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+//: Transform to maintain multiple variants of a recipe depending on the
+//: number and types of the ingredients and products. Allows us to use nice
+//: names like 'print' or 'length' in many mutually extensible ways.
+
+:(scenario static_dispatch)
+def main [
+  7:number/raw <- test 3
+]
+def test a:number -> z:number [
+  z <- copy 1
+]
+def test a:number, b:number -> z:number [
+  z <- copy 2
+]
++mem: storing 1 in location 7
+
+//: When loading recipes, accumulate variants if headers don't collide, and
+//: flag an error if headers collide.
+
+:(before "End Globals")
+map<string, vector<recipe_ordinal> > Recipe_variants;
+:(before "End One-time Setup")
+put(Recipe_variants, "main", vector<recipe_ordinal>());  // since we manually added main to Recipe_ordinal
+
+:(before "End Globals")
+map<string, vector<recipe_ordinal> > Recipe_variants_snapshot;
+:(before "End save_snapshots")
+Recipe_variants_snapshot = Recipe_variants;
+:(before "End restore_snapshots")
+Recipe_variants = Recipe_variants_snapshot;
+
+:(before "End Load Recipe Header(result)")
+// there can only ever be one variant for main
+if (result.name != "main" && contains_key(Recipe_ordinal, result.name)) {
+  const recipe_ordinal r = get(Recipe_ordinal, result.name);
+  if (!contains_key(Recipe, r) || get(Recipe, r).has_header) {
+    string new_name = matching_variant_name(result);
+    if (new_name.empty()) {
+      // variant doesn't already exist
+      new_name = next_unused_recipe_name(result.name);
+      put(Recipe_ordinal, new_name, Next_recipe_ordinal++);
+      get_or_insert(Recipe_variants, result.name).push_back(get(Recipe_ordinal, new_name));
+    }
+    trace(9999, "load") << "switching " << result.name << " to " << new_name << end();
+    result.name = new_name;
+  }
+}
+else {
+  // save first variant
+  put(Recipe_ordinal, result.name, Next_recipe_ordinal++);
+  get_or_insert(Recipe_variants, result.name).push_back(get(Recipe_ordinal, result.name));
+}
+
+:(code)
+string matching_variant_name(const recipe& rr) {
+  const vector<recipe_ordinal>& variants = get_or_insert(Recipe_variants, rr.name);
+  for (int i = 0; i < SIZE(variants); ++i) {
+    if (!contains_key(Recipe, variants.at(i))) continue;
+    const recipe& candidate = get(Recipe, variants.at(i));
+    if (!all_reagents_match(rr, candidate)) continue;
+    return candidate.name;
+  }
+  return "";
+}
+
+bool all_reagents_match(const recipe& r1, const recipe& r2) {
+  if (SIZE(r1.ingredients) != SIZE(r2.ingredients)) return false;
+  if (SIZE(r1.products) != SIZE(r2.products)) return false;
+  for (int i = 0; i < SIZE(r1.ingredients); ++i) {
+    if (!deeply_equal_type_names(r1.ingredients.at(i), r2.ingredients.at(i))) {
+      return false;
+    }
+  }
+  for (int i = 0; i < SIZE(r1.products); ++i) {
+    if (!deeply_equal_type_names(r1.products.at(i), r2.products.at(i))) {
+      return false;
+    }
+  }
+  return true;
+}
+
+:(before "End Globals")
+set<string> Literal_type_names;
+:(before "End One-time Setup")
+Literal_type_names.insert("number");
+Literal_type_names.insert("character");
+:(code)
+bool deeply_equal_type_names(const reagent& a, const reagent& b) {
+  return deeply_equal_type_names(a.type, b.type);
+}
+bool deeply_equal_type_names(const type_tree* a, const type_tree* b) {
+  if (!a) return !b;
+  if (!b) return !a;
+  if (a->name == "literal" && b->name == "literal")
+    return true;
+  if (a->name == "literal")
+    return Literal_type_names.find(b->name) != Literal_type_names.end();
+  if (b->name == "literal")
+    return Literal_type_names.find(a->name) != Literal_type_names.end();
+  return a->name == b->name
+      && deeply_equal_type_names(a->left, b->left)
+      && deeply_equal_type_names(a->right, b->right);
+}
+
+string next_unused_recipe_name(const string& recipe_name) {
+  for (int i = 2; ; ++i) {
+    ostringstream out;
+    out << recipe_name << '_' << i;
+    if (!contains_key(Recipe_ordinal, out.str()))
+      return out.str();
+  }
+}
+
+//: Once all the recipes are loaded, transform their bodies to replace each
+//: call with the most suitable variant.
