refactor(util/lazy_list): 'lazier' lazy_lists

In the new implementation, even the head of the lazy list is computed on demand.

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/library/tactic/tactic.cpp

@@ -6,6 +6,7 @@ Author: Leonardo de Moura
 */
 #include <utility>
 #include <chrono>
+#include "util/sstream.h"
 #include "util/interrupt.h"
 #include "util/lazy_list_fn.h"
 #include "library/tactic/tactic_exception.h"
@@ -22,9 +23,10 @@ tactic & tactic::operator=(tactic && s) {
 
 expr tactic::solve(environment const & env, io_state const & io, proof_state const & s) {
     proof_state_seq r   = operator()(env, io, s);
-    if (!r)
+    auto p = r.pull();
+    if (!p)
         throw exception("tactic failed to solve input");
-    proof_state final = head(r);
+    proof_state final = p->first;
     assignment a(final.get_menv());
     proof_map  m;
     return final.get_proof_builder()(m, env, a);
@@ -37,7 +39,7 @@ expr tactic::solve(environment const & env, io_state const & io, context const &
 
 tactic id_tactic() {
     return mk_tactic([](environment const &, io_state const &, proof_state const & s) -> proof_state_seq {
-            return proof_state_seq(s);
+            return to_proof_state_seq(s);
         });
 }
 
@@ -52,10 +54,28 @@ tactic now_tactic() {
             if (!empty(s.get_goals()))
                 return proof_state_seq();
             else
-                return proof_state_seq(s);
+                return to_proof_state_seq(s);
         });
 }
 
+tactic trace_tactic(std::string const & msg) {
+    return mk_tactic([=](environment const &, io_state const & io, proof_state const & s) -> proof_state_seq {
+            return proof_state_seq([=]() {
+                    io.get_diagnostic_channel() << msg << "\n";
+                    io.get_diagnostic_channel().get_stream().flush();
+                    return some(mk_pair(s, proof_state_seq()));
+                });
+        });
+}
+
+tactic trace_tactic(sstream const & msg) {
+    return trace_tactic(msg.str());
+}
+
+tactic trace_tactic(char const * msg) {
+    return trace_tactic(std::string(msg));
+}
+
 tactic assumption_tactic() {
     return mk_tactic([](environment const &, io_state const &, proof_state const & s) -> proof_state_seq {
             list<std::pair<name, expr>> proofs;
@@ -84,7 +104,7 @@ tactic assumption_tactic() {
                     }
                     return p(new_m, env, a);
                 });
-            return proof_state_seq(proof_state(s, new_goals, new_p));
+            return to_proof_state_seq(proof_state(s, new_goals, new_p));
         });
 }
 
@@ -102,14 +122,8 @@ tactic then(tactic t1, tactic t2) {
 tactic orelse(tactic t1, tactic t2) {
     return mk_tactic([=](environment const & env, io_state const & io, proof_state const & s) -> proof_state_seq {
             tactic _t1(t1);
-            proof_state_seq r = _t1(env, io, s);
+            tactic _t2(t2);
-            if (r) {
+            return orelse(_t1(env, io, s), _t2(env, io, s));
-                return r;
-            } else {
-                check_interrupted();
-                tactic _t2(t2);
-                return _t2(env, io, s);
-            }
         });
 }
 
