--- a/src/Pure/unify.ML Mon Jan 29 13:58:15 1996 +0100
+++ b/src/Pure/unify.ML Mon Jan 29 14:16:13 1996 +0100
@@ -1,6 +1,6 @@
-(* Title: unify
+(* Title: unify
ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright Cambridge University 1992
Higher-Order Unification
@@ -28,16 +28,16 @@
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)
+ -> (Envir.env Sequence.seq)
val unifiers: Sign.sg * Envir.env * ((term*term)list)
- -> (Envir.env * (term * term)list) Sequence.seq
+ -> (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 =
+ : UNIFY =
struct
structure Sign = Sign;
@@ -47,11 +47,11 @@
(*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 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.proto_pure);
@@ -62,14 +62,14 @@
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')
+ 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')
+ None => [] | Some(T') => bTs T')
| bTs _ = []
in bTs end;
@@ -82,7 +82,7 @@
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!)
+ rbinder = [(x1,T),...,(xm,Tm)] (user's var names preserved!)
args = [arg1,...,argn]
the value of
(xm,...,x1)(head(arg1,...,argn)) remains invariant.
@@ -92,18 +92,18 @@
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
+ (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;
@@ -113,18 +113,18 @@
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$u]))
+ (case (fast (rbinder, f)) of
+ Type("fun",[_,T]) => T
+ | TVar(ixn,_) =>
+ (case assoc(iTs,ixn) of
+ Some(Type("fun",[_,T])) => T
+ | _ => raise TERM(funerr, [f$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]))
+ (#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;
@@ -133,14 +133,14 @@
(*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;
+ 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)
+ Abs(a, T, eta_nm ((a,T)::rbinder, body))
+ | eta_nm (rbinder, t) = etif(fastype env (rbinder,t), t)
in eta_nm end;
@@ -150,22 +150,22 @@
"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 =
+ env: Envir.env, v: indexname, ts: term list): bool =
let fun occurs [] = false
- | occurs (t::ts) = occur t orelse occurs ts
+ | 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$t) = occur t orelse occur f
+ | occur (Bound _) = false
+ | occur (Free _) = false
+ | occur (Var (w,_)) =
+ if w mem !seen then false
+ else if v=w then true
+ (*no need to lookup: v has no assignment*)
+ else (seen := w:: !seen;
+ case Envir.lookup(env,w) of
+ None => false
+ | Some t => occur t)
+ | occur (Abs(_,_,body)) = occur body
+ | occur (f$t) = occur t orelse occur f
in occurs ts end;
@@ -174,7 +174,7 @@
fun head_of_in (env,t) : term = case t of
f$_ => head_of_in(env,f)
| Var (v,_) => (case Envir.lookup(env,v) of
- Some u => head_of_in(env,u) | None => t)
+ Some u => head_of_in(env,u) | None => t)
| _ => t;
@@ -205,9 +205,9 @@
*)
fun rigid_occurs_term (seen: (indexname list)ref, env, v: indexname, t) =
let fun nonrigid t = if occurs_terms(seen,env,v,[t]) then Nonrigid
- else NoOcc
+ else NoOcc
fun occurs [] = NoOcc
- | occurs (t::ts) =
+ | occurs (t::ts) =
(case occur t of
Rigid => Rigid
| oc => (case occurs ts of NoOcc => oc | oc2 => oc2))
@@ -217,28 +217,28 @@
| oc => (case occomb f of NoOcc => oc | oc2 => oc2))
| occomb t = occur t
and occur (Const _) = NoOcc
- | occur (Bound _) = NoOcc
- | occur (Free _) = NoOcc
- | occur (Var (w,_)) =
- if w mem !seen then NoOcc
- else if v=w then Rigid
- else (seen := w:: !seen;
- case Envir.lookup(env,w) of
- None => NoOcc
- | Some t => occur t)
- | occur (Abs(_,_,body)) = occur body
- | occur (t as f$_) = (*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)
+ | 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*)
+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}) =
@@ -261,8 +261,8 @@
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
+ if n=i then get_eta_var (rbinder, n+1, f)
+ else raise ASSIGN
| get_eta_var _ = raise ASSIGN;
@@ -277,11 +277,11 @@
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
+ 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;
@@ -291,9 +291,9 @@
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
+ 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);
@@ -301,8 +301,8 @@
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);
+ eta_norm env (rbinder, head_norm(env,t)),
+ eta_norm env (rbinder, head_norm(env,u)), env);
@@ -313,34 +313,34 @@
do so caused numerous problems with no compensating advantage.