+
+:(scenario static_dispatch_picks_most_similar_variant)
+def main [
+  7:number/raw <- test 3, 4, 5
+]
+def test a:number -> z:number [
+  z <- copy 1
+]
+def test a:number, b:number -> z:number [
+  z <- copy 2
+]
++mem: storing 2 in location 7
+
+//: support recipe headers in a previous transform to fill in missing types
+:(before "End check_or_set_invalid_types")
+for (int i = 0; i < SIZE(caller.ingredients); ++i)
+  check_or_set_invalid_types(caller.ingredients.at(i).type, maybe(caller.name), "recipe header ingredient");
+for (int i = 0; i < SIZE(caller.products); ++i)
+  check_or_set_invalid_types(caller.products.at(i).type, maybe(caller.name), "recipe header product");
+
+//: after filling in all missing types (because we'll be introducing 'blank' types in this transform in a later layer, for shape-shifting recipes)
+:(after "Transform.push_back(transform_names)")
+Transform.push_back(resolve_ambiguous_calls);  // idempotent
+
+//: In a later layer we'll introduce recursion in resolve_ambiguous_calls, by
+//: having it generate code for shape-shifting recipes and then transform such
+//: code. This data structure will help error messages be more useful.
+//:
+//: We're punning the 'call' data structure just because it has slots for
+//: calling recipe and calling instruction.
+:(before "End Globals")
+list<call> resolve_stack;
+
+:(code)
+void resolve_ambiguous_calls(recipe_ordinal r) {
+  recipe& caller_recipe = get(Recipe, r);
+  trace(9991, "transform") << "--- resolve ambiguous calls for recipe " << caller_recipe.name << end();
+  for (int index = 0; index < SIZE(caller_recipe.steps); ++index) {
+    instruction& inst = caller_recipe.steps.at(index);
+    if (inst.is_label) continue;
+    if (non_ghost_size(get_or_insert(Recipe_variants, inst.name)) == 0) continue;
+    trace(9992, "transform") << "instruction " << inst.original_string << end();
+    resolve_stack.push_front(call(r));
+    resolve_stack.front().running_step_index = index;
+    string new_name = best_variant(inst, caller_recipe);
+    if (!new_name.empty())
+      inst.name = new_name;
+    assert(resolve_stack.front().running_recipe == r);
+    assert(resolve_stack.front().running_step_index == index);
+    resolve_stack.pop_front();
+  }
+}
+
+string best_variant(instruction& inst, const recipe& caller_recipe) {
+  vector<recipe_ordinal>& variants = get(Recipe_variants, inst.name);
+  vector<recipe_ordinal> candidates;
+
+  // Static Dispatch Phase 1
+  candidates = strictly_matching_variants(inst, variants);
+  if (!candidates.empty()) return best_variant(inst, candidates).name;
+
+  // Static Dispatch Phase 2
+  candidates = strictly_matching_variants_except_literal_zero_against_address(inst, variants);
+  if (!candidates.empty()) return best_variant(inst, candidates).name;
+
+  // Static Dispatch Phase 3
+  //: (shape-shifting recipes in a later layer)
+  // End Static Dispatch Phase 3
+
+  // Static Dispatch Phase 4
+  candidates = strictly_matching_variants_except_literal_against_address_or_boolean(inst, variants);
+  if (!candidates.empty()) return best_variant(inst, candidates).name;
+
+  // Static Dispatch Phase 5
+  candidates = matching_variants(inst, variants);
+  if (!candidates.empty()) return best_variant(inst, candidates).name;
+
+  // error messages
+  if (get(Recipe_ordinal, inst.name) >= MAX_PRIMITIVE_RECIPES) {  // we currently don't check types for primitive variants
+    raise << maybe(caller_recipe.name) << "failed to find a matching call for '" << to_original_string(inst) << "'\n" << end();
+    for (list<call>::iterator p = /*skip*/++resolve_stack.begin(); p != resolve_stack.end(); ++p) {
+      const recipe& specializer_recipe = get(Recipe, p->running_recipe);
