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+//: Arrays contain a variable number of elements of the same type. Their value
+//: starts with the length of the array.
+//:
+//: You can create arrays of containers, but containers can only contain
+//: elements of a fixed size, so you can't create containers containing arrays.
+//: Create containers containing addresses to arrays instead.
+
+//: You can create arrays using 'create-array'.
+:(scenario create_array)
+def main [
+  # create an array occupying locations 1 (for the size) and 2-4 (for the elements)
+  1:array:num:3 <- create-array
+]
++run: creating array of size 4
+
+:(before "End Primitive Recipe Declarations")
+CREATE_ARRAY,
+:(before "End Primitive Recipe Numbers")
+put(Recipe_ordinal, "create-array", CREATE_ARRAY);
+:(before "End Primitive Recipe Checks")
+case CREATE_ARRAY: {
+  if (inst.products.empty()) {
+    raise << maybe(get(Recipe, r).name) << "'create-array' needs one product and no ingredients but got '" << to_original_string(inst) << '\n' << end();
+    break;
+  }
+  reagent/*copy*/ product = inst.products.at(0);
+  // Update CREATE_ARRAY product in Check
+  if (!is_mu_array(product)) {
+    raise << maybe(get(Recipe, r).name) << "'create-array' cannot create non-array '" << product.original_string << "'\n" << end();
+    break;
+  }
+  if (!product.type->right) {
+    raise << maybe(get(Recipe, r).name) << "create array of what? '" << to_original_string(inst) << "'\n" << end();
+    break;
+  }
+  // 'create-array' will need to check properties rather than types
+  type_tree* array_length_from_type = product.type->right->right;
+  if (!array_length_from_type) {
+    raise << maybe(get(Recipe, r).name) << "create array of what size? '" << to_original_string(inst) << "'\n" << end();
+    break;
+  }
+  if (!product.type->right->right->atom)
+    array_length_from_type = array_length_from_type->left;
+  if (!is_integer(array_length_from_type->name)) {
+    raise << maybe(get(Recipe, r).name) << "'create-array' product should specify size of array after its element type, but got '" << product.type->right->right->name << "'\n" << end();
+    break;
+  }
+  break;
+}
+:(before "End Primitive Recipe Implementations")
+case CREATE_ARRAY: {
+  reagent/*copy*/ product = current_instruction().products.at(0);
+  // Update CREATE_ARRAY product in Run
+  int base_address = product.value;
+  type_tree* array_length_from_type = product.type->right->right;
+  if (!product.type->right->right->atom)
+    array_length_from_type = array_length_from_type->left;
+  int array_length = to_integer(array_length_from_type->name);
+  // initialize array length, so that size_of will work
+  trace("mem") << "storing " << array_length << " in location " << base_address << end();
+  put(Memory, base_address, array_length);  // in array elements
+  int size = size_of(product);  // in locations
+  trace(9998, "run") << "creating array of size " << size << end();
+  // initialize array
+  for (int i = 1;  i <= size_of(product);  ++i)
+    put(Memory, base_address+i, 0);
+  // no need to update product
+  write_products = false;
+  break;
+}
+
+:(scenario copy_array)
+# Arrays can be copied around with a single instruction just like numbers,
+# no matter how large they are.
+# You don't need to pass the size around, since each array variable stores its
+# size in memory at run-time. We'll call a variable with an explicit size a
+# 'static' array, and one without a 'dynamic' array since it can contain
+# arrays of many different sizes.
