Function the element at index i of stack x

output an element of x at index i

Format:

the element at index i of stack x

Input:

Output:

Properties that reference this function:

Conditional properties that reference this function:

• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj.append(x), ys ], rest ] ]
  • Value Stack at time t = [ [ value, [ ] ], [ next_level, other_levels ] ]
  • value at obj in map (Variables Map at time t) = Python reference idx
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Python Object Store at time (t + 1) = result of storing (Python list (result of appending value to entries)) at index idx of stack (Python Object Store at time t)

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj.append(x), ys ], rest ] ]
  • Value Stack at time t = [ [ value, [ ] ], [ next_level, other_levels ] ]
  • value at obj in map (Variables Map at time t) = Python reference idx
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Value Stack at time (t + 1) = [ [ None, next_level ], other_levels ]

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ function call with name: "__getitem__" and arguments: args, ys ], rest ] ]
  • Value Stack at time t = [ [ a, [ Python reference idx, [ ] ] ], [ next_level, other_levels ] ]
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Value Stack at time (t + 1) = [ [ the element at index a of stack entries, next_level ], other_levels ]

  (link)
• if the following are true:
  • Value Stack at time t = [ [ Python reference idx, [ ] ], [ next_level, other_levels ] ]
  • Expression Stack at time t = [ [ ], [ [ function call with name: "len" and arguments: args, ys ], rest ] ]
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Value Stack at time (t + 1) = [ [ length of stack entries, next_level ], other_levels ]

  (link)
• if the following are true:
  • Value Stack at time t = [ [ a, [ ] ], [ next_level, other_levels ] ]
  • Expression Stack at time t = [ [ ], [ [ name."pop"(args), ys ], rest ] ]
  • value at name in map (Variables Map at time t) = Python reference idx
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Python Object Store at time (t + 1) = result of storing (Python list (stack after popping a value from stack entries at index a)) at index idx of stack (Python Object Store at time t)

  (link)
• if the following are true:
  • Value Stack at time t = [ [ a, [ ] ], [ next_level, other_levels ] ]
  • Expression Stack at time t = [ [ ], [ [ name."pop"(args), ys ], rest ] ]
  • value at name in map (Variables Map at time t) = Python reference idx
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Value Stack at time (t + 1) = [ [ the element at index a of stack entries, next_level ], other_levels ]

  (link)
• if the following are true:
  • Value Stack at time t = [ [ a, [ Python reference idx, [ ] ] ], [ next_level, other_levels ] ]
  • Expression Stack at time t = [ [ ], [ [ function call with name: "__contains__" and arguments: args, ys ], rest ] ]
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Value Stack at time (t + 1) = [ [ stack entries contains a, next_level ], other_levels ]

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ function call with name: "__getitem__" and arguments: args, ys ], rest ] ]
  • Value Stack at time t = [ [ a, [ Python reference idx, [ ] ] ], [ next_level, other_levels ] ]
  • the element at index idx of stack (Python Object Store at time t) = Python dictionary entries

  then Value Stack at time (t + 1) = [ [ value at a in map entries, next_level ], other_levels ]

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ function call with name: "__setitem__" and arguments: args, ys ], rest ] ]
  • Value Stack at time t = [ [ value, [ key, [ Python reference idx, [ ] ] ] ], [ next_level, other_levels ] ]
  • the element at index idx of stack (Python Object Store at time t) = Python dictionary entries

  then Python Object Store at time (t + 1) = result of storing (Python dictionary (result of storing value at key: key in map: entries)) at index idx of stack (Python Object Store at time t)

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ function call with name: "__setitem__" and arguments: args, ys ], rest ] ]
  • Value Stack at time t = [ [ value, [ key, [ Python reference idx, [ ] ] ] ], [ next_level, other_levels ] ]
  • the element at index idx of stack (Python Object Store at time t) = Python dictionary entries

  then Value Stack at time (t + 1) = [ [ None, next_level ], other_levels ]

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ function call with name: "__setitem__" and arguments: args, ys ], rest ] ]
  • Value Stack at time t = [ [ value, [ key, [ Python reference idx, [ ] ] ] ], [ next_level, other_levels ] ]
  • the element at index idx of stack (Python Object Store at time t) = Python list elements

  then Python Object Store at time (t + 1) = result of storing (Python list (result of storing value at index key of stack elements)) at index idx of stack (Python Object Store at time t)