@@ -200,10 +214,7 @@ tactic par(tactic t1, tactic t2, unsigned check_ms) {
                 th2.request_interrupt();
                 th1.join();
                 th2.join();
-                if (r1)
+                return orelse(r1, r2);
-                    return r1;
-                else
-                    return r2;
             } catch (...) {
                 th1.request_interrupt();
                 th2.request_interrupt();
@@ -218,10 +229,11 @@ tactic repeat(tactic t) {
     return mk_tactic([=](environment const & env, io_state const & io, proof_state const & s1) -> proof_state_seq {
             tactic t1(t);
             proof_state_seq r = t1(env, io, s1);
-            if (!r) {
+            auto p = r.pull();
-                return proof_state_seq(s1);
+            if (!p) {
+                return to_proof_state_seq(s1);
             } else {
-                return map_append(r, [=](proof_state const & s2) {
+                return map_append(to_proof_state_seq(p), [=](proof_state const & s2) {
                         check_interrupted();
                         tactic t2 = repeat(t1);
                         return t2(env, io, s2);
@@ -233,13 +245,14 @@ tactic repeat(tactic t) {
 tactic repeat_at_most(tactic t, unsigned k) {
     return mk_tactic([=](environment const & env, io_state const & io, proof_state const & s1) -> proof_state_seq {
             if (k == 0)
-                return proof_state_seq(s1);
+                return to_proof_state_seq(s1);
             tactic t1(t);
             proof_state_seq r = t1(env, io, s1);
-            if (!r) {
+            auto p = r.pull();
-                return proof_state_seq(s1);
+            if (!p) {
+                return to_proof_state_seq(s1);
             } else {
-                return map_append(r, [=](proof_state const & s2) {
+                return map_append(to_proof_state_seq(p), [=](proof_state const & s2) {
                         check_interrupted();
                         tactic t2 = repeat_at_most(t1, k - 1);
                         return t2(env, io, s2);
@@ -260,10 +273,10 @@ tactic force(tactic t) {
             tactic _t(t);
             proof_state_seq r = _t(env, io, s);
             buffer<proof_state> buf;
-            for (auto s2 : r) {
+            for_each(r, [&](proof_state const & s2) {
-                buf.push_back(s2);
+                    buf.push_back(s2);
-                check_interrupted();
+                    check_interrupted();
-            }
+                });
             return to_lazy(to_list(buf.begin(), buf.end()));
         });
 }

src/library/tactic/tactic.h

@@ -9,6 +9,7 @@ Author: Leonardo de Moura
 #include <utility>
 #include <memory>
 #include <mutex>
+#include <string>
 #include "util/lazy_list.h"
 #include "library/io_state.h"
 #include "library/tactic/proof_state.h"
@@ -64,6 +65,19 @@ public:
 template<typename F>
 tactic mk_tactic(F && f) { return tactic(new simple_tactic_cell<F>(std::forward<F>(f))); }
 
+inline proof_state_seq to_proof_state_seq(proof_state const & s) {
+    return proof_state_seq([=]() { return some(mk_pair(s, proof_state_seq())); });
+}
+
+inline proof_state_seq to_proof_state_seq(proof_state_seq::maybe_pair const & p) {
+    lean_assert(p);
+    return proof_state_seq([=]() { return some(mk_pair(p->first, p->second)); });
+}
+
+inline proof_state_seq to_proof_state_seq(proof_state const & s, proof_state_seq const & t) {
+    return proof_state_seq([=]() { return some(mk_pair(s, t)); });
+}
+
 /**
    \brief Return a "do nothing" tactic (aka skip).
 */
@@ -80,15 +94,25 @@ tactic now_tactic();
    \brief Return a tactic that solves any goal of the form  <tt>..., H : A, ... |- A</tt>.
 */
 tactic assumption_tactic();
+/**
+   \brief Return a tactic that just returns the input state, and display the given message in the diagnostic channel.
+*/
+tactic trace_tactic(char const * msg);
+class sstream;
+tactic trace_tactic(sstream const & msg);
+tactic trace_tactic(std::string const & msg);
+
 /**
    \brief Return a tactic that performs \c t1 followed by \c t2.
 */
 tactic then(tactic t1, tactic t2);
+inline tactic operator<<(tactic t1, tactic t2) { return then(t1, t2); }
 /**
    \brief Return a tactic that applies \c t1, and if \c t1 returns the empty sequence of states,
    then applies \c t2.
 */
 tactic orelse(tactic t1, tactic t2);
+inline tactic operator||(tactic t1, tactic t2) { return orelse(t1, t2); }
 /**
    \brief Return a tactic that tries the tactic \c t for at most \c ms milliseconds.
    If the tactic does not terminate in \c ms milliseconds, then the empty
@@ -106,6 +130,7 @@ tactic try_for(tactic t, unsigned ms, unsigned check_ms = 1);
    from tactic \c t2.
 */
 tactic append(tactic t1, tactic t2);
+inline tactic operator+(tactic t1, tactic t2) { return append(t1, t2); }
 /**
    \brief Execute both tactics and and combines their results.
    The results produced by tactics \c t1 and \c t2 are interleaved

src/tests/library/tactic/tactic.cpp

@@ -25,17 +25,10 @@ tactic loop_tactic() {
         });
 }
 
-tactic msg_tactic(std::string msg) {
-    return mk_tactic([=](environment const &, io_state const &, proof_state const & s) -> proof_state_seq {
-            std::cout << msg << "\n";
-            return proof_state_seq(s);
-        });
-}
-
 tactic set_tactic(std::atomic<bool> * flag) {
     return mk_tactic([=](environment const &, io_state const &, proof_state const & s) -> proof_state_seq {
             *flag = true;
-            return proof_state_seq(s);
+            return to_proof_state_seq(s);
         });
 }
 
