//: A Mu program is a book of 'recipes' (functions)
:(before "End Globals")
//: Each recipe is stored at a specific page number, or ordinal.
map<recipe_ordinal, recipe> Recipe;
//: You can also refer to each recipe by its name.
map<string, recipe_ordinal> Recipe_ordinal;
recipe_ordinal Next_recipe_ordinal = 1;

//: Ordinals are like numbers, except you can't do arithmetic on them. Ordinal
//: 1 is not less than 2, it's just different. Phone numbers are ordinals;
//: adding two phone numbers is meaningless. Here each recipe does something
//: incommensurable with any other recipe.
:(after "Types")
typedef int recipe_ordinal;

:(before "End Types")
// Recipes are lists of instructions. To perform or 'run' a recipe, the
// computer runs its instructions.
struct recipe {
  recipe_ordinal ordinal;
  string name;
  vector<instruction> steps;
  // End recipe Fields
  recipe();
};

:(before "struct recipe")
// Each instruction is either of the form:
//   product1, product2, product3, ... <- operation ingredient1, ingredient2, ingredient3, ...
// or just a single 'label' starting with a non-alphanumeric character
//   +label
// Labels don't do anything, they're just named locations in a recipe.
struct instruction {
  bool is_label;
  string label;  // only if is_label
  string name;  // only if !is_label
  string original_string;  // for error messages
  recipe_ordinal operation;  // get(Recipe_ordinal, name)
  vector<reagent> ingredients;  // only if !is_label
  vector<reagent> products;  // only if !is_label
  // End instruction Fields
  instruction();
  void clear();
  bool is_empty();
};

:(before "struct instruction")
// Ingredients and products are a single species -- a reagent. Reagents refer
// either to numbers or to locations in memory along with 'type' tags telling
// us how to interpret them. They also can contain arbitrary other lists of
// properties besides types, but we're getting ahead of ourselves.
struct reagent {
  string original_string;
  string name;
  type_tree* type;
  vector<pair<string, string_tree*> > properties;  // can't be a map because the string_tree sometimes needs to be NULL, which can be confusing
  double value;
  bool initialized;
  // End reagent Fields
  reagent(const string& s);
  reagent() :type(NULL), value(0), initialized(false) {}
  reagent(type_tree* t) :type(t), value(0), initialized(false) {}
  ~reagent();
  void clear();
  reagent(const reagent& original);
  reagent& operator=(const reagent& original);
  void set_value(double v) { value = v;  initialized = true; }
};

:(before "struct reagent")
// Types can range from a simple type ordinal, to arbitrarily complex trees of
// type parameters, like (map (address array character) (list number))
struct type_tree {
  bool atom;
  string name;  // only if atom
  type_ordinal value;  // only if atom
  type_tree* left;  // only if !atom
  type_tree* right;  // only if !atom
  ~type_tree();
  type_tree(const type_tree& original);
  // atomic type ordinal
  explicit type_tree(string name);
  type_tree(string name, type_ordinal v) :atom(true), name(name), value(v), left(NULL), right(NULL) {}
  // tree of type ordinals
  type_tree(type_tree* l, type_tree* r) :atom(false), value(0), left(l), right(r) {}
  type_tree& operator=(const type_tree& original);
  bool operator==(const type_tree& other) const;
  bool operator!=(const type_tree& other) const { return !operator==(other); }
  bool operator<(const type_tree& other) const;
  bool operator>(const type_tree& other) const { return other.operator<(*this); }
};

struct string_tree {
  bool atom;
  string value;  // only if atom
  string_tree* left;  // only if !atom
  string_tree* right;  // only if !atom
  ~string_tree();
  string_tree(const string_tree& original);
  // atomic string
  explicit string_tree(string v) :atom(true), value(v), left(NULL), right(NULL) {}
  // tree of strings
  string_tree(string_tree* l, string_tree* r) :atom(false), left(l), right(r) {}
};

// End type_tree Definition
:(code)
type_tree::type_tree(string name) :atom(true), name(name), value(get(Type_ordinal, name)), left(NULL), right(NULL) {}

:(before "End Globals")
// Locations refer to a common 'memory'. Each location can store a number.
map<int, double> Memory;
:(before "End Reset")
Memory.clear();