+      const instruction& specializer_inst = specializer_recipe.steps.at(p->running_step_index);
+      if (specializer_recipe.name != "interactive")
+        raise << "  (from '" << to_original_string(specializer_inst) << "' in " << specializer_recipe.name << ")\n" << end();
+      else
+        raise << "  (from '" << to_original_string(specializer_inst) << "')\n" << end();
+      // One special-case to help with the rewrite_stash transform. (cross-layer)
+      if (specializer_inst.products.at(0).name.find("stash_") == 0) {
+        instruction stash_inst;
+        if (next_stash(*p, &stash_inst)) {
+          if (specializer_recipe.name != "interactive")
+            raise << "  (part of '" << stash_inst.original_string << "' in " << specializer_recipe.name << ")\n" << end();
+          else
+            raise << "  (part of '" << stash_inst.original_string << "')\n" << end();
+        }
+      }
+    }
+  }
+  return "";
+}
+
+// phase 1
+vector<recipe_ordinal> strictly_matching_variants(const instruction& inst, vector<recipe_ordinal>& variants) {
+  vector<recipe_ordinal> result;
+  for (int i = 0; i < SIZE(variants); ++i) {
+    if (variants.at(i) == -1) continue;
+    trace(9992, "transform") << "checking variant (strict) " << i << ": " << header_label(variants.at(i)) << end();
+    if (all_header_reagents_strictly_match(inst, get(Recipe, variants.at(i))))
+      result.push_back(variants.at(i));
+  }
+  return result;
+}
+
+bool all_header_reagents_strictly_match(const instruction& inst, const recipe& variant) {
+  for (int i = 0; i < min(SIZE(inst.ingredients), SIZE(variant.ingredients)); ++i) {
+    if (!types_strictly_match(variant.ingredients.at(i), inst.ingredients.at(i))) {
+      trace(9993, "transform") << "strict match failed: ingredient " << i << end();
+      return false;
+    }
+  }
+  for (int i = 0; i < min(SIZE(inst.products), SIZE(variant.products)); ++i) {
+    if (is_dummy(inst.products.at(i))) continue;
+    if (!types_strictly_match(variant.products.at(i), inst.products.at(i))) {
+      trace(9993, "transform") << "strict match failed: product " << i << end();
+      return false;
+    }
+  }
+  return true;
+}
+
+// phase 2
+vector<recipe_ordinal> strictly_matching_variants_except_literal_zero_against_address(const instruction& inst, vector<recipe_ordinal>& variants) {
+  vector<recipe_ordinal> result;
+  for (int i = 0; i < SIZE(variants); ++i) {
+    if (variants.at(i) == -1) continue;
+    trace(9992, "transform") << "checking variant (strict) " << i << ": " << header_label(variants.at(i)) << end();
+    if (all_header_reagents_strictly_match_except_literal_zero_against_address(inst, get(Recipe, variants.at(i))))
+      result.push_back(variants.at(i));
+  }
+  return result;
+}
+
+bool all_header_reagents_strictly_match_except_literal_zero_against_address(const instruction& inst, const recipe& variant) {
+  for (int i = 0; i < min(SIZE(inst.ingredients), SIZE(variant.ingredients)); ++i) {
+    if (!types_strictly_match_except_literal_zero_against_address(variant.ingredients.at(i), inst.ingredients.at(i))) {
+      trace(9993, "transform") << "strict match failed: ingredient " << i << end();
+      return false;
+    }
+  }
+  for (int i = 0; i < min(SIZE(inst.products), SIZE(variant.products)); ++i) {
+    if (is_dummy(inst.products.at(i))) continue;
+    if (!types_strictly_match(variant.products.at(i), inst.products.at(i))) {
+      trace(9993, "transform") << "strict match failed: product " << i << end();
+      return false;
+    }
+  }
+  return true;
+}
+
+bool types_strictly_match_except_literal_zero_against_address(const reagent& to, const reagent& from) {
+  // to sidestep type-checking, use /unsafe in the source.