@@ -71,7 +64,7 @@ static void tst1() {
     check_failure(try_for(loop_tactic(), 100), env, io, ctx, q);
     std::cout << "proof 1: " << try_for(t, 10000).solve(env, io, s) << "\n";
     check_failure(try_for(orelse(try_for(loop_tactic(), 10000),
-                                 msg_tactic(std::string("hello world"))),
+                                 trace_tactic(std::string("hello world"))),
                           100),
                   env, io, ctx, q);
     std::atomic<bool> flag1(false);
@@ -87,10 +80,16 @@ static void tst1() {
     std::cout << "proof 2: " << par(loop_tactic(), par(loop_tactic(), t)).solve(env, io, ctx, q) << "\n";
 #endif
 
-    std::cout << "proof 2: " << orelse(then(repeat_at_most(append(msg_tactic("hello1"), msg_tactic("hello2")), 5), fail_tactic()),
+    std::cout << "proof 2: " << orelse(then(repeat_at_most(append(trace_tactic("hello1"), trace_tactic("hello2")), 5), fail_tactic()),
                                        t).solve(env, io, ctx, q) << "\n";
     std::cout << "------------------\n";
-    std::cout << "proof 2: " << force(take(then(repeat_at_most(interleave(id_tactic(), id_tactic()), 100), then(msg_tactic("foo"), t)), 5)).solve(env, io, ctx, q) << "\n";
+    std::cout << "proof 2: " << ((trace_tactic("hello1.1") + trace_tactic("hello1.2") + trace_tactic("hello1.3") + trace_tactic("hello1.4")) <<
+                                 (trace_tactic("hello2.1") + trace_tactic("hello2.2")) <<
+                                 (trace_tactic("hello3.1") || trace_tactic("hello3.2")) <<
+                                 assumption_tactic()).solve(env, io, ctx, q) << "\n";
+    std::cout << "------------------\n";
+    std::cout << "proof 2: " << force(take(repeat_at_most(interleave(id_tactic(), id_tactic()), 100) << trace_tactic("foo") << t,
+                                           5)).solve(env, io, ctx, q) << "\n";
     std::cout << "done\n";
 }
 

src/tests/util/CMakeLists.txt

@@ -61,3 +61,6 @@ add_test(safe_arith ${CMAKE_CURRENT_BINARY_DIR}/safe_arith)
 add_executable(set set.cpp)
 target_link_libraries(set ${EXTRA_LIBS})
 add_test(set ${CMAKE_CURRENT_BINARY_DIR}/set)
+add_executable(optional optional.cpp)
+target_link_libraries(optional ${EXTRA_LIBS})
+add_test(optional ${CMAKE_CURRENT_BINARY_DIR}/optional)

src/tests/util/lazy_list.cpp

@@ -7,6 +7,7 @@ Author: Leonardo de Moura
 #include <iostream>
 #include <utility>
 #include "util/test.h"
+#include "util/optional.h"
 #include "util/numerics/mpz.h"
 #include "util/pair.h"
 #include "util/lazy_list.h"
@@ -15,18 +16,18 @@ Author: Leonardo de Moura
 using namespace lean;
 
 lazy_list<int> seq(int s) {
-    return lazy_list<int>(s, [=]() { return seq(s + 1); });
+    return lazy_list<int>([=]() { return some(mk_pair(s, seq(s + 1))); });
 }
 
 lazy_list<int> from(int begin, int step, int end) {
     if (begin > end)
         return lazy_list<int>();
     else
-        return lazy_list<int>(begin, [=]() { return from(begin + step, step, end); });
+        return lazy_list<int>([=]() { return some(mk_pair(begin, from(begin + step, step, end))); });
 }
 
 lazy_list<mpz> fact_list_core(mpz i, mpz n) {
-    return lazy_list<mpz>(n, [=]() { return fact_list_core(i+1, n*(i+1)); });
+    return lazy_list<mpz>([=]() { return some(mk_pair(n, fact_list_core(i+1, n*(i+1)))); });
 }
 
 lazy_list<mpz> fact_list() {
@@ -51,36 +52,41 @@ lazy_list<int> mk_simple3() {
 
 template<typename T>
 void display(lazy_list<T> const & l) {
-    for (auto v : l) {
+    int buffer[20000];
-        std::cout << v << " ";
+    int i = 0;
-    }
+    for_each(l, [&](T const & v) {
+            std::cout << v << " ";
+            buffer[i] = i;
+            i++;
+        });
     std::cout << "\n";
 }
 
