uhead of
+		 Const _ => Sequence.maps joinargs (copyargs uargs)
+	       | Free _  => Sequence.maps joinargs (copyargs uargs)
+	       | _ => Sequence.null)  (*if Var, would be a loop!*)
+in case uhead of
+	Abs(a, T, body) =>
+	    Sequence.maps(fn (body', ed') => (Abs (a,T,body'), ed')) 
+		(mc ((a,T)::rbinder,
+			(map (incr_boundvars 1) targs) @ [Bound 0], body, ed))
+      | Var (w,uary) => 
+	    (*a flex-flex dpair: make variable for t*)
+	    let val (env', newhd) = Envir.genvar (#1 w) (env, Ts---> base)
+		val tabs = combound(newhd, 0, length Ts)
+		val tsub = list_comb(newhd,targs)
+	    in  Sequence.single (tabs, (env', (rbinder,tsub,u):: dpairs)) 
+	    end
+      | _ =>  matchfun(rev(make_projs(Ts, targs)))
+end
+in mc end;
+
+
+(*Call matchcopy to produce assignments to the variable in the dpair*)
+fun MATCH (env, (rbinder,t,u), dpairs)
+	: (Envir.env * dpair list)Sequence.seq = 
+  let val (Var(v,T), targs) = strip_comb t;
+      val Ts = binder_types env T;
+      fun new_dset (u', (env',dpairs')) =
+	  (*if v was updated to s, must unify s with u' *)
+	  case Envir.lookup(env',v) of
+	      None => (Envir.update ((v, types_abs(Ts, u')), env'),  dpairs')
+	    | Some s => (env', ([], s, types_abs(Ts, u'))::dpairs')
+  in Sequence.maps new_dset
+         (matchcopy (#1 v) (rbinder, targs, u, (env,dpairs)))
+  end;
+
+
+
+(**** Flex-flex processing ****)
+
+(*At end of unification, do flex-flex assignments like ?a -> ?f(?b) 
+  Attempts to update t with u, raising ASSIGN if impossible*)
+fun ff_assign(env, rbinder, t, u) : Envir.env = 
+let val (v,T) = get_eta_var(rbinder,0,t)
+in if occurs_terms (ref[], env, v, [u]) then raise ASSIGN
+   else let val env = unify_types(body_type env T,fastype env (rbinder,u),env)
+	in Envir.vupdate ((v, rlist_abs(rbinder, u)), env) end
+end;
+
+
+(*Flex argument: a term, its type, and the index that refers to it.*)
+type flarg = {t: term,  T: typ,  j: int};
+
+
+(*Form the arguments into records for deletion/sorting.*)
+fun flexargs ([],[],[]) = [] : flarg list
+  | flexargs (j::js, t::ts, T::Ts) = {j=j, t=t, T=T} :: flexargs(js,ts,Ts)
+  | flexargs _ = error"flexargs";
+
+
+(*If an argument contains a banned Bound, then it should be deleted.
+  But if the path is flexible, this is difficult; the code gives up!*)
+exception CHANGE and CHANGE_FAIL;   (*rigid and flexible occurrences*)
+
+
+(*Squash down indices at level >=lev to delete the js from a term.
+  flex should initially be false, since the empty path is rigid.*)
+fun change_bnos (lev, js, flex) t = 
+  let val (head,args) = strip_comb t 
+      val flex' = flex orelse is_Var head
+      val head' = case head of
+	    Bound i => 
+		if i<lev then Bound i
+		else  if (i-lev) mem js  
+                      then  if flex then raise CHANGE_FAIL
+                                    else raise CHANGE
+		else  Bound (i - length (filter (fn j => j < i-lev) js))
+	  | Abs (a,T,t) => Abs (a, T, change_bnos(lev+1, js, flex) t)
+	  | _ => head
+  in  list_comb (head', map (change_bnos (lev, js, flex')) args)
+  end;
+
+
+(*Change indices, delete the argument if it contains a banned Bound*)
+fun change_arg js ({j,t,T}, args) : flarg list =
+    {j=j, t= change_bnos(0,js,false)t, T=T} :: args    handle CHANGE => args;
+
+
+(*Sort the arguments to create assignments if possible:
+  create eta-terms like ?g(B.1,B.0) *)
+fun arg_less ({t= Bound i1,...}, {t= Bound i2,...}) = (i2<i1)
+  | arg_less (_:flarg, _:flarg) = false;
+
+(*Test whether the new term would be eta-equivalent to a variable --
+  if so then there is no point in creating a new variable*)
+fun decreasing n ([]: flarg list) = (n=0)
+  | decreasing n ({j,...}::args) = j=n-1 andalso decreasing (n-1) args;
+
+(*Delete banned indices in the term, simplifying it.