:(after "Types")
// Mu types encode how the numbers stored in different parts of memory are
// interpreted. A location tagged as a 'character' type will interpret the
// value 97 as the letter 'a', while a different location of type 'number'
// would not.
//
// Unlike most computers today, Mu stores types in a single big table, shared
// by all the Mu programs on the computer. This is useful in providing a
// seamless experience to help understand arbitrary Mu programs.
typedef int type_ordinal;
:(before "End Globals")
map<string, type_ordinal> Type_ordinal;
map<type_ordinal, type_info> Type;
type_ordinal Next_type_ordinal = 1;
type_ordinal Number_type_ordinal = 0;
type_ordinal Boolean_type_ordinal = 0;
type_ordinal Character_type_ordinal = 0;
type_ordinal Address_type_ordinal = 0;
type_ordinal Array_type_ordinal = 0;
:(code)
void setup_types() {
  Type.clear();  Type_ordinal.clear();
  put(Type_ordinal, "literal", 0);
  Next_type_ordinal = 1;
  // Mu Types Initialization
  Number_type_ordinal = put(Type_ordinal, "number", Next_type_ordinal++);
  get_or_insert(Type, Number_type_ordinal).name = "number";
  put(Type_ordinal, "location", Number_type_ordinal);  // synonym of number for addresses we'll never look up
  Address_type_ordinal = put(Type_ordinal, "address", Next_type_ordinal++);
  get_or_insert(Type, Address_type_ordinal).name = "address";
  Boolean_type_ordinal = put(Type_ordinal, "boolean", Next_type_ordinal++);
  get_or_insert(Type, Boolean_type_ordinal).name = "boolean";
  Character_type_ordinal = put(Type_ordinal, "character", Next_type_ordinal++);
  get_or_insert(Type, Character_type_ordinal).name = "character";
  // Array types are a special modifier to any other type. For example,
  // array:number or array:address:boolean.
  Array_type_ordinal = put(Type_ordinal, "array", Next_type_ordinal++);
  get_or_insert(Type, Array_type_ordinal).name = "array";
  // End Mu Types Initialization
}
void teardown_types() {
  for (map<type_ordinal, type_info>::iterator p = Type.begin();  p != Type.end();  ++p) {
    for (int i = 0;  i < SIZE(p->second.elements);  ++i)
      p->second.elements.clear();
  }
  Type_ordinal.clear();
}
:(before "End One-time Setup")
setup_types();
atexit(teardown_types);

:(before "End Types")
// You can construct arbitrary new types. New types are either 'containers'
// with multiple 'elements' of other types, or 'exclusive containers' containing
// one of multiple 'variants'. (These are similar to C structs and unions,
// respectively, though exclusive containers implicitly include a tag element
// recording which variant they should be interpreted as.)
//
// For example, storing bank balance and name for an account might require a
// container, but if bank accounts may be either for individuals or groups,
// with different properties for each, that may require an exclusive container
// whose variants are individual-account and joint-account containers.
enum kind_of_type {
  PRIMITIVE,
  CONTAINER,
  EXCLUSIVE_CONTAINER
};

struct type_info {
  string name;
  kind_of_type kind;
  vector<reagent> elements;
  // End type_info Fields
  type_info() :kind(PRIMITIVE) {
    // End type_info Constructor
  }
};

enum primitive_recipes {
  IDLE = 0,
  COPY,
  // End Primitive Recipe Declarations
  MAX_PRIMITIVE_RECIPES,
};
:(code)
//: It's all very well to construct recipes out of other recipes, but we need
//: to know how to do *something* out of the box. For the following
//: recipes there are only codes, no entries in the book, because Mu just knows
//: what to do for them.
void setup_recipes() {
  Recipe.clear();  Recipe_ordinal.clear();
  put(Recipe_ordinal, "idle", IDLE);
  // Primitive Recipe Numbers
  put(Recipe_ordinal, "copy", COPY);
  // End Primitive Recipe Numbers
}
//: We could just reset the recipe table after every test, but that gets slow
//: all too quickly. Instead, initialize the common stuff just once at
//: startup. Later layers will carefully undo each test's additions after
//: itself.
:(before "End One-time Setup")
setup_recipes();
assert(MAX_PRIMITIVE_RECIPES < 200);  // level 0 is primitives; until 199
Next_recipe_ordinal = 200;
put(Recipe_ordinal, "main", Next_recipe_ordinal++);
// Load Mu Prelude
// End Mu Prelude
:(before "End Commandline Parsing")
assert(Next_recipe_ordinal < 1000);  // recipes being tested didn't overflow into test space
:(before "End Reset")
Next_recipe_ordinal = 1000;  // consistent new numbers for each test