-int main() {
+static void tst1() {
-    lean_assert(head(lazy_list<int>(10)) == 10);
+    lazy_list<int> l([]() { return some(mk_pair(10, lazy_list<int>())); });
-    lean_assert(!lazy_list<int>());
+    lazy_list<int> empty;
-    lean_assert(!tail(lazy_list<int>(10)));
+    lean_assert(l.pull()->first == 10);
-    lazy_list<int> l(-10, from(10, 20, 100));
+    lean_assert(!empty.pull());
-    l = cons(-20, l);
+    lean_assert(!l.pull()->second.pull());
-    lean_assert(head(l) == -20);
-    for (auto c : l) {
-        std::cout << c << "\n";
-    }
-    int i = 1;
-    for (auto c : take(30, zip(seq(1), fact_list()))) {
-        lean_assert(c.first == i);
-        std::cout << c.first << " " << c.second << "\n";
-        i++;
-    }
     list<int> l2{1, 2, 3};
-    i = 1;
+    int i = 1;
-    for (auto c : to_lazy(l2)) {
+    for_each(to_lazy(l2), [&](int c) {
-        lean_assert(c == i);
+            std::cout << "c: " << c << ", i: " << i << "\n";
-        i++;
+            lean_assert(c == i);
-    }
+            i++;
+        });
     display(mk_simple1(4));
     display(mk_simple2());
-    display(take(12, mk_simple3()));
+    display(take(10, fact_list()));
+    display(take(20, mk_simple3()));
+    display(orelse(take(10, seq(1)), take(10, seq(100))));
+    display(orelse(take(10, seq(1)), lazy_list<int>()));
+    display(orelse(lazy_list<int>(), take(10, seq(100))));
+    display(orelse(take(0, seq(1)), take(10, seq(100))));
+    display(orelse(filter(take(100, seq(1)), [](int i) { return i < 0; }), take(10, seq(1000))));
+}
+
+int main() {
+    tst1();
     return 0;
 }

src/util/lazy_list.h

@@ -5,8 +5,9 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Author: Leonardo de Moura
 */
 #pragma once
-#include "util/rc.h"
 #include "util/debug.h"
+#include "util/rc.h"
+#include "util/optional.h"
 
 namespace lean {
 /**
@@ -15,70 +16,45 @@ namespace lean {
 template<typename T>
 class lazy_list {
 public:
-    class cell {
+    typedef optional<std::pair<T, lazy_list>> maybe_pair; // head and tail pair
+private:
+    class cell_base {
         MK_LEAN_RC();
         void dealloc() { delete this; }
-        T      m_head;
     public:
-        cell(T const & h):m_rc(0), m_head(h) {}
+        cell_base():m_rc(0) {}
+        virtual ~cell_base() {}
+        virtual maybe_pair pull() const = 0;
+    };
+
+    template<typename F>
+    class cell : public cell_base {
+        F m_f;
+    public:
+        cell(F && f):cell_base(), m_f(f) {}
         virtual ~cell() {}
-        T const & head() const { return m_head; }
+        virtual maybe_pair pull() const { return m_f(); }
-        virtual lazy_list tail() const { return lazy_list(); }
     };
 