+  Force an assignment, if possible, by sorting the arguments.
+  Update its head; squash indices in arguments. *)
+fun clean_term banned (env,t) =
+    let val (Var(v,T), ts) = strip_comb t
+	val (Ts,U) = strip_type env T
+	and js = length ts - 1  downto 0
+	val args = sort arg_less
+		(foldr (change_arg banned) (flexargs (js,ts,Ts), []))
+	val ts' = map (#t) args
+    in
+    if decreasing (length Ts) args then (env, (list_comb(Var(v,T), ts')))
+    else let val (env',v') = Envir.genvar (#1v) (env, map (#T) args ---> U)
+	     val body = list_comb(v', map (Bound o #j) args)
+	     val env2 = Envir.vupdate (((v, types_abs(Ts, body)),   env'))
+	     (*the vupdate affects ts' if they contain v*)
+	 in  
+	     (env2, Envir.norm_term env2 (list_comb(v',ts')))
+         end
+    end;
+
+
+(*Add tpair if not trivial or already there.
+  Should check for swapped pairs??*)
+fun add_tpair (rbinder, (t0,u0), tpairs) : (term*term) list =
+  if t0 aconv u0 then tpairs  
+  else
+  let val t = rlist_abs(rbinder, t0)  and  u = rlist_abs(rbinder, u0);
+      fun same(t',u') = (t aconv t') andalso (u aconv u')
+  in  if exists same tpairs  then tpairs  else (t,u)::tpairs  end;
+
+
+(*Simplify both terms and check for assignments.
+  Bound vars in the binder are "banned" unless used in both t AND u *)
+fun clean_ffpair ((rbinder, t, u), (env,tpairs)) = 
+  let val loot = loose_bnos t  and  loou = loose_bnos u
+      fun add_index (((a,T), j), (bnos, newbinder)) = 
+            if  j mem loot  andalso  j mem loou 
+            then  (bnos, (a,T)::newbinder)
+            else  (j::bnos, newbinder);
+      val indices = 0 upto (length rbinder - 1);
+      val (banned,rbin') = foldr add_index (rbinder~~indices, ([],[]));
+      val (env', t') = clean_term banned (env, t);
+      val (env'',u') = clean_term banned (env',u)
+  in  (ff_assign(env'', rbin', t', u'), tpairs)
+      handle ASSIGN => (ff_assign(env'', rbin', u', t'), tpairs)
+      handle ASSIGN => (env'', add_tpair(rbin', (t',u'), tpairs))
+  end
+  handle CHANGE_FAIL => (env, add_tpair(rbinder, (t,u), tpairs));
+
+
+(*IF the flex-flex dpair is an assignment THEN do it  ELSE  put in tpairs
+  eliminates trivial tpairs like t=t, as well as repeated ones
+  trivial tpairs can easily escape SIMPL:  ?A=t, ?A=?B, ?B=t gives t=t 
+  Resulting tpairs MAY NOT be in normal form:  assignments may occur here.*)
+fun add_ffpair ((rbinder,t0,u0), (env,tpairs)) 
+      : Envir.env * (term*term)list =
+  let val t = Envir.norm_term env t0  and  u = Envir.norm_term env u0
+  in  case  (head_of t, head_of u) of
+      (Var(v,T), Var(w,U)) =>  (*Check for identical variables...*)
+	if v=w then		(*...occur check would falsely return true!*)
+	    if T=U then (env, add_tpair (rbinder, (t,u), tpairs))
+	    else raise TERM ("add_ffpair: Var name confusion", [t,u])
+	else if xless(v,w) then (*prefer to update the LARGER variable*)
+	     clean_ffpair ((rbinder, u, t), (env,tpairs))
+        else clean_ffpair ((rbinder, t, u), (env,tpairs))
+    | _ => raise TERM ("add_ffpair: Vars expected", [t,u])
+  end;
+
+
+(*Print a tracing message + list of dpairs.