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ function call with name: "__setitem__" and arguments: args, ys ], rest ] ]
  • Value Stack at time t = [ [ value, [ key, [ Python reference idx, [ ] ] ] ], [ next_level, other_levels ] ]
  • the element at index idx of stack (Python Object Store at time t) = Python list elements

  then Value Stack at time (t + 1) = [ [ None, next_level ], other_levels ]

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params
  • Parameters List at time t = None
  • Value Stack at time t = [ values, v_stack ]

  then Parameters List at time (t + 1) = params

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params
  • Parameters List at time t = None
  • Value Stack at time t = [ values, v_stack ]

  then Value Stack at time (t + 1) = v_stack

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params
  • Parameters List at time t = None
  • Value Stack at time t = [ values, v_stack ]

  then Function Variables Map at time (t + 1) = [ ]

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params
  • Parameters List at time t = None
  • Value Stack at time t = [ values, v_stack ]

  then Argument Values at time (t + 1) = [ Python reference index, reverse of values ]

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params
  • Parameters List at time t = None
  • Value Stack at time t = [ values, v_stack ]

  then Expression Stack at time (t + 1) = Expression Stack at time t

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params
  • Parameters List at time t = None
  • Value Stack at time t = [ values, v_stack ]

  then Variables Map at time (t + 1) = Variables Map at time t

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params
  • Parameters List at time t = None
  • Value Stack at time t = [ values, v_stack ]

  then Control Map at time (t + 1) = Control Map at time t

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params
  • Parameters List at time t = None
  • Value Stack at time t = [ values, v_stack ]

  then Python Object Store at time (t + 1) = Python Object Store at time t

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params
  • Parameters List at time t = None
  • Value Stack at time t = [ values, v_stack ]

  then Context Stack at time (t + 1) = Context Stack at time t

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params
  • Parameters List at time t = None
  • Value Stack at time t = [ values, v_stack ]

  then the line at time (t + 1) = the line at time t

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params
  • Parameters List at time t = None
  • Value Stack at time t = [ values, v_stack ]

  then the tab at time (t + 1) = the tab at time t

  (link)
• if the following are true:
  • Parameters List at time t = [ ]
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • line number of method method_name of class class_name in (Class Map at time t) = line

  then the line at time (t + 1) = line + 1

  (link)
• if the following are true:
  • Parameters List at time t = [ ]
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • line number of method method_name of class class_name in (Class Map at time t) = line

  then the tab at time (t + 1) = 2

  (link)
• if the following are true:
  • Parameters List at time t = [ ]
  • Expression Stack at time t = [ [ ], [ [ obj_name.method_name(args), ys ], rest ] ]
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • line number of method method_name of class class_name in (Class Map at time t) = line

  then Control Map at time (t + 1) = [ entry 0: (pair ("class", class_name)), [ entry 1: (pair ("method", method_name)), [ ] ] ]

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj.attr, ys ], rest ] ]
  • Value Stack at time t = [ [ Python reference index, [ ] ], [ next_level, other_levels ] ]
  • the element at index index of stack (Python Object Store at time t) = Python object: attributes

  then Value Stack at time (t + 1) = [ [ value at attr in map attributes, next_level ], other_levels ]

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj.attribute = val, ys ], rest ] ]
  • Value Stack at time t = [ [ value, [ Python reference idx, [ ] ] ], [ next_level, other_levels ] ]
  • the element at index idx of stack (Python Object Store at time t) = Python object: entries

  then Python Object Store at time (t + 1) = result of storing (Python object: (result of storing value at key: attribute in map: entries)) at index idx of stack (Python Object Store at time t)

  (link)
• if the following are true:
  • Expression Stack at time t = [ [ ], [ [ obj.attribute = val, ys ], rest ] ]
  • Value Stack at time t = [ [ value, [ Python reference idx, [ ] ] ], [ next_level, other_levels ] ]
  • the element at index idx of stack (Python Object Store at time t) = Python object: entries

  then Value Stack at time (t + 1) = [ [ None, next_level ], other_levels ]