+def main [
+  1:array:num:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  5:array:num <- copy 1:array:num:3
+]
++mem: storing 3 in location 5
++mem: storing 14 in location 6
++mem: storing 15 in location 7
++mem: storing 16 in location 8
+
+:(scenario stash_array)
+def main [
+  1:array:num:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  stash [foo:], 1:array:num:3
+]
++app: foo: 3 14 15 16
+
+:(before "End types_coercible Special-cases")
+if (is_mu_array(from) && is_mu_array(to))
+  return types_strictly_match(array_element(from.type), array_element(to.type));
+
+:(before "End size_of(reagent r) Special-cases")
+if (!r.type->atom && r.type->left->atom && r.type->left->value == Array_type_ordinal) {
+  if (!r.type->right) {
+    raise << maybe(current_recipe_name()) << "'" << r.original_string << "' is an array of what?\n" << end();
+    return 1;
+  }
+  return /*space for length*/1 + array_length(r)*size_of(array_element(r.type));
+}
+
+:(before "End size_of(type) Non-atom Special-cases")
+if (type->left->value == Array_type_ordinal) return static_array_length(type);
+:(code)
+int static_array_length(const type_tree* type) {
+  if (!type->atom && type->right && !type->right->atom && type->right->right && !type->right->right->atom && !type->right->right->right  // exactly 3 types
+      && type->right->right->left && type->right->right->left->atom && is_integer(type->right->right->left->name)) {  // third 'type' is a number
+    // get size from type
+    return to_integer(type->right->right->left->name);
+  }
+  cerr << to_string(type) << '\n';
+  assert(false);
+}
+
+//: disable the size mismatch check for arrays since the destination array
+//: need not be initialized
+:(before "End size_mismatch(x) Special-cases")
+if (x.type && !x.type->atom && x.type->left->value == Array_type_ordinal) return false;
+
+//:: arrays inside containers
+//: arrays are disallowed inside containers unless their length is fixed in
+//: advance
+
+:(scenario container_permits_static_array_element)
+container foo [
+  x:array:num:3
+]
+$error: 0
+
+:(before "End insert_container Special-cases")
+else if (is_integer(type->name)) {  // sometimes types will contain non-type tags, like numbers for the size of an array
+  type->value = 0;
+}
+
+:(scenario container_disallows_dynamic_array_element)
+% Hide_errors = true;
+container foo [
+  x:array:num
+]
++error: container 'foo' cannot determine size of element 'x'
+
+:(before "End Load Container Element Definition")
+{
+  const type_tree* type = info.elements.back().type;
+  if (type && type->atom && type->name == "array") {
+    raise << "container '" << name << "' doesn't specify type of array elements for '" << info.elements.back().name << "'\n" << end();
+    continue;
+  }
+  if (type && !type->atom && type->left->atom && type->left->name == "array") {
+    if (!type->right) {
+      raise << "container '" << name << "' doesn't specify type of array elements for '" << info.elements.back().name << "'\n" << end();
+      continue;
+    }
+    if (!type->right->right || !is_integer(type->right->right->left->name)) {  // array has no length
+      raise << "container '" << name << "' cannot determine size of element '" << info.elements.back().name << "'\n" << end();
+      continue;
+    }
+  }
+}
+
+//: disable the size mismatch check for 'merge' instructions since containers
+//: can contain arrays, and since we already do plenty of checking for them
+:(before "End size_mismatch(x) Special-cases")
+if (current_call().running_step_index < SIZE(get(Recipe, current_call().running_recipe).steps)
+    && current_instruction().operation == MERGE) {
+  return false;
+}
+
+:(scenario merge_static_array_into_container)
+container foo [
+  x:num
+  y:array:num:3
+]
+def main [
+  1:array:num:3 <- create-array
+  10:foo <- merge 34, 1:array:num:3
+]
+# no errors
+
+:(scenario code_inside_container)
+% Hide_errors = true;
+container card [
+  rank:num <- next-ingredient
+]
+def foo [
+  1:card <- merge 3
+  2:num <- get 1:card rank:offset
+]
+# shouldn't die