+  // this will be highlighted in red inside vim. just for setting up some tests.
+  if (is_literal(from) && is_mu_address(to))
+    return from.name == "0";
+  return types_strictly_match(to, from);
+}
+
+// phase 4
+vector<recipe_ordinal> strictly_matching_variants_except_literal_against_address_or_boolean(const instruction& inst, vector<recipe_ordinal>& variants) {
+  vector<recipe_ordinal> result;
+  for (int i = 0; i < SIZE(variants); ++i) {
+    if (variants.at(i) == -1) continue;
+    trace(9992, "transform") << "checking variant (strict except literals-against-booleans) " << i << ": " << header_label(variants.at(i)) << end();
+    if (all_header_reagents_strictly_match_except_literal_against_address_or_boolean(inst, get(Recipe, variants.at(i))))
+      result.push_back(variants.at(i));
+  }
+  return result;
+}
+
+bool all_header_reagents_strictly_match_except_literal_against_address_or_boolean(const instruction& inst, const recipe& variant) {
+  for (int i = 0; i < min(SIZE(inst.ingredients), SIZE(variant.ingredients)); ++i) {
+    if (!types_strictly_match_except_literal_against_address_or_boolean(variant.ingredients.at(i), inst.ingredients.at(i))) {
+      trace(9993, "transform") << "strict match failed: ingredient " << i << end();
+      return false;
+    }
+  }
+  for (int i = 0; i < min(SIZE(variant.products), SIZE(inst.products)); ++i) {
+    if (is_dummy(inst.products.at(i))) continue;
+    if (!types_strictly_match_except_literal_against_address_or_boolean(variant.products.at(i), inst.products.at(i))) {
+      trace(9993, "transform") << "strict match failed: product " << i << end();
+      return false;
+    }
+  }
+  return true;
+}
+
+bool types_strictly_match_except_literal_against_address_or_boolean(const reagent& to, const reagent& from) {
+  // to sidestep type-checking, use /unsafe in the source.
+  // this will be highlighted in red inside vim. just for setting up some tests.