+  In t==u print u first because it may be rigid or flexible --
+    t is always flexible.*)
+fun print_dpairs msg (env,dpairs) =
+  let fun pdp (rbinder,t,u) =
+        let fun termT t = Sign.pretty_term (!sgr)
+                              (Envir.norm_term env (rlist_abs(rbinder,t)))
+            val bsymbs = [termT u, Pretty.str" =?=", Pretty.brk 1,
+                          termT t];
+        in writeln(Pretty.string_of(Pretty.blk(0,bsymbs))) end;
+  in  writeln msg;  seq pdp dpairs  end;
+
+
+(*Unify the dpairs in the environment.
+  Returns flex-flex disagreement pairs NOT IN normal form. 
+  SIMPL may raise exception CANTUNIFY. *)
+fun hounifiers (sg,env, tus : (term*term)list) 
+  : (Envir.env * (term*term)list)Sequence.seq =
+  let fun add_unify tdepth ((env,dpairs), reseq) =
+	  Sequence.seqof (fn()=>
+	  let val (env',flexflex,flexrigid) = 
+	       (if tdepth> !trace_bound andalso !trace_simp
+		then print_dpairs "Enter SIMPL" (env,dpairs)  else ();
+		SIMPL (env,dpairs))
+	  in case flexrigid of
+	      [] => Some (foldr add_ffpair (flexflex, (env',[])), reseq)
+	    | dp::frigid' => 
+		if tdepth > !search_bound then
+		    (prs"***Unification bound exceeded\n"; Sequence.pull reseq)
+		else
+		(if tdepth > !trace_bound then
+		    print_dpairs "Enter MATCH" (env',flexrigid@flexflex)
+		 else ();
+		 Sequence.pull (Sequence.its_right (add_unify (tdepth+1))
+			   (MATCH (env',dp, frigid'@flexflex), reseq)))
+	  end
+	  handle CANTUNIFY => 
+	    (if tdepth > !trace_bound then writeln"Failure node" else ();
+	     Sequence.pull reseq));
+     val dps = map (fn(t,u)=> ([],t,u)) tus
+  in sgr := sg;
+     add_unify 1 ((env,dps), Sequence.null) 
+  end;
+
+fun unifiers(params) =
+      Sequence.cons((Pattern.unify(params), []),   Sequence.null)
+      handle Pattern.Unif => Sequence.null
+           | Pattern.Pattern => hounifiers(params);
+
+
+(*For smash_flexflex1*)
+fun var_head_of (env,t) : indexname * typ =
+  case head_of (strip_abs_body (Envir.norm_term env t)) of
+      Var(v,T) => (v,T)
+    | _ => raise CANTUNIFY;  (*not flexible, cannot use trivial substitution*)
+
+
+(*Eliminate a flex-flex pair by the trivial substitution, see Huet (1975)
+  Unifies ?f(t1...rm) with ?g(u1...un) by ?f -> %x1...xm.?a, ?g -> %x1...xn.?a
+  Unfortunately, unifies ?f(t,u) with ?g(t,u) by ?f, ?g -> %(x,y)?a, 
+	though just ?g->?f is a more general unifier.
+  Unlike Huet (1975), does not smash together all variables of same type --
+    requires more work yet gives a less general unifier (fewer variables).
+  Handles ?f(t1...rm) with ?f(u1...um) to avoid multiple updates. *)
+fun smash_flexflex1 ((t,u), env) : Envir.env =
+  let val (v,T) = var_head_of (env,t)
+      and (w,U) = var_head_of (env,u);
+      val (env', var) = Envir.genvar (#1v) (env, body_type env T)
+      val env'' = Envir.vupdate((w, type_abs(env',U,var)),  env')
+  in  if (v,T)=(w,U) then env''  (*the other update would be identical*)
+      else Envir.vupdate((v, type_abs(env',T,var)), env'')
+  end;
+
+
+(*Smash all flex-flexpairs.  Should allow selection of pairs by a predicate?*)
+fun smash_flexflex (env,tpairs) : Envir.env =
+  foldr smash_flexflex1 (tpairs, env);
+
+(*Returns unifiers with no remaining disagreement pairs*)
+fun smash_unifiers (sg, env, tus) : Envir.env Sequence.seq =
+    Sequence.maps smash_flexflex (unifiers(sg,env,tus));
+
+end;