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Editing: lazy_list.hpp

////////////////////////////////////////////////////////////////////////////
// lazy_list.hpp
//
// Build lazy operations for Phoenix equivalents for FC++
//
// These are equivalents of the Boost FC++ functoids in list.hpp
//
// Implemented so far:
//
// head tail null
//
// strict_list<T> and associated iterator.
//
// list<T> and odd_list<T>
//
// cons cat
//
// Comparisons between list and odd_list types and separately for strict_list.
//
// NOTES: There is a fix at the moment as I have not yet sorted out
// how to get back the return type of a functor returning a list type.
// For the moment I have fixed this as odd_list<T> at two locations,
// one in list<T> and one in Cons. I am going to leave it like this
// for now as reading the code, odd_list<T> seems to be correct.
//
// I am also not happy at the details needed to detect types in Cons.
//
// I think the structure of this file is now complete.
// John Fletcher February 2015.
//
////////////////////////////////////////////////////////////////////////////
/*=============================================================================
 Copyright (c) 2000-2003 Brian McNamara and Yannis Smaragdakis
 Copyright (c) 2001-2007 Joel de Guzman
 Copyright (c) 2015 John Fletcher

Distributed under the Boost Software License, Version 1.0. (See accompanying
    file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
==============================================================================*/

///////////////////////////////////////////////////////////////////////
// This is from Boost FC++ list.hpp reimplemented without Fun0 or Full0
///////////////////////////////////////////////////////////////////////

/*
concept ListLike: Given a list representation type L

L<T> inherits ListLike and has
 // typedefs just show typical values
 typedef T value_type
 typedef L<T> force_result_type
 typedef L<T> delay_result_type
 typedef L<T> tail_result_type
 template <class UU> struct cons_rebind {
 typedef L<UU> type; // force type
 typedef L<UU> delay_type; // delay type
 };

L()
 L( a_unique_type_for_nil )
 template <class F> L(F) // F :: ()->L

constructor: force_result_type( T, L<T> )
 template <class F>
 constructor: force_result_type( T, F ) // F :: ()->L

template <class It>
 L( It, It )

// FIX THIS instead of operator bool(), does Boost have something better?
   operator bool() const
   force_result_type force() const
   delay_result_type delay() const
   T head() const
   tail_result_type tail() const

static const bool is_lazy;   // true if can represent infinite lists

typedef const_iterator;
   typedef const_iterator iterator;  // ListLikes are immutable
   iterator begin() const
   iterator end() const
*/

//////////////////////////////////////////////////////////////////////
// End of section from Boost FC++ list.hpp
//////////////////////////////////////////////////////////////////////

#ifndef BOOST_PHOENIX_FUNCTION_LAZY_LIST
#define BOOST_PHOENIX_FUNCTION_LAZY_LIST

#include <boost/phoenix/core.hpp>
#include <boost/phoenix/function.hpp>
#include <boost/intrusive_ptr.hpp>
#include <boost/function.hpp>
#include <boost/type_traits/type_with_alignment.hpp>
//#include "lazy_reuse.hpp"

namespace boost {

namespace phoenix {

//////////////////////////////////////////////////////////////////////
// These are the list types being declared.
//////////////////////////////////////////////////////////////////////

template <class T> class strict_list;
 namespace impl {
 template <class T> class list;
 template <class T> class odd_list;
 }
 // in ref_count.hpp in BoostFC++ now in lazy_operator.hpp
 //typedef unsigned int RefCountType;

//////////////////////////////////////////////////////////////////////
// a_unique_type_for_nil moved to lazy_operator.hpp.
//////////////////////////////////////////////////////////////////////

//////////////////////////////////////////////////////////////////////
// Distinguish lazy lists (list and odd_list) from strict_list.
//////////////////////////////////////////////////////////////////////

namespace lazy {
 // Copied from Boost FC++ list.hpp
 template <class L, bool is_lazy> struct ensure_lazy_helper {};
 template <class L> struct ensure_lazy_helper<L,true> {
 static void requires_lazy_list_to_prevent_infinite_recursion() {}
 };
 template <class L>
 void ensure_lazy() {
 ensure_lazy_helper<L,L::is_lazy>::
 requires_lazy_list_to_prevent_infinite_recursion();
 }

}

//////////////////////////////////////////////////////////////////////
// Provide remove reference for types defined for list types.
//////////////////////////////////////////////////////////////////////

namespace result_of {

template < typename L >
 class ListType
 {
 public:
 typedef typename boost::remove_reference<L>::type LType;
 typedef typename LType::value_type value_type;
 typedef typename LType::tail_result_type tail_result_type;
 typedef typename LType::force_result_type force_result_type;
 typedef typename LType::delay_result_type delay_result_type;
 };

template <>
 class ListType<a_unique_type_for_nil>
 {
 public:
 typedef a_unique_type_for_nil LType;
 //typedef a_unique_type_for_nil value_type;
 };

template <typename F, typename T>
 struct ResultType {
 typedef typename impl::odd_list<T> type;
 };
 
 }

//////////////////////////////////////////////////////////////////////
// ListLike is a property inherited by any list type to enable it to
// work with the functions being implemented in this file.
// It provides the check for the structure described above.
//////////////////////////////////////////////////////////////////////

namespace listlike {

struct ListLike {};   // This lets us use is_base_and_derived() to see
       // (at compile-time) what classes are user-defined lists.

