| Larch: Data Analysis Tools for X-ray Spectroscopy

# 10.2. Basic and Complex Data Types

This section of the Larch tutorial describes the types of data that Larch has, and how to use them.

## 10.2.1. Basic Data Types

As with most programming languages, Larch has several built-in data types to express different kinds of data. These include the usual integers, floating point numbers, and strings common to many programming languages. A variable name can hold any of these types (or any of the other more complex types we’ll get to later), and does not need to be declared beforehand or to change its value or type. Some examples:

    larch> a = 2
    larch> b = 2.50

The normal ‘+’, ‘-’, ‘*’, and ‘/’ operations work on numerical values for addition, subtraction, multiplication, and division. Exponentiation is signified by ‘**’, and modulus by ‘%’. Larch uses the ‘/’ symbol for division or ‘true division’, giving a floating point value if needed, even if the numerator and denominator are integers, and ‘//’ for integer or ‘floor’ division. Thus:

    larch> 3 + a
    5
    larch> b*2
    5.0
    larch> 3/2
    1.5
    larch> 3//2
    1
    larch> 7 % 3
    1

Several other operators are supported for bit manipulation.

Literal strings are created with either matched closing single or double quotes:

    larch> s = 'a string'
    larch> s2 = "a different string"

A string can include a ‘\n’ character (for newline) or ‘\t’ (for tab) and several other control characters, as in many languages. The backslash character ‘\’ indicates these escape sequences, which includes newline as tab as well as several other standard escape sequence. The quote character and the backslash character themselves can be backslashed. Thus, to get an actual backslash character in the string, you would have to use ‘\\’, and to get a single quote, one might say:

    larch> s3 = 'A string with a backslash-> \\ '
    larch> s4 = 'Bob\'s string'

One can also use so-called a raw string, in which the backslash character is not used for escape sequences:

    larch s5 = r'A string with backslash \n but not a newline!'

For strings that may span over more than 1 line, a special “triple quoted” syntax is supported, so that:

    larch> long_string = """Now is the time for all good men
    .....> to come to the aid of their party"""
    larch> print(long_string)
    Now is the time for all good men
    to come to the aid of their party

It is important to keep in mind that mixing data types in a calculation may or may not make sense to Larch. For example, a string cannot be added to a integer:

    larch> '1' + 1
    Runtime Error:
    cannot concatenate 'str' and 'int' objects
    <StdInput>
         '1' + 1

but you can add an integer and a float:

    larch> 1 + 2.5
    3.5

and you can multiply a string by an integer:

    larch> 'string' * 2
    'stringstring'

Larch has special variables for boolean or logical operations: `True` and `False`. These are equal to 1 and 0, respectively, but are mostly used in logical operations, which include operators ‘and’, ‘or’, and ‘not’, as well as comparison operators ‘>’, ‘>=’, ‘<’, ‘<=’, ‘==’, ‘!=’, and ‘is’. Note that ‘is’ expresses identity, which is a slightly stricter test than ‘==’ (equality), and is most useful for complex objects.:

    larch> b = 5
    larch> 2 > 3
    False
    larch> (b > 0) and (b <= 10)
    True

The special value `None` is used as a null value throughout Larch and Python.

Finally, Larch knows about complex numbers, using a ‘j’ to indicate the imaginary part of the number:

    larch> sqrt(-1)
    Warning: invalid value encountered in sqrt
    nan
    larch> sqrt(-1+0j)
    1j
    larch> 1j*1j
    (-1+0j)
    larch> x = sin(1+1j)
    larch> print(x)
    (1.2984575814159773+0.63496391478473613j)
    larch> print(x.imag)
    0.63496391478473613

To be clear, all these primitive data types in Larch are derived from the corresponding Python objects, so you can consult python documentation for further details and notes.

## 10.2.2. Objects and Groups

Since Larch is built upon Python, an object-oriented programming language, all named quantities or variables in Larch are python objects. Because of this, most Larch variables come with built-in functionality derived from their python objects. Though Larch does not provide a way for the user to define their own new objects, objects created in Python this can be used by Larch, so that extensions and plugins for Larch can define new classes of object types.