//: One final detail: tests can modify our global tables of recipes and types,
//: so we need some way to clean up after each test is done so it doesn't
//: influence later ones.
:(before "End Globals")
map<string, recipe_ordinal> Recipe_ordinal_snapshot;
map<recipe_ordinal, recipe> Recipe_snapshot;
map<string, type_ordinal> Type_ordinal_snapshot;
map<type_ordinal, type_info> Type_snapshot;
:(before "End One-time Setup")
save_snapshots();
:(before "End Reset")
restore_snapshots();

:(code)
void save_snapshots() {
  Recipe_ordinal_snapshot = Recipe_ordinal;
  Recipe_snapshot = Recipe;
  Type_ordinal_snapshot = Type_ordinal;
  Type_snapshot = Type;
  // End save_snapshots
}

void restore_snapshots() {
  Recipe = Recipe_snapshot;
  Recipe_ordinal = Recipe_ordinal_snapshot;
  restore_non_recipe_snapshots();
}
// when running sandboxes in the edit/ app we'll want to restore everything except recipes defined in the app
void restore_non_recipe_snapshots() {
  Type_ordinal = Type_ordinal_snapshot;
  Type = Type_snapshot;
  // End restore_snapshots
}

//:: Helpers

:(code)
recipe::recipe() {
  ordinal = -1;
  // End recipe Constructor
}

instruction::instruction() :is_label(false), operation(IDLE) {
  // End instruction Constructor
}
void instruction::clear() {
  is_label=false;
  label.clear();
  name.clear();
  operation=IDLE;
  ingredients.clear();
  products.clear();
  original_string.clear();
  // End instruction Clear
}
bool instruction::is_empty() { return !is_label && name.empty(); }

// Reagents have the form <name>:<type>:<type>:.../<property>/<property>/...
reagent::reagent(const string& s) :original_string(s), type(NULL), value(0), initialized(false) {
  // Parsing reagent(string s)
  istringstream in(s);
  in >> std::noskipws;
  // name and type
  istringstream first_row(slurp_until(in, '/'));
  first_row >> std::noskipws;
  name = slurp_until(first_row, ':');
  string_tree* type_names = parse_property_list(first_row);
  // End Parsing Reagent Type Property(type_names)
  type = new_type_tree(type_names);
  delete type_names;
  // special cases
  if (is_integer(name) && type == NULL)
    type = new type_tree("literal");
  if (name == "_" && type == NULL)
    type = new type_tree("literal");
  // other properties
  slurp_properties(in, properties);
  // End Parsing reagent
}

void slurp_properties(istream& in, vector<pair<string, string_tree*> >& out) {
  while (has_data(in)) {
    istringstream row(slurp_until(in, '/'));
    row >> std::noskipws;
    string key = slurp_until(row, ':');
    string_tree* value = parse_property_list(row);
    out.push_back(pair<string, string_tree*>(key, value));
  }
}

string_tree* parse_property_list(istream& in) {
  skip_whitespace_but_not_newline(in);
  if (!has_data(in)) return NULL;
  string_tree* first = new string_tree(slurp_until(in, ':'));
  if (!has_data(in)) return first;
  string_tree* rest = parse_property_list(in);
  if (!has_data(in) && rest->atom)
    return new string_tree(first, new string_tree(rest, NULL));
  return new string_tree(first, rest);
}
:(before "End Unit Tests")
void test_parse_property_list_atom() {
  istringstream in("a");
  string_tree* x = parse_property_list(in);
  CHECK(x->atom);
  delete x;
}
void test_parse_property_list_list() {
  istringstream in("a:b");
  string_tree* x = parse_property_list(in);
  CHECK(!x->atom);
  CHECK(x->left->atom);
  CHECK_EQ(x->left->value, "a");
  CHECK(!x->right->atom);
  CHECK(x->right->left->atom);
  CHECK_EQ(x->right->left->value, "b");
  CHECK(x->right->right == NULL);
  delete x;
}