  (link)
• if the following are true:
  • the line at time t = i
  • the tab at time t = j
  • statement at line i, tab j = for target in iterable_ex:
  • Expression Stack at time t = [ [ ], [ ] ]
  • Value Stack at time t = [ [ Python reference index, [ ] ], v_stack ]
  • the element at index index of stack (Python Object Store at time t) = Python list elements

  then Control Map at time (t + 1) = result of storing (trio ("for", i, elements)) at key: j in map: (Control Map at time t)

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ value, [ ] ], stack ]
  • the expression at time t = obj.append(x)
  • value at obj in map (Variables Map at time t) = Python reference idx
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Python Object Store at time (t + 1) = result of storing (Python list (result of appending value to entries)) at index idx of stack (Python Object Store at time t)

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • the expression at time t = obj_name.method_name(args)
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • map (Class Map at time t) contains key class_name = True

  then expression state at time (t + 1) = "call_build_args"

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • the expression at time t = obj_name.method_name(args)
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params

  then Parameters List at time (t + 1) = params

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • the expression at time t = obj_name.method_name(args)
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • method parameters where the Class Map is (Class Map at time t), class name is class_name, and method name is method_name = params

  then Python Object Store at time (t + 1) = Python Object Store at time t

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • the expression at time t = obj_name.method_name(args)
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • Value Stack at time t = [ values, v_stack ]
  • definition of method method_name of class class_name in (Class Map at time t) = method_map

  then Argument Values at time (t + 1) = [ Python reference index, reverse of values ]

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • the expression at time t = obj_name.method_name(args)
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • Value Stack at time t = [ values, v_stack ]
  • definition of method method_name of class class_name in (Class Map at time t) = method_map

  then Value Stack at time (t + 1) = v_stack

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ a, [ Python reference idx, [ ] ] ], stack ]
  • the expression at time t = function call with name: "__getitem__" and arguments: args
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Return Value at time (t + 1) = the element at index a of stack entries

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ Python reference idx, [ ] ], stack ]
  • the expression at time t = function call with name: "len" and arguments: args
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Return Value at time (t + 1) = length of stack entries

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ a, [ ] ], stack ]
  • the expression at time t = name."pop"(args)
  • value at obj in map (Variables Map at time t) = Python reference idx
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Python Object Store at time (t + 1) = result of storing (Python list (stack after popping a value from stack entries at index a)) at index idx of stack (Python Object Store at time t)

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ a, [ ] ], stack ]
  • the expression at time t = name."pop"(args)
  • value at obj in map (Variables Map at time t) = Python reference idx
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Return Value at time (t + 1) = the element at index a of stack entries

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ a, [ Python reference idx, [ ] ] ], stack ]
  • the expression at time t = function call with name: "__contains__" and arguments: args
  • the element at index idx of stack (Python Object Store at time t) = Python list entries

  then Return Value at time (t + 1) = stack entries contains a

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ a, [ Python reference idx, [ ] ] ], stack ]
  • the expression at time t = function call with name: "__getitem__" and arguments: args
  • the element at index idx of stack (Python Object Store at time t) = Python dictionary entries

  then Return Value at time (t + 1) = value at a in map entries

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ value, [ key, [ Python reference idx, [ ] ] ] ], stack ]
  • the expression at time t = function call with name: "__setitem__" and arguments: [ obj, rest ]
  • the element at index idx of stack (Python Object Store at time t) = Python dictionary entries

  then Python Object Store at time (t + 1) = result of storing (Python dictionary (result of storing value at key: key in map: entries)) at index idx of stack (Python Object Store at time t)

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ value, [ key, [ Python reference idx, [ ] ] ] ], stack ]
  • the expression at time t = function call with name: "__setitem__" and arguments: [ obj, rest ]
  • the element at index idx of stack (Python Object Store at time t) = Python dictionary entries

  then Value Stack at time (t + 1) = stack

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ value, [ key, [ Python reference idx, [ ] ] ] ], stack ]
  • the expression at time t = function call with name: "__setitem__" and arguments: [ obj, rest ]
  • the element at index idx of stack (Python Object Store at time t) = Python list elements

  then Python Object Store at time (t + 1) = result of storing (Python list (result of storing value at index key of stack elements)) at index idx of stack (Python Object Store at time t)