-private:
+    cell_base * m_ptr;
-    class explicit_cell : public cell {
-        lazy_list m_tail;
-    public:
-        explicit_cell(T const & h, lazy_list const & l):cell(h), m_tail(l) {}
-        virtual ~explicit_cell() {}
-        virtual lazy_list tail() const { return m_tail; }
-    };
-
-    template<typename Tail>
-    class lazy_cell : public cell {
-        Tail m_tail;
-    public:
-        lazy_cell(T const & h, Tail const & t):cell(h), m_tail(t) {}
-        virtual ~lazy_cell() {}
-        virtual lazy_list tail() const { return m_tail(); }
-    };
-
-    cell * m_ptr;
 public:
     lazy_list():m_ptr(nullptr) {}
-    lazy_list(T const & h):m_ptr(new cell(h)) { m_ptr->inc_ref(); }
-    lazy_list(T const & h, lazy_list const & t):m_ptr(new explicit_cell(h, t)) { m_ptr->inc_ref(); }
-    template<typename F>
-    lazy_list(T const & h, F const & f):m_ptr(new lazy_cell<F>(h, f)) { m_ptr->inc_ref(); }
     lazy_list(lazy_list const & s):m_ptr(s.m_ptr) { if (m_ptr) m_ptr->inc_ref(); }
-    lazy_list(lazy_list&& s):m_ptr(s.m_ptr) { s.m_ptr = nullptr; }
+    lazy_list(lazy_list && s):m_ptr(s.m_ptr) { s.m_ptr = nullptr; }
+    template<typename F> explicit lazy_list(F && f):m_ptr(new cell<F>(std::forward<F>(f))) { m_ptr->inc_ref(); }
     ~lazy_list() { if (m_ptr) m_ptr->dec_ref(); }
 
-    lazy_list & operator=(lazy_list const & s) { LEAN_COPY_REF(list, s); }
+    lazy_list & operator=(lazy_list const & s) { LEAN_COPY_REF(lazy_list, s); }
-    lazy_list & operator=(lazy_list && s) { LEAN_MOVE_REF(list, s); }
+    lazy_list & operator=(lazy_list && s) { LEAN_MOVE_REF(lazy_list, s); }
 
-    operator bool() const { return m_ptr != nullptr; }
+    maybe_pair pull() const {
+        if (m_ptr)
+            return m_ptr->pull();
+        else
+            return maybe_pair();
+    }
 
-    friend T const & head(lazy_list const & l) { lean_assert(l); return l.m_ptr->head(); }
+    friend T head(lazy_list const & l) { return l.pull()->first; }
-    friend lazy_list tail(lazy_list const & l) { lean_assert(l); return l.m_ptr->tail(); }
+    friend lazy_list tail(lazy_list const & l) { return l.pull()->second; }
-    friend lazy_list cons(T const & h, lazy_list const & t) { return lazy_list(h, t); }
-
-    class iterator {
-        friend class lazy_list;
-        lazy_list m_it;
-        iterator(lazy_list const & it):m_it(it) {}
-    public:
-        iterator(iterator const & s):m_it(s.m_it) {}
-        iterator & operator++() { m_it = tail(m_it); return *this; }
-        iterator operator++(int) { iterator tmp(*this); operator++(); return tmp; }
-        bool operator==(iterator const & s) const { return m_it == s.m_it; }
-        bool operator!=(iterator const & s) const { return !operator==(s); }
-        T const & operator*() { lean_assert(m_it); return head(m_it); }
-        T const * operator->() { lean_assert(m_it); return &(head(m_it)); }
-    };
-
-    iterator begin() const { return iterator(*this); }
-    iterator end() const { return iterator(lazy_list()); }
 };
 }

src/util/lazy_list_fn.h

@@ -10,78 +10,117 @@ Author: Leonardo de Moura
 #include "util/list.h"
 
 namespace lean {
-template<typename T>
+template<typename T, typename F>
-lazy_list<T> take(unsigned sz, lazy_list<T> l) {
+void for_each(lazy_list<T> l, F && f) {
-    if (sz == 0 || !l) {
+    while (true) {
-        return lazy_list<T>();
+        auto p = l.pull();
-    } else {
+        if (p) {
-        return lazy_list<T>(head(l), [=]() { return take(sz - 1, tail(l)); });
+            f(p->first);
-    }
+            l = p->second;
-}
+        } else {
-
+            break;
-template<typename T1, typename T2>
+        }
-lazy_list<std::pair<T1, T2>> zip(lazy_list<T1> const & l1, lazy_list<T2> const & l2) {
-    if (l1 && l2) {
-        return lazy_list<std::pair<T1, T2>>(mk_pair(head(l1), head(l2)), [=]() { return zip(tail(l1), tail(l2)); });
-    } else {
-        return lazy_list<std::pair<T1, T2>>();
     }
 }
 