template <class L, bool is_lazy> struct ensure_lazy_helper {};
 template <class L> struct ensure_lazy_helper<L,true> {
 static void requires_lazy_list_to_prevent_infinite_recursion() {}
 };
 template <class L>
 void ensure_lazy() {
 ensure_lazy_helper<L,L::is_lazy>::
 requires_lazy_list_to_prevent_infinite_recursion();
 }

template <class L, bool b>
 struct EnsureListLikeHelp {
 static void trying_to_call_a_list_function_on_a_non_list() {}
 };
 template <class L> struct EnsureListLikeHelp<L,false> { };
 template <class L>
 void EnsureListLike() {
 typedef typename result_of::ListType<L>::LType LType;
 EnsureListLikeHelp<L,boost::is_base_and_derived<ListLike,LType>::value>::
 trying_to_call_a_list_function_on_a_non_list();
 }

template <class L>
 bool is_a_unique_type_for_nil(const L& /*l*/) {
 return false;
 }

template <>
 bool is_a_unique_type_for_nil<a_unique_type_for_nil>
 (const a_unique_type_for_nil& /* n */) {
 return true;
 }

template <class L>
 struct detect_nil {
 static const bool is_nil = false;
 };

template <>
 struct detect_nil<a_unique_type_for_nil> {
 static const bool is_nil = true;
 };

template <>
 struct detect_nil<a_unique_type_for_nil&> {
 static const bool is_nil = true;
 };

template <>
 struct detect_nil<const a_unique_type_for_nil&> {
 static const bool is_nil = true;
 };
 
 }

//////////////////////////////////////////////////////////////////////
// Implement lazy functions for list types. cat and cons come later.
//////////////////////////////////////////////////////////////////////

#ifndef BOOST_PHOENIX_FUNCTION_MAX_LAZY_LIST_LENGTH
#define BOOST_PHOENIX_FUNCTION_MAX_LAZY_LIST_LENGTH 1000
#endif

namespace impl {

struct Head
 {
 template <typename Sig>
 struct result;

template <typename This, typename L>
 struct result<This(L)>
 {
 typedef typename result_of::ListType<L>::value_type type;
 };

template <typename L>
 typename result<Head(L)>::type
 operator()(const L & l) const
 {
 listlike::EnsureListLike<L>();
 return l.head();
 }

};

struct Tail
 {
 template <typename Sig>
 struct result;

template <typename This, typename L>
 struct result<This(L)>
 {
 typedef typename result_of::ListType<L>::tail_result_type type;
 };

template <typename L>
 typename result<Tail(L)>::type
 operator()(const L & l) const
 {
 listlike::EnsureListLike<L>();
 return l.tail();
 }

};

struct Null
 {
 template <typename Sig>
 struct result;

template <typename This, typename L>
 struct result<This(L)>
 {
 typedef bool type;
 };

template <typename L>
 typename result<Null(L)>::type
 //bool
 operator()(const L& l) const
 {
 listlike::EnsureListLike<L>();
 return !l;
 }

};

struct Delay {
 template <typename Sig>
 struct result;

template <typename This, typename L>
 struct result<This(L)>
 {
 typedef typename result_of::ListType<L>::delay_result_type type;
 };

template <typename L>
 typename result<Delay(L)>::type
 operator()(const L & l) const
 {
 listlike::EnsureListLike<L>();
 return l.delay();
 }

};

struct Force {
 template <typename Sig>
 struct result;

template <typename This, typename L>
 struct result<This(L)>
 {
 typedef typename result_of::ListType<L>::force_result_type type;
 };

template <typename L>
 typename result<Force(L)>::type
 operator()(const L & l) const
 {
 listlike::EnsureListLike<L>();
 return l.force();
 }

};

}
 //BOOST_PHOENIX_ADAPT_CALLABLE(head, impl::head, 1)
 //BOOST_PHOENIX_ADAPT_CALLABLE(tail, impl::tail, 1)
 //BOOST_PHOENIX_ADAPT_CALLABLE(null, impl::null, 1)
 typedef boost::phoenix::function<impl::Head> Head;
 typedef boost::phoenix::function<impl::Tail> Tail;
 typedef boost::phoenix::function<impl::Null> Null;
 typedef boost::phoenix::function<impl::Delay> Delay;
 typedef boost::phoenix::function<impl::Force> Force;
 Head head;
 Tail tail;
 Null null;
 Delay delay;
 Force force;

//////////////////////////////////////////////////////////////////////
// These definitions used for strict_list are imported from BoostFC++
// unchanged.
//////////////////////////////////////////////////////////////////////

namespace impl {
template <class T>
struct strict_cons : public boost::noncopyable {
 mutable RefCountType refC;
 T head;
 typedef boost::intrusive_ptr<strict_cons> tail_type;
 tail_type tail;
 strict_cons( const T& h, const tail_type& t ) : refC(0), head(h), tail(t) {}

};
template <class T>
void intrusive_ptr_add_ref( const strict_cons<T>* p ) {
 ++ (p->refC);
}
template <class T>
void intrusive_ptr_release( const strict_cons<T>* p ) {
 if( !--(p->refC) ) delete p;
}

template <class T>
class strict_list_iterator {
 typedef boost::intrusive_ptr<strict_cons<T> > rep_type;
 rep_type l;
 bool is_nil;
 void advance() {
 l = l->tail;
 if( !l )
 is_nil = true;
 }
 class Proxy { // needed for operator->
 const T x;
 friend class strict_list_iterator;
 Proxy( const T& xx ) : x(xx) {}
 public:
 const T* operator->() const { return &x; }
 };
public:
 typedef std::input_iterator_tag iterator_category;
 typedef T value_type;
 typedef ptrdiff_t difference_type;
 typedef T* pointer;
 typedef T& reference;

strict_list_iterator() : l(), is_nil(true) {}
 explicit strict_list_iterator( const rep_type& ll ) : l(ll), is_nil(!ll) {}
 
 const T operator*() const { return l->head; }
 const Proxy operator->() const { return Proxy(l->head); }
 strict_list_iterator<T>& operator++() {
 advance();
 return *this;
 }
 const strict_list_iterator<T> operator++(int) {
 strict_list_iterator<T> i( *this );
 advance();
 return i;
 }
 bool operator==( const strict_list_iterator<T>& i ) const {
 return is_nil && i.is_nil;
 }
 bool operator!=( const strict_list_iterator<T>& i ) const {
 return ! this->operator==(i);
 }
};
}