*)
fun SIMPL0 (dp0, (env,flexflex,flexrigid))
- : Envir.env * dpair list * dpair list =
+ : 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);
+ 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
+ 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))
+ ((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))
+ ((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
+ 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
+ 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
+ if a=b then SIMRANDS(t,u, unify_types(T,U,env))
+ else raise CANTUNIFY
| _ => raise CANTUNIFY
end;
@@ -356,8 +356,8 @@
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
+ 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;
@@ -376,7 +376,7 @@
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)
+ val (env', vars) = Envir.genvars name (env, map funtype Ts)
in (env', map (fn var=> combound(var, 0, length binder)) vars) end;
@@ -398,60 +398,60 @@
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 =
+ : (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*)
+ 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));
+ 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;
+ 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)
+ (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))
+ (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!*)
+ (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))
+ 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
+ (*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;
@@ -459,14 +459,14 @@
(*Call matchcopy to produce assignments to the variable in the dpair*)
fun MATCH (env, (rbinder,t,u), dpairs)
- : (Envir.env * dpair list)Sequence.seq =
+ : (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')
+ (*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;
@@ -481,9 +481,9 @@
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
+ fastype env (rbinder,u),
+ env)
+ in Envir.vupdate ((v, rlist_abs(rbinder, u)), env) end
end;
@@ -508,30 +508,30 @@
let val (head,args) = strip_comb t
in
case head of
- Bound i => (i-lev) mem banned orelse
- exists (rigid_bound (lev, banned)) args
- | Var _ => false (*no rigid occurrences here!*)
- | Abs (_,_,u) =>
- rigid_bound(lev+1, banned) u orelse
- exists (rigid_bound (lev, banned)) args
- | _ => exists (rigid_bound (lev, banned)) args
+ Bound i => (i-lev) mem banned orelse
+ exists (rigid_bound (lev, banned)) args
+ | Var _ => false (*no rigid occurrences here!*)
+ | Abs (_,_,u) =>
+ rigid_bound(lev+1, banned) u orelse
+ exists (rigid_bound (lev, banned)) args
+ | _ => exists (rigid_bound (lev, banned)) args
end;
(*Squash down indices at level >=lev to delete the banned from a term.*)
fun change_bnos banned =
let fun change lev (Bound i) =
- if i<lev then Bound i
- else if (i-lev) mem banned
- then raise CHANGE_FAIL (**flexible occurrence: give up**)
- else Bound (i - length (filter (fn j => j < i-lev) banned))
- | change lev (Abs (a,T,t)) = Abs (a, T, change(lev+1) t)
- | change lev (t$u) = change lev t $ change lev u
- | change lev t = t
+ if i<lev then Bound i
+ else if (i-lev) mem banned
+ then raise CHANGE_FAIL (**flexible occurrence: give up**)
+ else Bound (i - length (filter (fn j => j < i-lev) banned))
+ | change lev (Abs (a,T,t)) = Abs (a, T, change(lev+1) t)
+ | change lev (t$u) = change lev t $ change lev u
+ | change lev t = t
in change 0 end;
(*Change indices, delete the argument if it contains a banned Bound*)
fun change_arg banned ({j,t,T}, args) : flarg list =
- if rigid_bound (0, banned) t then args (*delete argument!*)
+ if rigid_bound (0, banned) t then args (*delete argument!*)
else {j=j, t= change_bnos banned t, T=T} :: args;
@@ -550,19 +550,19 @@
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
+ 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')))
+ 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;
@@ -583,8 +583,8 @@
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) (*needed by both: keep*)
- else (j::bnos, newbinder); (*remove*)
+ then (bnos, (a,T)::newbinder) (*needed by both: keep*)
+ else (j::bnos, newbinder); (*remove*)
val indices = 0 upto (length rbinder - 1);
val (banned,rbin') = foldr add_index (rbinder~~indices, ([],[]));
val (env', t') = clean_term banned (env, t);
@@ -605,11 +605,11 @@
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))
+ 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;
@@ -634,26 +634,26 @@
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));
+ 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)
@@ -675,7 +675,7 @@
(*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.
+ 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. *)