+  if (is_literal(from)
+      && to.type && to.type->value == get(Type_ordinal, "boolean"))
+    return boolean_matches_literal(to, from);
+  if (is_literal(from) && is_mu_address(to))
+    return from.name == "0";
+  return types_strictly_match(to, from);
+}
+
+// phase 5
+vector<recipe_ordinal> matching_variants(const instruction& inst, vector<recipe_ordinal>& variants) {
+  vector<recipe_ordinal> result;
+  for (int i = 0; i < SIZE(variants); ++i) {
+    if (variants.at(i) == -1) continue;
+    trace(9992, "transform") << "checking variant " << i << ": " << header_label(variants.at(i)) << end();
+    if (all_header_reagents_match(inst, get(Recipe, variants.at(i))))
+      result.push_back(variants.at(i));
+  }
+  return result;
+}
+
+bool all_header_reagents_match(const instruction& inst, const recipe& variant) {
+  for (int i = 0; i < min(SIZE(inst.ingredients), SIZE(variant.ingredients)); ++i) {
+    if (!types_match(variant.ingredients.at(i), inst.ingredients.at(i))) {
+      trace(9993, "transform") << "strict match failed: ingredient " << i << end();
+      return false;
+    }
+  }
+  for (int i = 0; i < min(SIZE(variant.products), SIZE(inst.products)); ++i) {
+    if (is_dummy(inst.products.at(i))) continue;
+    if (!types_match(variant.products.at(i), inst.products.at(i))) {
+      trace(9993, "transform") << "strict match failed: product " << i << end();
+      return false;
+    }
+  }
+  return true;
+}
+
+// tie-breaker for each phase
+const recipe& best_variant(const instruction& inst, vector<recipe_ordinal>& candidates) {
+  assert(!candidates.empty());
+  int min_score = 999;
+  int min_index = 0;
+  for (int i = 0; i < SIZE(candidates); ++i) {
+    const recipe& candidate = get(Recipe, candidates.at(i));
+    int score = abs(SIZE(candidate.products)-SIZE(inst.products))
+                          + abs(SIZE(candidate.ingredients)-SIZE(inst.ingredients));
+    assert(score < 999);
+    if (score < min_score) {
+      min_score = score;
+      min_index = i;
+    }
+  }
+  return get(Recipe, candidates.at(min_index));
+}
+
+int non_ghost_size(vector<recipe_ordinal>& variants) {
+  int result = 0;
+  for (int i = 0; i < SIZE(variants); ++i)
+    if (variants.at(i) != -1) ++result;
+  return result;
+}
+
+bool next_stash(const call& c, instruction* stash_inst) {
+  const recipe& specializer_recipe = get(Recipe, c.running_recipe);
+  int index = c.running_step_index;
+  for (++index; index < SIZE(specializer_recipe.steps); ++index) {
+    const instruction& inst = specializer_recipe.steps.at(index);
+    if (inst.name == "stash") {
+      *stash_inst = inst;
+      return true;
+    }
+  }
+  return false;
+}
+
+:(scenario static_dispatch_disabled_in_recipe_without_variants)
+def main [
+  1:number <- test 3
+]
+def test [
+  2:number <- next-ingredient  # ensure no header
+  return 34
+]
++mem: storing 34 in location 1
+
+:(scenario static_dispatch_disabled_on_headerless_definition)
+% Hide_errors = true;
+def test a:number -> z:number [
+  z <- copy 1
+]
+def test [
+  return 34
+]
++error: redefining recipe test
+
+:(scenario static_dispatch_disabled_on_headerless_definition_2)
+% Hide_errors = true;
+def test [
+  return 34
+]
+def test a:number -> z:number [
+  z <- copy 1
+]
++error: redefining recipe test
+
+:(scenario static_dispatch_on_primitive_names)
+def main [
+  1:number <- copy 34
+  2:number <- copy 34
+  3:boolean <- equal 1:number, 2:number
+  4:boolean <- copy 0/false
+  5:boolean <- copy 0/false
+  6:boolean <- equal 4:boolean, 5:boolean
+]
+
+# temporarily hardcode number equality to always fail
+def equal x:number, y:number -> z:boolean [
+  local-scope
+  load-ingredients
+  z <- copy 0/false
+]
+# comparing numbers used overload
++mem: storing 0 in location 3
+# comparing booleans continues to use primitive
++mem: storing 1 in location 6
+
+:(scenario static_dispatch_works_with_dummy_results_for_containers)
+def main [