//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////

template <class T>
 class strict_list : public listlike::ListLike
 {
 typedef boost::intrusive_ptr<impl::strict_cons<T> > rep_type;
 rep_type rep;
 struct Make {};

template <class Iter>
 static rep_type help( Iter a, const Iter& b ) {
 rep_type r;
 while( a != b ) {
 T x( *a );
 r = rep_type( new impl::strict_cons<T>( x, r ) );
 ++a;
 }
 return r;
 }

public:
       static const bool is_lazy = false;

typedef T value_type;
 typedef strict_list force_result_type;
 typedef strict_list delay_result_type;
 typedef strict_list tail_result_type;
 template <class UU> struct cons_rebind {
 typedef strict_list<UU> type;
 typedef strict_list<UU> delay_type;
 };

strict_list( Make, const rep_type& r ) : rep(r) {}

strict_list() : rep() {}

strict_list( a_unique_type_for_nil ) : rep() {}

template <class F>
 strict_list( const F& f ) : rep( f().rep ) {
 // I cannot do this yet.
 //functoid_traits<F>::template ensure_accepts<0>::args();
 }

strict_list( const T& x, const strict_list& y )
 : rep( new impl::strict_cons<T>(x,y.rep) ) {}

template <class F>
 strict_list( const T& x, const F& f )
 : rep( new impl::strict_cons<T>(x,f().rep) ) {}
 
 operator bool() const { return (bool)rep; }
 force_result_type force() const { return *this; }
 delay_result_type delay() const { return *this; }
 T head() const {
#ifndef BOOST_PHOENIX_NO_LAZY_EXCEPTIONS
 if( !*this )
 throw lazy_exception("Tried to take head() of empty strict_list");
#endif
 return rep->head;
 }
 tail_result_type tail() const {
#ifndef BOOST_PHOENIX_NO_LAZY_EXCEPTIONS
 if( !*this )
 throw lazy_exception("Tried to take tail() of empty strict_list");
#endif
 return strict_list(Make(),rep->tail);
 }

template <class Iter>
 strict_list( const Iter& a, const Iter& b ) : rep( rep_type() ) {
 // How ironic. We need to reverse the iterator range in order to
 // non-recursively build this!
 std::vector<T> tmp(a,b);
 rep = help( tmp.rbegin(), tmp.rend() );
 }

// Since the strict_cons destructor can't call the strict_list
   // destructor, the "simple" iterative destructor is correct and
   // efficient.  Hurray.
   ~strict_list() { while(rep && (rep->refC == 1)) rep = rep->tail; }

// The following helps makes strict_list almost an STL "container"
 typedef impl::strict_list_iterator<T> const_iterator;
 typedef const_iterator iterator; // strict_list is immutable
 iterator begin() const { return impl::strict_list_iterator<T>( rep ); }
 iterator end() const { return impl::strict_list_iterator<T>(); }

};

// All of these null head and tail are now non lazy using e.g. null(a)().
 // They need an extra () e.g. null(a)().
 template <class T>
 bool operator==( const strict_list<T>& a, a_unique_type_for_nil ) {
 return null(a)();
 }
 template <class T>
 bool operator==( a_unique_type_for_nil, const strict_list<T>& a ) {
 return null(a)();
 }
 template <class T>
 bool operator==( const strict_list<T>& a, const strict_list<T>& b ) {
 if( null(a)() && null(b)() )
 return true;
 if( null(a)() || null(b)() )
 return false;
 return (head(a)()==head(b)()) &&
 (tail(a)()==tail(b)());
 }

template <class T>
 bool operator<( const strict_list<T>& a, const strict_list<T>& b ) {
 if( null(a)() && !null(b)() ) return true;
 if( null(b)() ) return false;
 if( head(b)() < head(a)() ) return false;
 if( head(a)() < head(b)() ) return true;
 return (tail(a)() < tail(b)());
 }
 template <class T>
 bool operator<( const strict_list<T>&, a_unique_type_for_nil ) {
 return false;
 }
 template <class T>
 bool operator<( a_unique_type_for_nil, const strict_list<T>& b ) {
 return !(null(b)());
 }

//////////////////////////////////////////////////////////////////////
// Class list<T> is the primary interface to the user for lazy lists.
//////////////////////////////////////////////////////////////////////{
 namespace impl {
 using fcpp::INV;
 using fcpp::VAR;
 using fcpp::reuser2;

struct CacheEmpty {};

template <class T> class Cache;
 template <class T> class odd_list;
 template <class T> class list_iterator;
 template <class It, class T>
 struct ListItHelp2 /*: public c_fun_type<It,It,odd_list<T> >*/ {
 // This will need a return type.
 typedef odd_list<T> return_type;
 odd_list<T> operator()( It begin, const It& end,
 reuser2<INV,VAR,INV,ListItHelp2<It,T>,It,It> r = NIL ) const;
 };
 template <class U,class F> struct cvt;
 template <class T, class F, class R> struct ListHelp;
 template <class T> Cache<T>* xempty_helper();
 template <class T, class F, class L, bool b> struct ConsHelp2;

struct ListRaw {};

template <class T>
 class list : public listlike::ListLike
 {
 // never NIL, unless an empty odd_list
 boost::intrusive_ptr<Cache<T> > rep;

template <class U> friend class Cache;
 template <class U> friend class odd_list;
 template <class TT, class F, class L, bool b> friend struct ConsHelp2;
 template <class U,class F> friend struct cvt;

list( const boost::intrusive_ptr<Cache<T> >& p ) : rep(p) { }
 list( ListRaw, Cache<T>* p ) : rep(p) { }