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ value, [ key, [ Python reference idx, [ ] ] ] ], stack ]
  • the expression at time t = function call with name: "__setitem__" and arguments: [ obj, rest ]
  • the element at index idx of stack (Python Object Store at time t) = Python list elements

  then Value Stack at time (t + 1) = stack

  (link)
• if the following are true:
  • expression state at time t = "call_build_args"
  • Parameters List at time t = [ ]
  • the expression at time t = obj_name.method_name(args)
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • line number of method method_name of class class_name in (Class Map at time t) = line

  then the line at time (t + 1) = line + 1

  (link)
• if the following are true:
  • expression state at time t = "call_build_args"
  • Parameters List at time t = [ ]
  • the expression at time t = obj_name.method_name(args)
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • line number of method method_name of class class_name in (Class Map at time t) = line

  then the tab at time (t + 1) = 2

  (link)
• if the following are true:
  • expression state at time t = "call_build_args"
  • Parameters List at time t = [ ]
  • the expression at time t = obj_name.method_name(args)
  • value at obj_name in map (Variables Map at time t) = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python object: [ entry "__class_name__": class_name, e_rest ]
  • line number of method method_name of class class_name in (Class Map at time t) = line

  then Control Map at time (t + 1) = [ entry 0: (pair ("class", class_name)), [ entry 1: (pair ("method", method_name)), [ ] ] ]

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • the expression at time t = obj.attr
  • Value Stack at time t = [ [ Python reference index, [ ] ], v_stack ]
  • the element at index index of stack (Python Object Store at time t) = Python object: attributes

  then Return Value at time (t + 1) = value at attr in map attributes

  (link)
• if the following are true:
  • expression state at time t = "call_function_begin"
  • Value Stack at time t = [ [ value, [ Python reference idx, [ ] ] ], stack ]
  • the expression at time t = obj.attribute = val
  • the element at index idx of stack (Python Object Store at time t) = Python object: entries

  then Python Object Store at time (t + 1) = result of storing (Python object: (result of storing value at key: attribute in map: entries)) at index idx of stack (Python Object Store at time t)

  (link)
• if the following are true:
  • the line at time t = i
  • the tab at time t = j
  • statement at line i, tab j = for target in iterable_ex:
  • expression state at time t = "end_expr"
  • Return Value at time t = Python reference index
  • the element at index index of stack (Python Object Store at time t) = Python list elements

  then Control Map at time (t + 1) = result of storing (trio ("for", i, elements)) at key: j in map: (Control Map at time t)

  (link)
• if the following are true:
  • the element at index src of stack towers = src_tower
  • get subtowersrc_tower = sub_tower
  • length of sub_tower is even

  then towers of hanoi towers = towers of hanoi top disks towers

  (link)
• if the following are true:
  • the element at index src of stack towers = src_tower
  • get subtowersrc_tower = sub_tower
  • length of sub_tower is odd

  then towers of hanoi towers = towers of hanoi top disks towers

  (link)
• if the following are true:
  • the element at index src of stack towers = [ 1, rest ]
  • the element at index dst of stack towers = dst_tower

  then towers of hanoi top towers = move disk towers is even

  (link)
• if the following are true:
  • the element at index src of stack towers = [ x, rest ]
  • the element at index dst of stack towers = dst_tower
  • x > 1

  then towers of hanoi top towers = towers of hanoi (move disk towers is even)

  (link)
• if the element at index i of stack tree = node (v, (-1), (-1)), then Height of a tree tree and index i = 1 (link)
• if the element at index i of stack tree = node (v, left, (-1)), then Height of a tree tree and index i = (Height of a tree tree and index left) + 1 (link)
• if the element at index i of stack tree = node (v, (-1), right), then Height of a tree tree and index i = (Height of a tree tree and index right) + 1 (link)
• if the following are true:
  • the element at index i of stack tree = node (v, a, b)
  • Height of a tree tree and index a > Height of a tree tree and index b

  then Height of a tree tree and index i = (Height of a tree tree and index a) + 1

  (link)
• if the following are true:
  • the element at index i of stack tree = node (v, a, b)
  • Height of a tree tree and index a < Height of a tree tree and index b

  then Height of a tree tree and index i = (Height of a tree tree and index b) + 1

  (link)
• if the following are true:
  • the element at index i of stack tree = node (v, a, b)
  • Height of a tree tree and index a = Height of a tree tree and index b

  then Height of a tree tree and index i = (Height of a tree tree and index a) + 1

  (link)
• if the following are true:
  • val < a
  • the element at index i of stack tree = node (a, left, right)

  then output of the bst_insert function where input tree is tree, value is val and index is i = output of the bst_insert function where input tree is tree, value is val and index is left

