diff --git a/src/include/ranges/prange.cc.h b/src/include/ranges/prange.cc.h
index 6637919..c283682 100644
--- a/src/include/ranges/prange.cc.h
+++ b/src/include/ranges/prange.cc.h
@@ -153,21 +153,26 @@ namespace CNORXZ
     template <class I>
     decltype(auto) PIndex<Index>::format(const Sptr<I>& ind) const
     {
-	/*!!!*/
+	return ind;
     }
 
     template <class Index>
     template <class I>
     decltype(auto) PIndex<Index>::slice(const Sptr<I>& ind) const
     {
-	/*!!!*/
+	if(ind != nullptr){
+	    if(ind->dim() != 0){
+		return Sptr<PIndex<Index>>();
+	    }
+	}
+	return std::make_shared<PIndex<Index>>(*this);
     }
 
     template <class Index>
     template <class Xpr, class F>
     decltype(auto) PIndex<Index>::ifor(const Xpr& xpr, F&& f) const
     {
-	return For<0,Xpr,F>(this->pmax().val(), this->id(), xpr, std::forward<F>(f));
+	return PFor<0,0,Xpr,F>(this->lmax().val(), this->id(), mOrig->id(), xpr, std::forward<F>(f));
     }
 
     template <class Index>
diff --git a/src/include/ranges/urange.cc.h b/src/include/ranges/urange.cc.h
index 4964619..87b877d 100644
--- a/src/include/ranges/urange.cc.h
+++ b/src/include/ranges/urange.cc.h
@@ -158,10 +158,10 @@ namespace CNORXZ
     {
 	if(ind != nullptr){
 	    if(ind->dim() != 0) {
-		return Sptr<CIndex>();
+		return Sptr<UIndex<MetaType>>();
 	    }
 	}
-	return std::make_shared<CIndex>(*this);
+	return std::make_shared<UIndex<MetaType>>(*this);
     }
     
     template <typename MetaType>
diff --git a/src/include/xpr/for.cc.h b/src/include/xpr/for.cc.h
index de2cdb3..90d861c 100644
--- a/src/include/xpr/for.cc.h
+++ b/src/include/xpr/for.cc.h
@@ -207,6 +207,94 @@ namespace CNORXZ
 	return SFor<N,L,Xpr>(id, xpr, NoF {});
     }
     