bool priv_isEmpty() const {
 return rep->cache().second.rep == Cache<T>::XNIL();
 }
 T priv_head() const {
#ifndef BOOST_PHOENIX_NO_LAZY_EXCEPTIONS
 if( priv_isEmpty() )
 throw lazy_exception("Tried to take head() of empty list");
#endif
 return rep->cache().first();
 }
 list<T> priv_tail() const {
#ifndef BOOST_PHOENIX_NO_LAZY_EXCEPTIONS
 if( priv_isEmpty() )
 throw lazy_exception("Tried to take tail() of empty list");
#endif
 return rep->cache().second;
 }

public:
        static const bool is_lazy = true;

typedef T value_type;
 typedef list tail_result_type;
 typedef odd_list<T> force_result_type;
 typedef list delay_result_type;
 template <class UU> struct cons_rebind {
 typedef odd_list<UU> type;
 typedef list<UU> delay_type;
 };

list( a_unique_type_for_nil ) : rep( Cache<T>::XEMPTY() ) { }
 list() : rep( Cache<T>::XEMPTY() ) { }

template <class F> // works on both ()->odd_list and ()->list
 // At the moment this is fixed for odd_list<T>.
 // I need to do more work to get the general result.
 list( const F& f )
 : rep( ListHelp<T,F,odd_list<T> >()(f) ) { }
 //: rep( ListHelp<T,F,typename F::result_type>()(f) ) { }

operator bool() const { return !priv_isEmpty(); }
 const force_result_type& force() const { return rep->cache(); }
 const delay_result_type& delay() const { return *this; }
 // Note: force returns a reference;
 // implicit conversion now returns a copy.
 operator odd_list<T>() const { return force(); }

T head() const { return priv_head(); }
        tail_result_type tail() const { return priv_tail(); }

// The following helps makes list almost an STL "container"
 typedef list_iterator<T> const_iterator;
 typedef const_iterator iterator; // list is immutable
 iterator begin() const { return list_iterator<T>( *this ); }
 iterator end() const { return list_iterator<T>(); }

// end of list<T>
 };

//////////////////////////////////////////////////////////////////////
// Class odd_list<T> is not normally accessed by the user.
//////////////////////////////////////////////////////////////////////

struct OddListDummyY {};

template <class T>
 class odd_list : public listlike::ListLike
 {
 public:
 typedef
 typename boost::type_with_alignment<boost::alignment_of<T>::value>::type
 xfst_type;
 private:
 union { xfst_type fst; unsigned char dummy[sizeof(T)]; };

const T& first() const {
 return *static_cast<const T*>(static_cast<const void*>(&fst));
 }
 T& first() {
 return *static_cast<T*>(static_cast<void*>(&fst));
 }
 list<T> second; // If XNIL, then this odd_list is NIL

template <class U> friend class list;
 template <class U> friend class Cache;

odd_list( OddListDummyY )
 : second( Cache<T>::XBAD() ) { }

void init( const T& x ) {
 new (static_cast<void*>(&fst)) T(x);
 }

bool fst_is_valid() const {
 if( second.rep != Cache<T>::XNIL() )
 if( second.rep != Cache<T>::XBAD() )
 return true;
 return false;
 }

bool priv_isEmpty() const { return second.rep == Cache<T>::XNIL(); }
 T priv_head() const {
#ifndef BOOST_PHOENIX_NO_LAZY_EXCEPTIONS
 if( priv_isEmpty() )
 throw lazy_exception("Tried to take head() of empty odd_list");
#endif
 return first();
 }

list<T> priv_tail() const {
#ifndef BOOST_PHOENIX_NO_LAZY_EXCEPTIONS
 if( priv_isEmpty() )
 throw lazy_exception("Tried to take tail() of empty odd_list");
#endif
 return second;
 }

public:
        static const bool is_lazy = true;

typedef T value_type;
 typedef list<T> tail_result_type;
 typedef odd_list<T> force_result_type;
 typedef list<T> delay_result_type;
 template <class UU> struct cons_rebind {
 typedef odd_list<UU> type;
 typedef list<UU> delay_type;
 };

odd_list() : second( Cache<T>::XNIL() ) { }
 odd_list( a_unique_type_for_nil ) : second( Cache<T>::XNIL() ) { }
 odd_list( const T& x, const list<T>& y ) : second(y) { init(x); }
 odd_list( const T& x, a_unique_type_for_nil ) : second(NIL) { init(x); }

odd_list( const odd_list<T>& x ) : second(x.second) {
 if( fst_is_valid() ) {
 init( x.first() );
 }
 }

template <class It>
 odd_list( It begin, const It& end )
 : second( begin==end ? Cache<T>::XNIL() :
 ( init(*begin++), list<T>( begin, end ) ) ) {}

odd_list<T>& operator=( const odd_list<T>& x ) {
 if( this == &x ) return *this;
 if( fst_is_valid() ) {
 if( x.fst_is_valid() )
 first() = x.first();
 else
 first().~T();
 }
 else {
 if( x.fst_is_valid() )
 init( x.first() );
 }
 second = x.second;
 return *this;
 }
 
 ~odd_list() {
 if( fst_is_valid() ) {
 first().~T();
 }
 }

operator bool() const { return !priv_isEmpty(); }
 const force_result_type& force() const { return *this; }
 delay_result_type delay() const { return list<T>(*this); }

T head() const { return priv_head(); }
        tail_result_type tail() const { return priv_tail(); }

// The following helps makes odd_list almost an STL "container"
 typedef list_iterator<T> const_iterator;
 typedef const_iterator iterator; // odd_list is immutable
 iterator begin() const { return list_iterator<T>( this->delay() ); }
 iterator end() const { return list_iterator<T>(); }

// end of odd_list<T>
 };

//////////////////////////////////////////////////////////////////////
// struct cvt
//////////////////////////////////////////////////////////////////////