:(code)
type_tree* new_type_tree(const string_tree* properties) {
  if (!properties) return NULL;
  if (properties->atom) {
    const string& type_name = properties->value;
    int value = 0;
    if (contains_key(Type_ordinal, type_name))
      value = get(Type_ordinal, type_name);
    else if (is_integer(type_name))  // sometimes types will contain literal integers, like for the size of an array
      value = 0;
    else if (properties->value == "->")  // used in recipe types
      value = 0;
    else
      value = -1;  // should never happen; will trigger errors later
    return new type_tree(type_name, value);
  }
  return new type_tree(new_type_tree(properties->left),
                       new_type_tree(properties->right));
}

//: avoid memory leaks for the type tree

reagent::reagent(const reagent& other) {
  original_string = other.original_string;
  name = other.name;
  value = other.value;
  initialized = other.initialized;
  for (int i = 0;  i < SIZE(other.properties);  ++i) {
    properties.push_back(pair<string, string_tree*>(other.properties.at(i).first, copy(other.properties.at(i).second)));
  }
  type = copy(other.type);
  // End reagent Copy Constructor
}

type_tree::type_tree(const type_tree& original) {
  atom = original.atom;
  name = original.name;
  value = original.value;
  left = copy(original.left);
  right = copy(original.right);
}

type_tree& type_tree::operator=(const type_tree& original) {
  atom = original.atom;
  name = original.name;
  value = original.value;
  if (left) delete left;
  left = copy(original.left);
  if (right) delete right;
  right = copy(original.right);
  return *this;
}

bool type_tree::operator==(const type_tree& other) const {
  if (atom != other.atom) return false;
  if (atom)
    return name == other.name && value == other.value;
  return (left == other.left || *left == *other.left)
      && (right == other.right || *right == *other.right);
}

// only constraint we care about: if a < b then !(b < a)
bool type_tree::operator<(const type_tree& other) const {
  if (atom != other.atom) return atom > other.atom;  // atoms before non-atoms
  if (atom) return value < other.value;
  // first location in one that's missing in the other makes that side 'smaller'
  if (left && !other.left) return false;
  if (!left && other.left) return true;
  if (right && !other.right) return false;
  if (!right && other.right) return true;
  // now if either pointer is unequal neither side can be null
  // if one side is equal that's easy
  if (left == other.left || *left == *other.left) return right && *right < *other.right;
  if (right == other.right || *right == *other.right) return left && *left < *other.left;
  // if the two sides criss-cross, pick the side with the smaller lhs
  if ((left == other.right || *left == *other.right)
      && (right == other.left || *right == *other.left))
    return *left < *other.left;
  // now the hard case: both sides are not equal
  // make sure we stay consistent between (a < b) and (b < a)
  // just return the side with the smallest of the 4 branches
  if (*left < *other.left && *left < *other.right) return true;
  if (*right < *other.left && *right < *other.right) return true;
  return false;
}
:(before "End Unit Tests")
// These unit tests don't always use valid types.
void test_compare_atom_types() {
  reagent a("a:address"), b("b:boolean");
  CHECK(*a.type < *b.type);
  CHECK(!(*b.type < *a.type));
}
void test_compare_equal_atom_types() {
  reagent a("a:address"), b("b:address");
  CHECK(!(*a.type < *b.type));
  CHECK(!(*b.type < *a.type));
}
void test_compare_atom_with_non_atom() {
  reagent a("a:address:number"), b("b:boolean");
  CHECK(!(*a.type < *b.type));
  CHECK(*b.type < *a.type);
}
void test_compare_lists_with_identical_structure() {
  reagent a("a:address:address"), b("b:address:boolean");
  CHECK(*a.type < *b.type);
  CHECK(!(*b.type < *a.type));
}
void test_compare_identical_lists() {
  reagent a("a:address:boolean"), b("b:address:boolean");
  CHECK(!(*a.type < *b.type));
  CHECK(!(*b.type < *a.type));
}
void test_compare_list_with_extra_element() {
  reagent a("a:address:address"), b("b:address:address:number");
  CHECK(*a.type < *b.type);
  CHECK(!(*b.type < *a.type));
}
void test_compare_list_with_smaller_left_but_larger_right() {
  reagent a("a:number:character"), b("b:boolean:array");
  CHECK(*a.type < *b.type);
  CHECK(!(*b.type < *a.type));
}
void test_compare_list_with_smaller_left_but_larger_right_identical_types() {
  reagent a("a:address:boolean"), b("b:boolean:address");
  CHECK(*a.type < *b.type);
  CHECK(!(*b.type < *a.type));
}