  (link)
• if the following are true:
  • val > a
  • the element at index i of stack tree = node (a, left, right)

  then output of the bst_insert function where input tree is tree, value is val and index is i = output of the bst_insert function where input tree is tree, value is val and index is right

  (link)
• if the following are true:
  • val < a
  • the element at index i of stack tree = node (a, (-1), right)

  then output of the bst_insert function where input tree is tree, value is val and index is i = result of storing (node (a, (length of stack tree), right)) at index i of stack (result of appending (node (val, (-1), (-1))) to tree)

  (link)
• if the following are true:
  • val > a
  • the element at index i of stack tree = node (a, left, (-1))

  then output of the bst_insert function where input tree is tree, value is val and index is i = result of storing (node (a, left, (length of stack tree))) at index i of stack (result of appending (node (val, (-1), (-1))) to tree)

  (link)
• if the following are true:
  • find root index in tree = ri
  • the element at index ri of stack tree = node (root_val, left, right)
  • the element at index left of stack tree = node (l_val, l_left, l_right)
  • new_val < root_val
  • new_val < l_val

  then result of inserting new_val to tree tree = result of rotating (output of the bst_insert function where input tree is tree, value is new_val and index is ri) clockwise

  (link)
• if the following are true:
  • find root index in tree = ri
  • the element at index ri of stack tree = node (root_val, left, right)
  • the element at index left of stack tree = node (l_val, l_left, l_right)
  • new_val < root_val
  • new_val > l_val

  then result of inserting new_val to tree tree = result of rotating (result of rotating (output of the bst_insert function where input tree is tree, value is new_val and index is ri) twice) clockwise

  (link)
• if the following are true:
  • find root index in tree = ri
  • the element at index ri of stack tree = node (root_val, left, right)
  • the element at index left of stack tree = node (l_val, l_left, l_right)

  then result of rotating tree clockwise = result of storing (node (l_val, l_left, ri)) at index left of stack (result of storing (node (root_val, l_right, right)) at index ri of stack tree)

  (link)
• if the following are true:
  • find root index in tree = ri
  • the element at index ri of stack tree = node (root_val, left, right)
  • the element at index left of stack tree = node (l_val, l_left, g)
  • the element at index g of stack tree = node (g_val, g_left, g_right)

  then result of rotating tree twice = result of storing (node (root_val, g, right)) at index ri of stack (result of storing (node (g_val, left, g_right)) at index g of stack (result of storing (node (l_val, l_left, g_left)) at index left of stack tree))

  (link)
• if the element at index i of stack tree = node (value, left, right), then find nearest largertree = find nearest largertree (link)
• if the following are true:
  • val < a
  • the element at index i of stack tree = node (a, (-1), right)

  then find nearest largertree = i

  (link)
• if the following are true:
  • val < a
  • the element at index i of stack tree = node (a, left, right)

  then find nearest largertree = find nearest largertree

  (link)
• if the following are true:
  • val > a
  • the element at index i of stack tree = node (a, left, right)

  then find nearest largertree = find nearest largertree

  (link)
• if the following are true:
  • val = a
  • the element at index i of stack tree = node (a, left, right)

  then find nearest largertree = find nearest largertree

  (link)
• if the following are true:
  • index of value value in tree = i
  • the element at index i of stack tree = node (value, (-1), (-1))
  • find parent index of tree = p
  • the element at index p of stack tree = node (pval, pleft, i)

  then pop value from tree tree = result of storing (node (pval, pleft, (-1))) at index p of stack tree

  (link)
• if the following are true:
  • index of value value in tree = i
  • the element at index i of stack tree = node (value, left, (-1))
  • the element at index left of stack tree = node (lvalue, lleft, lright)
  • find parent index of tree = p
  • the element at index p of stack tree = node (pval, pleft, i)

  then pop value from tree tree = result of storing (node (value, (-1), (-1))) at index i of stack (result of storing (node (pval, pleft, left)) at index p of stack tree)