+    /************
+     *   PFor   *
+     ************/
+    
+    template <SizeT L1, SizeT L2, class Xpr, class F>
+    constexpr PFor<L1,L2,Xpr,F>::PFor(SizeT size, const IndexId<L1>& id1, const IndexId<L2>& id2,
+				      const SizeT* map, const Xpr& xpr, F&& f) :
+	mSize(size),
+	mId1(id1),
+	mId2(id2),
+	mXpr(xpr),
+	mExt1(mXpr.rootSteps(mId1)),
+	mExt2(mXpr.rootSteps(mId2)),
+	mPart(1, map),
+	mF(f)
+    {}
+
+    template <SizeT L1, SizeT L2, class Xpr, class F>
+    template <class PosT>
+    inline decltype(auto) PFor<L1,L2,Xpr,F>::operator()(const PosT& last) const
+    {
+	if constexpr(std::is_same<typename std::remove_reference<F>::type,NoF>::value){
+	    for(SizeT i = 0; i != mSize; ++i){
+		const auto pos1 = last + mExt1( UPos(i) );
+		const auto pos2 = pos1 + mExt2( mPart( UPos(i) ) );
+		mXpr(pos2);
+	    }
+	}
+	else {
+	    typedef typename
+		std::remove_reference<decltype(mXpr((last + mExt1( UPos(0) )) + mExt2( mPart( UPos(0) ) )))>::type OutT;
+	    auto o = OutT();
+	    for(SizeT i = 0; i != mSize; ++i){
+		const auto pos1 = last + mExt1( UPos(i) );
+		const auto pos2 = pos1 + mExt2( mPart( UPos(i) ) );
+		mF(o, mXpr(pos2));
+	    }
+	    return o;
+	}
+    }
+	
+    template <SizeT L1, SizeT L2, class Xpr, class F>
+    inline decltype(auto) PFor<L1,L2,Xpr,F>::operator()() const
+    {
+	if constexpr(std::is_same<typename std::remove_reference<F>::type,NoF>::value){
+	    for(SizeT i = 0; i != mSize; ++i){
+		const auto pos1 = mExt1( UPos(i) );
+		const auto pos2 = pos1 + mExt2( mPart( UPos(i) ) );
+		mXpr(pos2);
+	    }
+	}
+	else {
+	    typedef typename std::remove_reference<decltype(mExt1( UPos(0) ) + mExt2( mPart( UPos(0) ) ))>::type OutT;
+	    auto o = OutT();
+	    for(SizeT i = 0; i != mSize; ++i){
+		const auto pos1 = mExt1( UPos(i) );
+		const auto pos2 = pos1 + mExt2( mPart( UPos(i) ) );
+		mF(o, mXpr(pos2));
+	    }
+	    return o;
+	}
+    }
+
+    template <SizeT L1, SizeT L2, class Xpr, class F>
+    template <SizeT I>
+    inline decltype(auto) PFor<L1,L2,Xpr,F>::rootSteps(const IndexId<I>& id) const
+    {
+	return mXpr.rootSteps(id);
+    }
+
+    /*************************
+     *   PFor (non-member)   *
+     *************************/
+
+    template <SizeT L1, SizeT L2, class Xpr, class F>
+    constexpr decltype(auto) mkPFor(SizeT size, const IndexId<L1>& id1, const IndexId<L2>& id2,
+				    const Xpr& xpr, F&& f)
+    {
+	return PFor<L1,L2,Xpr,F>(size, id1, id2, xpr, std::forward<F>(f));
+    }
+
+    template <SizeT L1, SizeT L2, class Xpr, class F>
+    constexpr decltype(auto) mkPFor(SizeT size, const IndexId<L1>& id1, const IndexId<L2>& id2,
+				    const Xpr& xpr)
+    {
+	return PFor<L1,L2,Xpr>(size, id1, id2, xpr, NoF {});
+    }
+
     /************
      *   TFor   *
      ************/
diff --git a/src/include/xpr/for.h b/src/include/xpr/for.h
index 06709c2..1ef46fd 100644
--- a/src/include/xpr/for.h
+++ b/src/include/xpr/for.h
@@ -85,6 +85,43 @@ namespace CNORXZ
     template <SizeT N, SizeT L, class Xpr>
     constexpr decltype(auto) mkSFor(const IndexId<L>& id, const Xpr& xpr);
 
+    // partial for:
+    template <SizeT L1, SizeT L2, class Xpr, class F = NoF>
+    class PFor : public XprInterface<PFor<L1,L2,Xpr,F>>
+    {
+    public:
+	DEFAULT_MEMBERS(PFor);
+
+	constexpr PFor(SizeT size, const IndexId<L1>& id1, const IndexId<L2>& id2,
+		       const SizeT* map, const Xpr& xpr, F&& f);
+
+	template <class PosT>
+	inline decltype(auto) operator()(const PosT& last) const;
+	
+	inline decltype(auto) operator()() const;
+
+	template <SizeT I>
+	inline decltype(auto) rootSteps(const IndexId<I>& id) const;
+
+    private:
+	SizeT mSize = 0;
+	IndexId<L1> mId1;
+	IndexId<L2> mId2;
+	Xpr mXpr;
+	typedef decltype(mXpr.rootSteps(mId1)) XPosT1;
+	typedef decltype(mXpr.rootSteps(mId2)) XPosT2;
+	XPosT1 mExt1;
+	XPosT2 mExt2;
+	FPos mPart;
+	F mF;
+    };
+
+    template <SizeT L, class Xpr, class F>
+    constexpr decltype(auto) mkFor(SizeT size, const IndexId<L>& id, const Xpr& xpr, F&& f);
+
+    template <SizeT L, class Xpr>
+    constexpr decltype(auto) mkFor(SizeT size, const IndexId<L>& id, const Xpr& xpr);
+
     // multi-threading
     template <SizeT L, class Xpr, class F = NoF>
     class TFor : public XprInterface<TFor<L,Xpr,F>>