 template<typename T>
-lazy_list<T> to_lazy(list<T> const & l) {
+lazy_list<T> take(unsigned sz, lazy_list<T> const & l) {
-    if (l)
+    if (sz == 0) {
-        return lazy_list<T>(head(l), [=]() { return to_lazy(tail(l)); });
-    else
         return lazy_list<T>();
+    } else {
+        return lazy_list<T>([=]() {
+                auto p = l.pull();
+                if (p)
+                    return some(mk_pair(p->first, take(sz - 1, p->second)));
+                else
+                    return p;
+            });
+    }
+}
+
+template<typename T>
+lazy_list<T> to_lazy(list<T> l) {
+    if (l) {
+        return lazy_list<T>([=]() {
+                return some(mk_pair(head(l), to_lazy(tail(l))));
+            });
+    } else {
+        return lazy_list<T>();
+    }
 }
 
 template<typename T>
 lazy_list<T> append(lazy_list<T> const & l1, lazy_list<T> const & l2) {
-    if (!l1)
+    return lazy_list<T>([=]() {
-        return l2;
+            auto p = l1.pull();
-    else if (!l2)
+            if (!p)
-        return l1;
+                return l2.pull();
-    else
+            else
-        return lazy_list<T>(head(l1), [=]() { return append(tail(l1), l2); });
+                return some(mk_pair(p->first, append(p->second, l2)));
+        });
 }
 
-template<typename T, typename F>
+template<typename T>
-lazy_list<T> map(lazy_list<T> const & l, F && f) {
+lazy_list<T> orelse(lazy_list<T> const & l1, lazy_list<T> const & l2) {
-    if (!l)
+    return lazy_list<T>([=]() {
-        return l;
+            auto p = l1.pull();
-    else
+            if (!p)
-        return lazy_list<T>(f(head(l)), [=]() { return map(tail(l), f); });
+                return l2.pull();
+            else
+                return some(mk_pair(p->first, orelse(p->second, lazy_list<T>())));
+        });
 }
 
 template<typename T>
 lazy_list<T> interleave(lazy_list<T> const & l1, lazy_list<T> const & l2) {
-    if (!l1)
+    return lazy_list<T>([=]() {
-        return l2;
+            auto p = l1.pull();
-    else if (!l2)
+            if (!p)
-        return l1;
+                return l2.pull();
-    else
+            else
-        return lazy_list<T>(head(l1), [=]() { return interleave(l2, tail(l1)); });
+                return some(mk_pair(p->first, interleave(l2, p->second)));
+        });
+}
+
+template<typename T, typename F>
+lazy_list<T> map(lazy_list<T> const & l, F && f) {
+    return lazy_list<T>([=]() {
+            auto p = l.pull();
+            if (!p)
+                return p;
+            else
+                return some(mk_pair(f(p->first), map(p->second, f)));
+        });
 }
 
 template<typename T, typename P>
-lazy_list<T> filter(lazy_list<T> const & l, P && p) {
+lazy_list<T> filter(lazy_list<T> const & l, P && pred) {
-    if (!l)
+    return lazy_list<T>([=]() {
-        return l;
+            auto p = l.pull();
-    else if (p(head(l)))
+            if (!p)
-        return lazy_list<T>(head(l), [=]() { return filter(tail(l), p); });
+                return p;
-    else
+            else if (pred(p->first))
-        return filter(tail(l), p);
+                return some(mk_pair(p->first, p->second));
+            else
+                return filter(p->second, pred).pull();
+        });
 }
 
 template<typename T, typename F>
 lazy_list<T> map_append_aux(lazy_list<T> const & h, lazy_list<T> const & l, F && f) {
-    if (!l)
+    return lazy_list<T>([=]() {
-        return h;
+            auto p1 = h.pull();
-    else if (h)
+            if (p1) {
-        return lazy_list<T>(head(h), [=]() { return map_append_aux(tail(h), l, f); });
+                return some(mk_pair(p1->first, map_append_aux(p1->second, l, f)));
-    else
+            } else {
-        return map_append_aux(f(head(l)), tail(l), f);
+                auto p2 = l.pull();
+                if (p2) {
+                    return map_append_aux(f(p2->first), p2->second, f).pull();
+                } else {
+                    return typename lazy_list<T>::maybe_pair();
+                }
+            }
+        });
 }
 
 template<typename T, typename F>

src/util/optional.h

@@ -96,4 +96,9 @@ public:
             return !o1.m_some || o1.m_value == o2.m_value;
     }
 };
+
+template<typename T>
+optional<T> some(T && t) {
+    return optional<T>(std::forward<T>(t));
+}
 }