  (link)
• if the following are true:
  • index of value value in tree = i
  • the element at index i of stack tree = node (value, (-1), right)
  • the element at index right of stack tree = node (rvalue, rleft, rright)
  • find parent index of tree = p
  • the element at index p of stack tree = node (pval, i, pright)

  then pop value from tree tree = result of storing (node (value, (-1), (-1))) at index i of stack (result of storing (node (pval, right, pright)) at index p of stack tree)

  (link)
• if the following are true:
  • index of value value in tree = i
  • find nearest largertree = n
  • the element at index n of stack tree = node (larger, nleft, nright)
  • the element at index i of stack tree = node (value, left, right)

  then pop value from tree tree = result of storing (node (larger, left, right)) at index i of stack (pop larger from tree tree)

  (link)
• if the following are true:
  • find root index in tree = ri
  • the element at index ri of stack tree = node (rvalue, left, right)
  • Height of a tree tree and index left = Height of a tree tree and index right

  then result of balancing the tree tree = tree

  (link)
• if the following are true:
  • find root index in tree = ri
  • the element at index ri of stack tree = node (rvalue, left, right)
  • Height of a tree tree and index left > (Height of a tree tree and index right) + 1
  • the element at index left of stack tree = node (lvalue, lleft, lright)
  • Height of a tree tree and index lleft > Height of a tree tree and index lright

  then result of balancing the tree tree = result of rotating tree clockwise

  (link)
• if the following are true:
  • find root index in tree = ri
  • the element at index ri of stack tree = node (rvalue, left, right)
  • Height of a tree tree and index left > (Height of a tree tree and index right) + 1
  • the element at index left of stack tree = node (lvalue, lleft, lright)
  • Height of a tree tree and index lleft < Height of a tree tree and index lright

  then result of balancing the tree tree = result of rotating (result of rotating tree twice) clockwise

  (link)
• if the following are true:
  • ((length of stack tree) - 1) - index = back_i
  • the element at index back_i of stack tree = node (value, cs)

  then children of the node at backwards index index of tree tree in graph graph = output of the find_neighbors function where the input graph is graph, node is value, and children are [ ]

  (link)
• if the following are true:
  • ((length of stack tree) - 1) - index = back_i
  • the element at index back_i of stack tree = node (value, cs)
  • elements of numbers that are not in tree tree = new_elements
  • result of storing (node (value, new_elements)) at index back_i of stack tree = updated

  then result of adding numbers to tree tree as children of the node at backwards index index = result of pushing values new_elements to tree updated

  (link)
• if the following are true:
  • ((length of stack tree) - 1) - index = back_i
  • the element at index back_i of stack tree = node (value, distance, previous)

  then children of the node at backwards index index of tree tree in graph graph = output of the find_neighbors function where the input graph is graph, node is value, and children are [ ]

  (link)
• if the following are true:
  • the element at index child_i of stack tree = node (child_value, child_d, child_prev)
  • distance + weight < child_d
  • result of storing (node (child_value, (distance + weight), index)) at index child_i of stack tree = updated

  then result of updating nodes [ pair (child_i, weight), rest ] in tree tree with parent index index and parent distance distance = result of updating nodes rest in tree updated with parent index index and parent distance distance

  (link)
• if the following are true:
  • the element at index child_i of stack tree = node (child_value, child_d, child_prev)
  • distance + weight > child_d

  then result of updating nodes [ pair (child_i, weight), rest ] in tree tree with parent index index and parent distance distance = result of updating nodes rest in tree tree with parent index index and parent distance distance

  (link)
• if the following are true:
  • ((length of stack tree) - 1) - index = back_i
  • the element at index back_i of stack tree = node (value, distance, previous)
  • result of splitting pairs into nodes that exist in the tree tree and new nodes = pair (exists, new)
  • result of updating nodes exists in tree tree with parent index index and parent distance distance = updated

  then result of adding or updating children pairs of the node at backwards index index in tree tree = result of pushing nodes new into tree updated where parent is index and parent distance is distance

  (link)

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