// This converts ()->list<T> to ()->odd_list<T>.
 // In other words, here is the 'extra work' done when using the
 // unoptimized interface.
 template <class U,class F>
 struct cvt /*: public c_fun_type<odd_list >*/ {
 typedef odd_list return_type;
 F f;
 cvt( const F& ff ) : f(ff) {}
 odd_list operator()() const {
 list l = f();
 return l.force();
 }
 };

//////////////////////////////////////////////////////////////////////
// Cache<T> and associated functions.
//////////////////////////////////////////////////////////////////////

// I malloc a RefCountType to hold the refCount and init it to 1 to ensure the
// refCount will never get to 0, so the destructor-of-global-object
// order at the end of the program is a non-issue. In other words, the
// memory allocated here is only reclaimed by the operating system.
 template <class T>
 Cache<T>* xnil_helper() {
 void *p = std::malloc( sizeof(RefCountType) );
 *((RefCountType*)p) = 1;
 return static_cast<Cache<T>*>( p );
 }

template <class T>
 Cache<T>* xnil_helper_nil() {
 Cache<T>* p = xnil_helper<T>();
 return p;
 }

template <class T>
 Cache<T>* xnil_helper_bad() {
 Cache<T>* p = xnil_helper<T>();
 return p;
 }

template <class T>
 Cache<T>* xempty_helper() {
 Cache<T>* p = new Cache<T>( CacheEmpty() );
 return p;
 }

// This makes a boost phoenix function type with return type
 // odd_list<T>
 template <class T>
 struct fun0_type_helper{
 typedef boost::function0<odd_list<T> > fun_type;
 typedef boost::phoenix::function<fun_type> phx_type;
 };

template <class T>
 struct make_fun0_odd_list {

typedef typename fun0_type_helper<T>::fun_type fun_type;
 typedef typename fun0_type_helper<T>::phx_type phx_type;
 typedef phx_type result_type;

template <class F>
 result_type operator()(const F& f) const
 {
 fun_type ff(f);
 phx_type g(ff);
 return g;
 }

// Overload for the case where it is a boost phoenix function already.
 template <class F>
 typename boost::phoenix::function<F> operator()
 (const boost::phoenix::function<F>& f) const
 {
 return f;
 }

};

template <class T>
 class Cache : boost::noncopyable {
 mutable RefCountType refC;
 // This is the boost::function type
 typedef typename fun0_type_helper<T>::fun_type fun_odd_list_T;
 // This is the boost::phoenix::function type;
 typedef typename fun0_type_helper<T>::phx_type fun0_odd_list_T;
 mutable fun0_odd_list_T fxn;
 mutable odd_list<T> val;
 // val.second.rep can be XBAD, XNIL, or a valid ptr
 // - XBAD: val is invalid (fxn is valid)
 // - XNIL: this is the empty list
 // - anything else: val.first() is head, val.second is tail()

// This functoid should never be called; it represents a
 // self-referent Cache, which should be impossible under the current
 // implementation. Nonetheless, we need a 'dummy' function object to
 // represent invalid 'fxn's (val.second.rep!=XBAD), and this
 // implementation seems to be among the most reasonable.
 struct blackhole_helper /*: c_fun_type< odd_list<T> >*/ {
 typedef odd_list<T> return_type;
 odd_list<T> operator()() const {
#ifndef BOOST_PHOENIX_NO_LAZY_EXCEPTIONS
 throw lazy_exception("You have entered a black hole.");
#else
 return odd_list<T>();
#endif
 }
 };

// Don't get rid of these XFOO() functions; they impose no overhead,
 // and provide a useful place to add debugging code for tracking down
 // before-main()-order-of-initialization problems.
 static const boost::intrusive_ptr<Cache<T> >& XEMPTY() {
 static boost::intrusive_ptr<Cache<T> > xempty( xempty_helper<T>() );
 return xempty;
 }
 static const boost::intrusive_ptr<Cache<T> >& XNIL() {
 // this list is nil
 static boost::intrusive_ptr<Cache<T> > xnil( xnil_helper_nil<T>() );
 return xnil;
 }

static const boost::intrusive_ptr<Cache<T> >& XBAD() {
 // the pair is invalid; use fxn
 static boost::intrusive_ptr<Cache<T> > xbad( xnil_helper_bad<T>() );
 return xbad;
 }

static fun0_odd_list_T /*<odd_list<T> >*/ the_blackhole;
 static fun0_odd_list_T& blackhole() {
 static fun0_odd_list_T the_blackhole;
 //( make_fun0_odd_list<T>()( blackhole_helper() ) );
 return the_blackhole;
 }

odd_list<T>& cache() const {
 if( val.second.rep == XBAD() ) {
 val = fxn()();
 fxn = blackhole();
 }
 return val;
 }

template <class U> friend class list;
 template <class U> friend class odd_list;
 template <class TT, class F, class L, bool b> friend struct ConsHelp2;
 template <class U,class F> friend struct cvt;
 template <class U, class F, class R> friend struct ListHelp;
 template <class U> friend Cache* xempty_helper();

Cache( CacheEmpty ) : refC(0), fxn(blackhole()), val() {}
 Cache( const odd_list<T>& x ) : refC(0), fxn(blackhole()), val(x) {}
 Cache( const T& x, const list<T>& l ) : refC(0),fxn(blackhole()),val(x,l)
 {}

Cache( const fun0_odd_list_T& f )
         : refC(0), fxn(f), val( OddListDummyY() ) {}

// f must be a boost phoenix function object?
 template <class F>
 Cache( const F& f ) // ()->odd_list
 : refC(0), fxn(make_fun0_odd_list<T>()(f)), val( OddListDummyY() ) {}