:(code)
string_tree::string_tree(const string_tree& original) {
  atom = original.atom;
  value = original.value;
  left = copy(original.left);
  right = copy(original.right);
}

reagent& reagent::operator=(const reagent& other) {
  original_string = other.original_string;
  for (int i = 0;  i < SIZE(properties);  ++i)
    if (properties.at(i).second) delete properties.at(i).second;
  properties.clear();
  for (int i = 0;  i < SIZE(other.properties);  ++i)
    properties.push_back(pair<string, string_tree*>(other.properties.at(i).first, copy(other.properties.at(i).second)));
  name = other.name;
  value = other.value;
  initialized = other.initialized;
  if (type) delete type;
  type = copy(other.type);
  // End reagent Copy Operator
  return *this;
}

reagent::~reagent() {
  clear();
}

void reagent::clear() {
  for (int i = 0;  i < SIZE(properties);  ++i) {
    if (properties.at(i).second) {
      delete properties.at(i).second;
      properties.at(i).second = NULL;
    }
  }
  delete type;
  type = NULL;
}
type_tree::~type_tree() {
  delete left;
  delete right;
}
string_tree::~string_tree() {
  delete left;
  delete right;
}

void append(type_tree*& base, type_tree* extra) {
  if (!base) {
    base = extra;
    return;
  }
  type_tree* curr = base;
  while (curr->right) curr = curr->right;
  curr->right = extra;
}

void append(string_tree*& base, string_tree* extra) {
  if (!base) {
    base = extra;
    return;
  }
  string_tree* curr = base;
  while (curr->right) curr = curr->right;
  curr->right = extra;
}

string slurp_until(istream& in, char delim) {
  ostringstream out;
  char c;
  while (in >> c) {
    if (c == delim) {
      // drop the delim
      break;
    }
    out << c;
  }
  return out.str();
}

bool has_property(const reagent& x, const string& name) {
  for (int i = 0;  i < SIZE(x.properties);  ++i) {
    if (x.properties.at(i).first == name) return true;
  }
  return false;
}

string_tree* property(const reagent& r, const string& name) {
  for (int p = 0;  p != SIZE(r.properties);  ++p) {
    if (r.properties.at(p).first == name)
      return r.properties.at(p).second;
  }
  return NULL;
}

string_tree* copy(const string_tree* x) {
  if (x == NULL) return NULL;
  return new string_tree(*x);
}

type_tree* copy(const type_tree* x) {
  if (x == NULL) return NULL;
  return new type_tree(*x);
}

:(before "End Globals")
extern const string Ignore(",");  // commas are ignored in Mu except within [] strings
:(code)
void skip_whitespace_but_not_newline(istream& in) {
  while (true) {
    if (!has_data(in)) break;
    else if (in.peek() == '\n') break;
    else if (isspace(in.peek())) in.get();
    else if (Ignore.find(in.peek()) != string::npos) in.get();
    else break;
  }
}

void dump_memory() {
  for (map<int, double>::iterator p = Memory.begin();  p != Memory.end();  ++p) {
    cerr << p->first << ": " << no_scientific(p->second) << '\n';
  }
}

//:: Helpers for converting various values to string
//: Use to_string() in trace(), and try to keep it stable from run to run.
//: Use debug_string() while debugging, and throw everything into it.
//: Use inspect() only for emitting a canonical format that can be parsed back
//: into the value.