+
+//:: To access elements of an array, use 'index'
+
+:(scenario index)
+def main [
+  1:array:num:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  5:num <- index 1:array:num:3, 0/index  # the index must be a non-negative whole number
+]
++mem: storing 14 in location 5
+
+:(scenario index_compound_element)
+def main [
+  {1: (array (address number) 3)} <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  5:address:num <- index {1: (array (address number) 3)}, 0
+]
++mem: storing 14 in location 5
+
+:(scenario index_direct_offset)
+def main [
+  1:array:num:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  5:num <- copy 0
+  6:num <- index 1:array:num, 5:num
+]
++mem: storing 14 in location 6
+
+:(before "End Primitive Recipe Declarations")
+INDEX,
+:(before "End Primitive Recipe Numbers")
+put(Recipe_ordinal, "index", INDEX);
+:(before "End Primitive Recipe Checks")
+case INDEX: {
+  if (SIZE(inst.ingredients) != 2) {
+    raise << maybe(get(Recipe, r).name) << "'index' expects exactly 2 ingredients in '" << to_original_string(inst) << "'\n" << end();
+    break;
+  }
+  reagent/*copy*/ base = inst.ingredients.at(0);
+  // Update INDEX base in Check
+  if (!is_mu_array(base)) {
+    raise << maybe(get(Recipe, r).name) << "'index' on a non-array '" << base.original_string << "'\n" << end();
+    break;
+  }
+  reagent/*copy*/ index = inst.ingredients.at(1);
+  // Update INDEX index in Check
+  if (!is_mu_number(index)) {
+    raise << maybe(get(Recipe, r).name) << "second ingredient of 'index' should be a number, but got '" << index.original_string << "'\n" << end();
+    break;
+  }
+  if (inst.products.empty()) break;
+  reagent/*copy*/ product = inst.products.at(0);
+  // Update INDEX product in Check
+  reagent/*local*/ element(copy_array_element(base.type));
+  if (!types_coercible(product, element)) {
+    raise << maybe(get(Recipe, r).name) << "'index' on '" << base.original_string << "' can't be saved in '" << product.original_string << "'; type should be '" << names_to_string_without_quotes(element.type) << "'\n" << end();
+    break;
+  }
+  break;
+}
+:(before "End Primitive Recipe Implementations")
+case INDEX: {
+  reagent/*copy*/ base = current_instruction().ingredients.at(0);
+  // Update INDEX base in Run
+  int base_address = base.value;
+  trace(9998, "run") << "base address is " << base_address << end();
+  if (base_address == 0) {
+    raise << maybe(current_recipe_name()) << "tried to access location 0 in '" << to_original_string(current_instruction()) << "'\n" << end();
+    break;
+  }
+  reagent/*copy*/ index = current_instruction().ingredients.at(1);
+  // Update INDEX index in Run
+  vector<double> index_val(read_memory(index));
+  if (index_val.at(0) < 0 || index_val.at(0) >= get_or_insert(Memory, base_address)) {
+    raise << maybe(current_recipe_name()) << "invalid index " << no_scientific(index_val.at(0)) << " in '" << to_original_string(current_instruction()) << "'\n" << end();
+    break;
+  }
+  reagent/*local*/ element(copy_array_element(base.type));
+  element.set_value(base_address + /*skip length*/1 + index_val.at(0)*size_of(element.type));
+  trace(9998, "run") << "address to copy is " << element.value << end();
+  trace(9998, "run") << "its type is " << to_string(element.type) << end();
+  // Read element
+  products.push_back(read_memory(element));
+  break;
+}
+
+:(code)
+type_tree* copy_array_element(const type_tree* type) {
+  return new type_tree(*array_element(type));
+}
+
+type_tree* array_element(const type_tree* type) {
+  assert(type->right);
+  if (type->right->atom) {
+    return type->right;
+  }
+  else if (!type->right->right) {
+    return type->right->left;
+  }
+  // hack: support array:num:3 without requiring extra parens
+  else if (type->right->right->left && type->right->right->left->atom && is_integer(type->right->right->left->name)) {
+    assert(!type->right->right->right);
+    return type->right->left;
+  }
+  return type->right;
+}
+
+int array_length(const reagent& x) {
+  // x should already be canonized.