// This is for ()->list<T> to ()->odd_list<T>
 struct CvtFxn {};
 template <class F>
 Cache( CvtFxn, const F& f ) // ()->list
 : refC(0), fxn(make_fun0_odd_list<T>()(cvt<T,F>(f))), val( OddListDummyY() ) {}

template <class X>
 friend void intrusive_ptr_add_ref( const Cache<X>* p );
 template <class X>
 friend void intrusive_ptr_release( const Cache<X>* p );
 };

template <class T>
 void intrusive_ptr_add_ref( const Cache<T>* p ) {
 ++ (p->refC);
 }
 template <class T>
 void intrusive_ptr_release( const Cache<T>* p ) {
 if( !--(p->refC) ) delete p;
 }

//////////////////////////////////////////////////////////////////////
// Rest of list's stuff
//////////////////////////////////////////////////////////////////////

template <class T, class F> struct ListHelp<T,F,list<T> > {
 boost::intrusive_ptr<Cache<T> > operator()( const F& f ) const {
 return boost::intrusive_ptr<Cache<T> >
 (new Cache<T>(typename Cache<T>::CvtFxn(),f));
 }
};
template <class T, class F> struct ListHelp<T,F,odd_list<T> > {
 boost::intrusive_ptr<Cache<T> > operator()( const F& f ) const {
 return boost::intrusive_ptr<Cache<T> >(new Cache<T>(f));
 }
};

template <class T>
class list_iterator {
 list<T> l;
 bool is_nil;
 void advance() {
 l = l.tail();
 if( !l )
 is_nil = true;
 }
 class Proxy { // needed for operator->
 const T x;
 friend class list_iterator;
 Proxy( const T& xx ) : x(xx) {}
 public:
 const T* operator->() const { return &x; }
 };
public:
 typedef std::input_iterator_tag iterator_category;
 typedef T value_type;
 typedef ptrdiff_t difference_type;
 typedef T* pointer;
 typedef T& reference;

list_iterator() : l(), is_nil(true) {}
 explicit list_iterator( const list<T>& ll ) : l(ll), is_nil(!ll) {}
 
 const T operator*() const { return l.head(); }
 const Proxy operator->() const { return Proxy(l.head()); }
 list_iterator<T>& operator++() {
 advance();
 return *this;
 }
 const list_iterator<T> operator++(int) {
 list_iterator<T> i( *this );
 advance();
 return i;
 }
 bool operator==( const list_iterator<T>& i ) const {
 return is_nil && i.is_nil;
 }
 bool operator!=( const list_iterator<T>& i ) const {
 return ! this->operator==(i);
 }
};

} // namespace impl

using impl::list;
  using impl::odd_list;
  using impl::list_iterator;

//////////////////////////////////////////////////////////////////////
// op== and op<, overloaded for all combos of list, odd_list, and NIL
//////////////////////////////////////////////////////////////////////
// All of these null head and tail are now non lazy using e.g. null(a)().
// They need an extra () e.g. null(a)().

// FIX THIS comparison operators can be implemented simpler with enable_if
template <class T>
bool operator==( const odd_list<T>& a, a_unique_type_for_nil ) {
 return null(a)();
}
template <class T>
bool operator==( const list<T>& a, a_unique_type_for_nil ) {
 return null(a)();
}
template <class T>
bool operator==( a_unique_type_for_nil, const odd_list<T>& a ) {
 return null(a)();
}
template <class T>
bool operator==( a_unique_type_for_nil, const list<T>& a ) {
 return null(a)();
}
template <class T>
bool operator==( const list<T>& a, const list<T>& b ) {
 if( null(a)() && null(b)() )
 return true;
 if( null(a)() || null(b)() )
 return false;
 return (head(a)()==head(b)()) && (tail(a)()==tail(b)());
}
template <class T>
bool operator==( const odd_list<T>& a, const odd_list<T>& b ) {
 if( null(a)() && null(b)() )
 return true;
 if( null(a)() || null(b)() )
 return false;
 return (head(a)()==head(b)()) && (tail(a)()==tail(b)());
}
template <class T>
bool operator==( const list<T>& a, const odd_list<T>& b ) {
 if( null(a)() && null(b)() )
 return true;
 if( null(a)() || null(b)() )
 return false;
 return (head(a)()==head(b)()) && (tail(a)()==tail(b)());
}
template <class T>
bool operator==( const odd_list<T>& a, const list<T>& b ) {
 if( null(a)() && null(b)() )
 return true;
 if( null(a)() || null(b)() )
 return false;
 return (head(a)()==head(b)()) && (tail(a)()==tail(b)());
}

template <class T>
bool operator<( const list<T>& a, const list<T>& b ) {
 if( null(a)() && !null(b)() ) return true;
 if( null(b)() ) return false;
 if( head(b)() < head(a)() ) return false;
 if( head(a)() < head(b)() ) return true;
 return (tail(a)() < tail(b)());
}
template <class T>
bool operator<( const odd_list<T>& a, const list<T>& b ) {
 if( null(a)() && !null(b)() ) return true;
 if( null(b)() ) return false;
 if( head(b)() < head(a)() ) return false;
 if( head(a)() < head(b)() ) return true;
 return (tail(a)() < tail(b)());
}
template <class T>
bool operator<( const list<T>& a, const odd_list<T>& b ) {
 if( null(a) && !null(b) ) return true;
 if( null(b) ) return false;
 if( head(b) < head(a) ) return false;
 if( head(a) < head(b) ) return true;
 return (tail(a) < tail(b));
}
template <class T>
bool operator<( const odd_list<T>& a, const odd_list<T>& b ) {
 if( null(a)() && !null(b)() ) return true;
 if( null(b)() ) return false;
 if( head(b)() < head(a)() ) return false;
 if( head(a)() < head(b)() ) return true;
 return (tail(a)() < tail(b)());
}
template <class T>
bool operator<( const odd_list<T>&, a_unique_type_for_nil ) {
 return false;
}
template <class T>
bool operator<( const list<T>&, a_unique_type_for_nil ) {
 return false;
}
template <class T>
bool operator<( a_unique_type_for_nil, const odd_list<T>& b ) {
 return !null(b)();
}
template <class T>
bool operator<( a_unique_type_for_nil, const list<T>& b ) {
 return !null(b)();
}