string to_string(const recipe& r) {
  ostringstream out;
  out << "recipe " << r.name << " [\n";
  for (int i = 0;  i < SIZE(r.steps);  ++i)
    out << "  " << to_string(r.steps.at(i)) << '\n';
  out << "]\n";
  return out.str();
}

string to_original_string(const recipe& r) {
  ostringstream out;
  out << "recipe " << r.name << " [\n";
  for (int i = 0;  i < SIZE(r.steps);  ++i)
    out << "  " << to_original_string(r.steps.at(i)) << '\n';
  out << "]\n";
  return out.str();
}

string debug_string(const recipe& x) {
  ostringstream out;
  out << "- recipe " << x.name << '\n';
  // Begin debug_string(recipe x)
  for (int index = 0;  index < SIZE(x.steps);  ++index) {
    const instruction& inst = x.steps.at(index);
    out << "inst: " << to_string(inst) << '\n';
    out << "  ingredients\n";
    for (int i = 0;  i < SIZE(inst.ingredients);  ++i)
      out << "    " << debug_string(inst.ingredients.at(i)) << '\n';
    out << "  products\n";
    for (int i = 0;  i < SIZE(inst.products);  ++i)
      out << "    " << debug_string(inst.products.at(i)) << '\n';
  }
  return out.str();
}

string to_original_string(const instruction& inst) {
  if (inst.is_label) return inst.label;
  if (!inst.original_string.empty()) return inst.original_string;
  ostringstream out;
  for (int i = 0;  i < SIZE(inst.products);  ++i) {
    if (i > 0) out << ", ";
    out << inst.products.at(i).original_string;
  }
  if (!inst.products.empty()) out << " <- ";
  out << inst.name;
  if (!inst.ingredients.empty()) out << ' ';
  for (int i = 0;  i < SIZE(inst.ingredients);  ++i) {
    if (i > 0) out << ", ";
    out << inst.ingredients.at(i).original_string;
  }
  return out.str();
}

string to_string(const instruction& inst) {
  if (inst.is_label) return inst.label;
  ostringstream out;
  for (int i = 0;  i < SIZE(inst.products);  ++i) {
    if (i > 0) out << ", ";
    out << to_string(inst.products.at(i));
  }
  if (!inst.products.empty()) out << " <- ";
  out << inst.name << ' ';
  for (int i = 0;  i < SIZE(inst.ingredients);  ++i) {
    if (i > 0) out << ", ";
    out << to_string(inst.ingredients.at(i));
  }
  return out.str();
}

string to_string(const reagent& r) {
  if (is_dummy(r)) return "_";
  ostringstream out;
  out << "{";
  out << r.name << ": " << names_to_string(r.type);
  if (!r.properties.empty()) {
    for (int i = 0;  i < SIZE(r.properties);  ++i)
      out << ", \"" << r.properties.at(i).first << "\": " << to_string(r.properties.at(i).second);
  }
  out << "}";
  return out.str();
}

// special name for ignoring some products
bool is_dummy(const reagent& x) {
  return x.name == "_";
}

string debug_string(const reagent& x) {
  ostringstream out;
  out << x.name << ": " << x.value << ' ' << to_string(x.type) << " -- " << to_string(x);
  return out.str();
}

string to_string(const string_tree* property) {
  if (!property) return "()";
  ostringstream out;
  dump(property, out);
  return out.str();
}

void dump(const string_tree* x, ostream& out) {
  if (!x) return;
  if (x->atom) {
    out << '"' << x->value << '"';
    return;
  }
  out << '(';
  const string_tree* curr = x;
  while (curr && !curr->atom) {
    dump(curr->left, out);
    if (curr->right) out << ' ';
    curr = curr->right;
  }
  // check for dotted list; should never happen
  if (curr) {
    out << ". ";
    dump(curr, out);
  }
  out << ')';
}

string to_string(const type_tree* type) {
  if (type == NULL) return "()";
  ostringstream out;
  dump(type, out);
  return out.str();
}

void dump(const type_tree* x, ostream& out) {
  if (!x) return;
  if (x->atom) {
    dump(x->value, out);
    return;
  }
  out << '(';
  const type_tree* curr = x;
  while (curr && !curr->atom) {
    dump(curr->left, out);
    if (curr->right) out << ' ';
    curr = curr->right;
  }
  // check for dotted list; should never happen
  if (curr) {
    out << ". ";
    dump(curr, out);
  }
  out << ')';
}

void dump(type_ordinal type, ostream& out) {
  if (contains_key(Type, type))
    out << get(Type, type).name;
  else
    out << "?" << type;
}