+  // hack: look for length in type
+  if (!x.type->atom && x.type->right && !x.type->right->atom && x.type->right->right && !x.type->right->right->atom && !x.type->right->right->right  // exactly 3 types
+      && x.type->right->right->left && x.type->right->right->left->atom && is_integer(x.type->right->right->left->name)) {  // third 'type' is a number
+    // get size from type
+    return to_integer(x.type->right->right->left->name);
+  }
+  // this should never happen at transform time
+  return get_or_insert(Memory, x.value);
+}
+
+:(before "End Unit Tests")
+void test_array_length_compound() {
+  put(Memory, 1, 3);
+  put(Memory, 2, 14);
+  put(Memory, 3, 15);
+  put(Memory, 4, 16);
+  reagent x("1:array:address:num");  // 3 types, but not a static array
+  populate_value(x);
+  CHECK_EQ(array_length(x), 3);
+}
+
+void test_array_length_static() {
+  reagent x("1:array:num:3");
+  CHECK_EQ(array_length(x), 3);
+}
+
+:(scenario index_truncates)
+def main [
+  1:array:num:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  5:num <- index 1:array:num:3, 1.5  # non-whole number
+]
+# fraction is truncated away
++mem: storing 15 in location 5
+
+:(scenario index_out_of_bounds)
+% Hide_errors = true;
+def main [
+  1:array:num:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  5:num <- copy 14
+  6:num <- copy 15
+  7:num <- copy 16
+  index 1:array:num:3, 4  # less than size of array in locations, but larger than its length in elements
+]
++error: main: invalid index 4 in 'index 1:array:num:3, 4'
+
+:(scenario index_out_of_bounds_2)
+% Hide_errors = true;
+def main [
+  1:array:point:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  5:num <- copy 14
+  6:num <- copy 15
+  7:num <- copy 16
+  index 1:array:point, -1
+]
++error: main: invalid index -1 in 'index 1:array:point, -1'
+
+:(scenario index_product_type_mismatch)
+% Hide_errors = true;
+def main [
+  1:array:point:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  5:num <- copy 14
+  6:num <- copy 15
+  7:num <- copy 16
+  9:num <- index 1:array:point, 0
+]
++error: main: 'index' on '1:array:point' can't be saved in '9:num'; type should be 'point'
+
+//: we might want to call 'index' without saving the results, say in a sandbox
+
+:(scenario index_without_product)
+def main [
+  1:array:num:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  index 1:array:num:3, 0
+]
+# just don't die
+
+//:: To write to elements of arrays, use 'put'.
+
+:(scenario put_index)
+def main [
+  1:array:num:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  1:array:num <- put-index 1:array:num, 1, 34
+]
++mem: storing 34 in location 3
+
+:(before "End Primitive Recipe Declarations")
+PUT_INDEX,
+:(before "End Primitive Recipe Numbers")
+put(Recipe_ordinal, "put-index", PUT_INDEX);
+:(before "End Primitive Recipe Checks")
+case PUT_INDEX: {
+  if (SIZE(inst.ingredients) != 3) {
+    raise << maybe(get(Recipe, r).name) << "'put-index' expects exactly 3 ingredients in '" << to_original_string(inst) << "'\n" << end();
+    break;
+  }
+  reagent/*copy*/ base = inst.ingredients.at(0);
+  // Update PUT_INDEX base in Check
+  if (!is_mu_array(base)) {
+    raise << maybe(get(Recipe, r).name) << "'put-index' on a non-array '" << base.original_string << "'\n" << end();
+    break;
+  }
+  reagent/*copy*/ index = inst.ingredients.at(1);
+  // Update PUT_INDEX index in Check
+  if (!is_mu_number(index)) {
+    raise << maybe(get(Recipe, r).name) << "second ingredient of 'put-index' should have type 'number', but got '" << inst.ingredients.at(1).original_string << "'\n" << end();
+    break;
+  }
+  reagent/*copy*/ value = inst.ingredients.at(2);
+  // Update PUT_INDEX value in Check
+  reagent/*local*/ element(copy_array_element(base.type));
+  if (!types_coercible(element, value)) {
+    raise << maybe(get(Recipe, r).name) << "'put-index " << base.original_string << ", " << inst.ingredients.at(1).original_string << "' should store " << names_to_string_without_quotes(element.type) << " but '" << value.name << "' has type " << names_to_string_without_quotes(value.type) << '\n' << end();
+    break;
+  }
+  if (inst.products.empty()) break;  // no more checks necessary
+  if (inst.products.at(0).name != inst.ingredients.at(0).name) {
+    raise << maybe(get(Recipe, r).name) << "product of 'put-index' must be first ingredient '" << inst.ingredients.at(0).original_string << "', but got '" << inst.products.at(0).original_string << "'\n" << end();