//////////////////////////////////////////////////////////////////////
// Implement cat and cons after the list types are defined.
//////////////////////////////////////////////////////////////////////
    namespace impl {
      using listlike::ListLike;

template <class T, class F, class L>
 struct ConsHelp2<T,F,L,true>
 {
 typedef typename boost::remove_reference<T>::type TT;
 typedef typename L::force_result_type type;
 static type go( const TT& x, const F& f ) {
 return type( x, f );
 }
 };
 template <class T, class F>
 struct ConsHelp2<T,F,list<T>,true>
 {
 typedef typename boost::remove_reference<T>::type TT;
 typedef list<TT> L;
 typedef typename L::force_result_type type;
 static type go( const TT& x, const F& f ) {
 return odd_list<TT>(x, list<TT>(
 boost::intrusive_ptr<Cache<TT> >(new Cache<T>(
 typename Cache<TT>::CvtFxn(),f))));
 }
 };
 template <class T, class F>
 struct ConsHelp2<T,F,odd_list<T>,true>
 {
 typedef typename boost::remove_reference<T>::type TT;
 typedef odd_list<TT> L;
 typedef typename L::force_result_type type;
 static type go( const TT& x, const F& f ) {
 return odd_list<TT>(x, list<TT>( ListRaw(), new Cache<T>(f) ));
 }
 };
 template <class T, class F>
 struct ConsHelp2<T,F,a_unique_type_for_nil,false>
 {
 typedef typename boost::remove_reference<T>::type TT;
 typedef odd_list<TT> type;
 static type go( const TT& x, const F& f ) {
 return odd_list<TT>(x, list<TT>( ListRaw(), new Cache<T>(f) ));
 }
 };

template <class T, class L, bool b> struct ConsHelp1 {
 typedef typename boost::remove_reference<T>::type TT;
 typedef typename L::force_result_type type;
 static type go( const TT& x, const L& l ) {
 return type(x,l);
 }
 };
 template <class T> struct ConsHelp1<T,a_unique_type_for_nil,false> {
 typedef typename boost::remove_reference<T>::type TT;
 typedef odd_list<TT> type;
 static type go( const TT& x, const a_unique_type_for_nil& n ) {
 return type(x,n);
 }
 };
 template <class T, class F> struct ConsHelp1<T,F,false> {
 // It's a function returning a list
 // This is the one I have not fixed yet....
 // typedef typename F::result_type L;
 // typedef typename result_of::template ListType<F>::result_type L;
 typedef odd_list<T> L;
 typedef ConsHelp2<T,F,L,boost::is_base_and_derived<ListLike,L>::value> help;
 typedef typename help::type type;
 static type go( const T& x, const F& f ) {
 return help::go(x,f);
 }
 };

template <class T, class L, bool b>
 struct ConsHelp0;

template <class T>
 struct ConsHelp0<T,a_unique_type_for_nil,true> {
 typedef typename boost::remove_reference<T>::type TT;
 typedef odd_list<T> type;
 };

template <class T>
 struct ConsHelp0<const T &,const a_unique_type_for_nil &,true> {
 typedef typename boost::remove_reference<T>::type TT;
 typedef odd_list<TT> type;
 };

template <class T>
 struct ConsHelp0<T &,a_unique_type_for_nil &,true> {
 typedef typename boost::remove_reference<T>::type TT;
 typedef odd_list<TT> type;
 };

template <class T, class L>
 struct ConsHelp0<T,L,false> {
 // This removes any references from L for correct return type
 // identification.
 typedef typename boost::remove_reference<L>::type LType;
 typedef typename ConsHelp1<T,LType,
 boost::is_base_and_derived<ListLike,LType>::value>::type type;
 };

/////////////////////////////////////////////////////////////////////
 // cons (t,l) - cons a value to the front of a list.
 // Note: The first arg, t, must be a value.
 // The second arg, l, can be a list or NIL
 // or a function that returns a list.
 /////////////////////////////////////////////////////////////////////
 struct Cons
 {
 /* template <class T, class L> struct sig : public fun_type<
 typename ConsHelp1<T,L,
 boost::is_base_and_derived<ListLike,L>::value>::type> {};
 */
 template <typename Sig> struct result;

template <typename This, typename T, typename L>
 struct result<This(T, L)>
 {
 typedef typename ConsHelp0<T,L,
 listlike::detect_nil<L>::is_nil>::type type;
 };

template <typename This, typename T>
 struct result<This(T,a_unique_type_for_nil)>
 {
 typedef typename boost::remove_reference<T>::type TT;
 typedef odd_list<TT> type;
 };

template <typename T, typename L>
 typename result<Cons(T,L)>::type
 operator()( const T& x, const L& l ) const {
 typedef typename result_of::ListType<L>::LType LType;
 typedef ConsHelp1<T,LType,
 boost::is_base_and_derived<ListLike,LType>::value> help;
 return help::go(x,l);
 }
 
 template <typename T>
 typename result<Cons(T,a_unique_type_for_nil)>::type
 operator()( const T& x, const a_unique_type_for_nil &n ) const {
 typedef typename result<Cons(T,a_unique_type_for_nil)>::type LL;
 typedef ConsHelp1<T,LL,
 boost::is_base_and_derived<ListLike,LL>::value> help;
 return help::go(x,n);
 }