+  _ <- test 3, 4
+]
+def test a:number -> z:point [
+  local-scope
+  load-ingredients
+  z <- merge a, 0
+]
+def test a:number, b:number -> z:point [
+  local-scope
+  load-ingredients
+  z <- merge a, b
+]
+$error: 0
+
+:(scenario static_dispatch_works_with_compound_type_containing_container_defined_after_first_use)
+def main [
+  x:address:foo <- new foo:type
+  test x
+]
+container foo [
+  x:number
+]
+def test a:address:foo -> z:number [
+  local-scope
+  load-ingredients
+  z:number <- get *a, x:offset
+]
+$error: 0
+
+:(scenario static_dispatch_works_with_compound_type_containing_container_defined_after_second_use)
+def main [
+  x:address:foo <- new foo:type
+  test x
+]
+def test a:address:foo -> z:number [
+  local-scope
+  load-ingredients
+  z:number <- get *a, x:offset
+]
+container foo [
+  x:number
+]
+$error: 0
+
+:(scenario static_dispatch_prefers_literals_to_be_numbers_rather_than_addresses)
+def main [
+  1:number <- foo 0
+]
+def foo x:address:number -> y:number [
+  return 34
+]
+def foo x:number -> y:number [
+  return 35
+]
++mem: storing 35 in location 1
+
+:(scenario static_dispatch_on_non_literal_character_ignores_variant_with_numbers)
+% Hide_errors = true;
+def main [
+  local-scope
+  x:character <- copy 10/newline
+  1:number/raw <- foo x
+]
+def foo x:number -> y:number [
+  load-ingredients
+  return 34
+]
++error: main: ingredient 0 has the wrong type at '1:number/raw <- foo x'
+-mem: storing 34 in location 1
+
+:(scenario static_dispatch_dispatches_literal_to_boolean_before_character)
+def main [
+  1:number/raw <- foo 0  # valid literal for boolean
+]
+def foo x:character -> y:number [
+  local-scope
+  load-ingredients
+  return 34
+]
+def foo x:boolean -> y:number [
+  local-scope
+  load-ingredients
+  return 35
+]
+# boolean variant is preferred
++mem: storing 35 in location 1
+
+:(scenario static_dispatch_dispatches_literal_to_character_when_out_of_boolean_range)
+def main [
+  1:number/raw <- foo 97  # not a valid literal for boolean
+]
+def foo x:character -> y:number [
+  local-scope
+  load-ingredients
+  return 34
+]
+def foo x:boolean -> y:number [
+  local-scope
+  load-ingredients
+  return 35
+]
+# character variant is preferred
++mem: storing 34 in location 1
+
+:(scenario static_dispatch_dispatches_literal_to_number_if_at_all_possible)
+def main [
+  1:number/raw <- foo 97
+]
+def foo x:character -> y:number [
+  local-scope
+  load-ingredients
+  return 34
+]
+def foo x:number -> y:number [
+  local-scope
+  load-ingredients
+  return 35
+]
+# number variant is preferred
++mem: storing 35 in location 1
+
+:(code)
+string header_label(recipe_ordinal r) {
+  const recipe& caller = get(Recipe, r);
+  ostringstream out;
+  out << "recipe " << caller.name;
+  for (int i = 0; i < SIZE(caller.ingredients); ++i)
+    out << ' ' << to_string(caller.ingredients.at(i));
+  if (!caller.products.empty()) out << " ->";
+  for (int i = 0; i < SIZE(caller.products); ++i)
+    out << ' ' << to_string(caller.products.at(i));
+  return out.str();
+}
+
+:(scenario reload_variant_retains_other_variants)
+def main [
+  1:number <- copy 34
+  2:number <- foo 1:number
+]
+def foo x:number -> y:number [
+  local-scope
+  load-ingredients
+  return 34
+]
+def foo x:address:number -> y:number [
+  local-scope
+  load-ingredients
+  return 35
+]
+def! foo x:address:number -> y:number [
+  local-scope
+  load-ingredients
+  return 36
+]
++mem: storing 34 in location 2
+$error: 0
+
+:(scenario dispatch_errors_come_after_unknown_name_errors)
+% Hide_errors = true;
+def main [
+  y:number <- foo x
+]
+def foo a:number -> b:number [
+  local-scope
+  load-ingredients
+  return 34
+]
+def foo a:boolean -> b:number [
+  local-scope
+  load-ingredients
+  return 35
+]
++error: main: missing type for x in 'y:number <- foo x'
++error: main: failed to find a matching call for 'y:number <- foo x'
+
+:(before "End Includes")
+using std::abs;