+    break;
+  }
+  // End PUT_INDEX Product Checks
+  break;
+}
+:(before "End Primitive Recipe Implementations")
+case PUT_INDEX: {
+  reagent/*copy*/ base = current_instruction().ingredients.at(0);
+  // Update PUT_INDEX base in Run
+  int base_address = base.value;
+  if (base_address == 0) {
+    raise << maybe(current_recipe_name()) << "tried to access location 0 in '" << to_original_string(current_instruction()) << "'\n" << end();
+    break;
+  }
+  reagent/*copy*/ index = current_instruction().ingredients.at(1);
+  // Update PUT_INDEX index in Run
+  vector<double> index_val(read_memory(index));
+  if (index_val.at(0) < 0 || index_val.at(0) >= get_or_insert(Memory, base_address)) {
+    raise << maybe(current_recipe_name()) << "invalid index " << no_scientific(index_val.at(0)) << " in '" << to_original_string(current_instruction()) << "'\n" << end();
+    break;
+  }
+  int address = base_address + /*skip length*/1 + index_val.at(0)*size_of(array_element(base.type));
+  trace(9998, "run") << "address to copy to is " << address << end();
+  // optimization: directly write the element rather than updating 'product'
+  // and writing the entire array
+  write_products = false;
+  vector<double> value = read_memory(current_instruction().ingredients.at(2));
+  // Write Memory in PUT_INDEX in Run
+  for (int i = 0;  i < SIZE(value);  ++i) {
+    trace("mem") << "storing " << no_scientific(value.at(i)) << " in location " << address+i << end();
+    put(Memory, address+i, value.at(i));
+  }
+  break;
+}
+
+:(scenario put_index_out_of_bounds)
+% Hide_errors = true;
+def main [
+  1:array:point:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  5:num <- copy 14
+  6:num <- copy 15
+  7:num <- copy 16
+  8:point <- merge 34, 35
+  1:array:point <- put-index 1:array:point, 4, 8:point  # '4' is less than size of array in locations, but larger than its length in elements
+]
++error: main: invalid index 4 in '1:array:point <- put-index 1:array:point, 4, 8:point'
+
+:(scenario put_index_out_of_bounds_2)
+% Hide_errors = true;
+def main [
+  1:array:point:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  5:num <- copy 14
+  6:num <- copy 15
+  7:num <- copy 16
+  8:point <- merge 34, 35
+  1:array:point <- put-index 1:array:point, -1, 8:point
+]
++error: main: invalid index -1 in '1:array:point <- put-index 1:array:point, -1, 8:point'
+
+:(scenario put_index_product_error)
+% Hide_errors = true;
+def main [
+  local-scope
+  load-ingredients
+  1:array:num:3 <- create-array
+  4:array:num:3 <- put-index 1:array:num:3, 0, 34
+]
++error: main: product of 'put-index' must be first ingredient '1:array:num:3', but got '4:array:num:3'
+
+//:: compute the length of an array
+
+:(scenario array_length)
+def main [
+  1:array:num:3 <- create-array
+  2:num <- copy 14
+  3:num <- copy 15
+  4:num <- copy 16
+  5:num <- length 1:array:num:3
+]
++mem: storing 3 in location 5
+
+:(before "End Primitive Recipe Declarations")
+LENGTH,
+:(before "End Primitive Recipe Numbers")
+put(Recipe_ordinal, "length", LENGTH);
+:(before "End Primitive Recipe Checks")
+case LENGTH: {
+  if (SIZE(inst.ingredients) != 1) {
+    raise << maybe(get(Recipe, r).name) << "'length' expects exactly 2 ingredients in '" << to_original_string(inst) << "'\n" << end();
+    break;
+  }
+  reagent/*copy*/ array = inst.ingredients.at(0);
+  // Update LENGTH array in Check
+  if (!is_mu_array(array)) {
+    raise << "tried to calculate length of non-array '" << array.original_string << "'\n" << end();
+    break;
+  }
+  break;
+}
+:(before "End Primitive Recipe Implementations")
+case LENGTH: {
+  reagent/*copy*/ array = current_instruction().ingredients.at(0);
+  // Update LENGTH array in Run
+  if (array.value == 0) {
+    raise << maybe(current_recipe_name()) << "tried to access location 0 in '" << to_original_string(current_instruction()) << "'\n" << end();
+    break;
+  }
+  products.resize(1);
+  products.at(0).push_back(get_or_insert(Memory, array.value));
+  break;
+}
+
+//: optimization: none of the instructions in this layer use 'ingredients' so
+//: stop copying potentially huge arrays into it.
+:(before "End should_copy_ingredients Special-cases")
+recipe_ordinal r = current_instruction().operation;
+if (r == CREATE_ARRAY || r == INDEX || r == PUT_INDEX || r == LENGTH)
+  return false;