string names_to_string(const type_tree* type) {
  if (type == NULL) return "()";  // should never happen
  ostringstream out;
  dump_names(type, out);
  return out.str();
}

void dump_names(const type_tree* x, ostream& out) {
  if (!x) return;
  if (x->atom) {
    out << '"' << x->name << '"';
    return;
  }
  out << '(';
  const type_tree* curr = x;
  while (curr && !curr->atom) {
    dump_names(curr->left, out);
    if (curr->right) out << ' ';
    curr = curr->right;
  }
  // check for dotted list; should never happen
  if (curr) {
    out << ". ";
    dump_names(curr, out);
  }
  out << ')';
}

string names_to_string_without_quotes(const type_tree* type) {
  if (type == NULL) return "()";
  ostringstream out;
  dump_names_without_quotes(type, out);
  return out.str();
}

void dump_names_without_quotes(const type_tree* x, ostream& out) {
  if (!x) return;
  if (x->atom) {
    out << x->name;
    return;
  }
  out << '(';
  const type_tree* curr = x;
  while (curr && !curr->atom) {
    dump_names_without_quotes(curr->left, out);
    if (curr->right) out << ' ';
    curr = curr->right;
  }
  // check for dotted list; should never happen
  if (curr) {
    out << ". ";
    dump_names_without_quotes(curr, out);
  }
  out << ')';
}

bool is_integer(const string& s) {
  return s.find_first_not_of("0123456789-") == string::npos  // no other characters
      && s.find_first_of("0123456789") != string::npos  // at least one digit
      && s.find('-', 1) == string::npos;  // '-' only at first position
}

int to_integer(string n) {
  char* end = NULL;
  // safe because string.c_str() is guaranteed to be null-terminated
  int result = strtoll(n.c_str(), &end, /*any base*/0);
  if (*end != '\0') cerr << "tried to convert " << n << " to number\n";
  assert(*end == '\0');
  return result;
}

void test_is_integer() {
  CHECK(is_integer("1234"));
  CHECK(is_integer("-1"));
  CHECK(!is_integer("234.0"));
  CHECK(is_integer("-567"));
  CHECK(!is_integer("89-0"));
  CHECK(!is_integer("-"));
  CHECK(!is_integer("1e3"));  // not supported
}

//: helper to print numbers without excessive precision

:(before "End Types")
struct no_scientific {
  double x;
  explicit no_scientific(double y) :x(y) {}
};

:(code)
ostream& operator<<(ostream& os, no_scientific x) {
  if (!isfinite(x.x)) {
    // Infinity or NaN
    os << x.x;
    return os;
  }
  ostringstream tmp;
  // more accurate, but too slow
//?   tmp.precision(308);  // for 64-bit numbers
  tmp << std::fixed << x.x;
  os << trim_floating_point(tmp.str());
  return os;
}

string trim_floating_point(const string& in) {
  if (in.empty()) return "";
  if (in.find('.') == string::npos) return in;
  int length = SIZE(in);
  while (length > 1) {
    if (in.at(length-1) != '0') break;
    --length;
  }
  if (in.at(length-1) == '.') --length;
  if (length == 0) return "0";
  return in.substr(0, length);
}

void test_trim_floating_point() {
  CHECK_EQ(trim_floating_point(""), "");
  CHECK_EQ(trim_floating_point(".0"), "0");
  CHECK_EQ(trim_floating_point("1.5000"), "1.5");
  CHECK_EQ(trim_floating_point("1.000001"), "1.000001");
  CHECK_EQ(trim_floating_point("23.000000"), "23");
  CHECK_EQ(trim_floating_point("23.0"), "23");
  CHECK_EQ(trim_floating_point("23."), "23");
  CHECK_EQ(trim_floating_point("23"), "23");
  CHECK_EQ(trim_floating_point("230"), "230");
  CHECK_EQ(trim_floating_point("3.000000"), "3");
  CHECK_EQ(trim_floating_point("3.0"), "3");
  CHECK_EQ(trim_floating_point("3."), "3");
  CHECK_EQ(trim_floating_point("3"), "3");
}

:(before "End Includes")
#include <map>
using std::map;
#include <utility>
using std::pair;
#include <math.h>