};
    }

typedef boost::phoenix::function<impl::Cons> Cons;
 Cons cons;

namespace impl {

template <class L, class M, bool b>
 struct CatHelp0;

template <class LL>
 struct CatHelp0<LL,a_unique_type_for_nil,true> {
 typedef typename result_of::template ListType<LL>::LType type;
 };

template <class LL>
 struct CatHelp0<const LL &,const a_unique_type_for_nil &,true> {
 typedef typename result_of::template ListType<LL>::LType type;
 //typedef L type;
 };

template <class LL>
 struct CatHelp0<LL &,a_unique_type_for_nil &,true> {
 typedef typename result_of::template ListType<LL>::LType type;
 //typedef L type;
 };

template <class LL, class MM>
 struct CatHelp0<LL,MM,false> {
 // This removes any references from L for correct return type
 // identification.
 typedef typename result_of::template ListType<LL>::LType type;
 // typedef typename ConsHelp1<T,LType,
 // boost::is_base_and_derived<ListLike,LType>::value>::type type;
 };

/////////////////////////////////////////////////////////////////////
 // cat (l,m) - concatenate lists.
 // Note: The first arg, l, must be a list or NIL.
 // The second arg, m, can be a list or NIL
 // or a function that returns a list.
 /////////////////////////////////////////////////////////////////////
 struct Cat
 {
 template <class L, class M, bool b, class R>
 struct Helper /*: public c_fun_type<L,M,R>*/ {
 template <typename Sig> struct result;
 
 template <typename This>
 struct result<This(L,M)>
 {
 typedef typename result_of::ListType<L>::tail_result_type type;
 };

typedef R return_type;
 R operator()( const L& l, const M& m,
 reuser2<INV,VAR,INV,Helper,
 typename result_of::template ListType<L>::tail_result_type,M>
 r = NIL ) const {
 if( null(l)() )
 return m().force();
 else
 return cons( head(l)(), r( Helper<L,M,b,R>(), tail(l), m )() );
 }
 };
 template <class L, class M, class R>
 struct Helper<L,M,true,R> /*: public c_fun_type<L,M,R>*/ {
 template <typename Sig> struct result;
 
 template <typename This>
 struct result<This(L,M)>
 {
 typedef typename result_of::ListType<L>::tail_result_type type;
 };
 typedef R return_type;
 R operator()( const L& l, const M& m,
 reuser2<INV,VAR,INV,Helper,
 typename result_of::template ListType<L>::tail_result_type,M>
 r = NIL ) const {
 if( null(l)() )
 return m.force();
 else
 return cons( head(l)(), r(Helper<L,M,true,R>(), tail(l), m )());
 }
 };
 template <class L, class R>
 struct Helper<L,a_unique_type_for_nil,false,R>
 /*: public c_fun_type<L,
 a_unique_type_for_nil,odd_list<typename L::value_type> > */
 {
 typedef odd_list<typename result_of::template ListType<L>::value_type> type;
 odd_list<typename result_of::template ListType<L>::value_type>
 operator()( const L& l, const a_unique_type_for_nil& ) const {
 return l;
 }
 };
 public:
 /*template <class L, class M> struct sig : public fun_type<
 typename RT<cons_type,typename L::value_type,M>::result_type>
 {}; */
 // Need to work out the return type here.
 template <typename Sig> struct result;

template <typename This, typename L, typename M>
 struct result<This(L,M)>
 {
 typedef typename CatHelp0<L,M,
 listlike::detect_nil<M>::is_nil>::type type;
 // typedef typename result_of::ListType<L>::tail_result_type type;
 };
 
 template <typename This, typename L>
 struct result<This(L,a_unique_type_for_nil)>
 {
 typedef typename result_of::ListType<L>::tail_result_type type;
 };
 template <class L, class M>
 typename result<Cat(L,M)>::type operator()( const L& l, const M& m ) const
 {
 listlike::EnsureListLike<L>();
 return Helper<L,M,
 boost::is_base_and_derived<typename listlike::ListLike,M>::value,
 typename result<Cat(L,M)>::type>()(l,m);
 }

template <class L>
 typename result<Cat(L,a_unique_type_for_nil)>::type operator()( const L& l, const a_unique_type_for_nil& /* n */ ) const
 {
 listlike::EnsureListLike<L>();
 return l;
 }
 
 };

}

typedef boost::phoenix::function<impl::Cat> Cat;
 Cat cat;

//////////////////////////////////////////////////////////////////////
// Handy functions for making list literals
//////////////////////////////////////////////////////////////////////
// Yes, these aren't functoids, they're just template functions.  I'm
// lazy and created these mostly to make it easily to make little lists
// in the sample code snippets that appear in papers.

struct UseList {
 template <class T> struct List { typedef list<T> type; };
};
struct UseOddList {
 template <class T> struct List { typedef odd_list<T> type; };
};
struct UseStrictList {
 template <class T> struct List { typedef strict_list<T> type; };
};

template <class Kind = UseList>
struct list_with {
 template <class T>
 typename Kind::template List<T>::type
 operator()( const T& a ) const {
 typename Kind::template List<T>::type l;
 l = cons( a, l );
 return l;
 }
 
 template <class T>
 typename Kind::template List<T>::type
 operator()( const T& a, const T& b ) const {
 typename Kind::template List<T>::type l;
 l = cons( b, l );
 l = cons( a, l );
 return l;
 }
 
 template <class T>
 typename Kind::template List<T>::type
 operator()( const T& a, const T& b, const T& c ) const {
 typename Kind::template List<T>::type l;
 l = cons( c, l );
 l = cons( b, l );
 l = cons( a, l );
 return l;
 }
 
 template <class T>
 typename Kind::template List<T>::type
 operator()( const T& a, const T& b, const T& c, const T& d ) const {
 typename Kind::template List<T>::type l;
 l = cons( d, l );
 l = cons( c, l );
 l = cons( b, l );
 l = cons( a, l );
 return l;
 }
 
 template <class T>
 typename Kind::template List<T>::type
 operator()( const T& a, const T& b, const T& c, const T& d,
 const T& e ) const {
 typename Kind::template List<T>::type l;
 l = cons( e, l );
 l = cons( d, l );
 l = cons( c, l );
 l = cons( b, l );
 l = cons( a, l );
 return l;
 }
};
//////////////////////////////////////////////////////////////////////

}

#endif

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