### 10.2.2.1. Objects

All Larch variables are Python objects, and so have a well-defined type and a set of attributes and methods that go with it. To see the Python type of any variable, use the builtin `type()` function:

    larch> type(1)
    <type 'int'>
    larch> type('1')
    <type 'str'>
    larch> type(1.0)
    <type 'float'>
    larch> type(1+0j)
    <type 'complex'>
    larch> type(sin)
    <type 'numpy.ufunc'>

The attributes and methods differ for each type of object, but are all accessed the same way – with a ‘.’ (dot) separating the variable name or value from the name of the attribute or method. As above, complex data have `real` and `imag` attributes for the real and imaginary parts, which can be accessed:

    larch> x = sin(1+1j)
    larch> print(x)
    (1.2984575814159773+0.63496391478473613j)
    larch> print(x.imag)
    0.63496391478473613

Methods are attributes of an object that happen to be callable as a function. Since they belong to to an object, they know about the data and other attributes in that object. To call a method or function, simply add parentheses ‘()’ after its name, possibly with arguments inside the parentheses to change the methods behavior. For example, a complex number has a `conjugate()` method:

    larch> x.conjugate
    <built-in method conjugate of complex object at 0x178e54b8>
    larch> x.conjugate()
    (1.2984575814159773-0.63496391478473613j)

Note that just using `x.conjugate` returns the method itself, while using `x.conjugate()` actually runs the method. It’s fair to ask why `real` and `imag` are simple attributes of complex number object while `conjugate` is a method that must be called. In general, the idea is that simple attributes are static data belonging to the object, while a method is something that has to be computed. These rules are not fixed, however, and it is sometimes a matter of knowing which attributes are callable methods.

Many data types have their own attribues and methods. As we’ll see below, strings have many attributes and methods, as do the container objects (list, array, tuple, dictionary) we’ll see shortly.

To get a listing of all the attributes and methods of a object, use the builtin `dir()` function:

    larch> dir(1)
    ['__abs__', '__add__', '__and__', '__class__', '__cmp__', '__coerce__', '__delattr__', '__div__', '__divmod__', '__doc__', '__float__', '__floordiv__', '__format__', '__getattribute__', '__getnewargs__', '__hash__', '__hex__', '__index__', '__init__', '__int__', '__invert__', '__long__', '__lshift__', '__mod__', '__mul__', '__neg__', '__new__', '__nonzero__', '__oct__', '__or__', '__pos__', '__pow__', '__radd__', '__rand__', '__rdiv__', '__rdivmod__', '__reduce__', '__reduce_ex__', '__repr__', '__rfloordiv__', '__rlshift__', '__rmod__', '__rmul__', '__ror__', '__rpow__', '__rrshift__', '__rshift__', '__rsub__', '__rtruediv__', '__rxor__', '__setattr__', '__sizeof__', '__str__', '__sub__', '__subclasshook__', '__truediv__', '__trunc__', '__xor__', 'conjugate', 'denominator', 'imag', 'numerator', 'real']
    larch> dir('a string')
    ['__add__', '__class__', '__contains__', '__delattr__', '__doc__', '__eq__', '__format__', '__ge__', '__getattribute__', '__getitem__', '__getnewargs__', '__getslice__', '__gt__', '__hash__', '__init__', '__le__', '__len__', '__lt__', '__mod__', '__mul__', '__ne__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__rmod__', '__rmul__', '__setattr__', '__sizeof__', '__str__', '__subclasshook__', '_formatter_field_name_split', '_formatter_parser', 'capitalize', 'center', 'count', 'decode', 'encode', 'endswith', 'expandtabs', 'find', 'format', 'index', 'isalnum', 'isalpha', 'isdigit', 'islower', 'isspace', 'istitle', 'isupper', 'join', 'ljust', 'lower', 'lstrip', 'partition', 'replace', 'rfind', 'rindex', 'rjust', 'rpartition', 'rsplit', 'rstrip', 'split', 'splitlines', 'startswith', 'strip', 'swapcase', 'title', 'translate', 'upper', 'zfill']

Again, we’ll see properties of objects below, as we look into more interesting data types, or you can look into Python documentation.

### 10.2.2.2. Groups

While all values in Larch are Python objects, Larch organizes data into Groups, which are a key concept to Larch. A Group is simply a named container for variables of any kind, including other Groups. As Larch doesn’t directly provide a way to definie your own objects, a Group is the way to organize your data in Larch. The organization of data with nested Groups provides a heirarchical structure to all data in a Larch session, much like a directory of files. Each Larch variable belongs to a Group, and can always be accessed by its full Group name. The top-level Group is called ‘_main’. You’ll rarely need to use that fact, but it’s there:

    larch> myvar = 22.13
    larch> print(_main.myvar)
    22.13
    larch> print(myvar)
    22.13

You can create your own groups and add data to it with the builtin `group()` function:

    larch> g = group()
    larch> g
    <Group 0x17ee50f0>

You can add variables to your Group ‘g’, using the ‘.’ (dot) to separate the parent group from the child object:

    larch> g.x = 1002.8
    larch> g.label = 'here is a string'
    larch> g.data = arange(100)
    larch> print(g.x/5)
    200.56

(`arange()` is a builtin function to create an array of numbers). As from the above discussion of objects, the ‘.’ (dot) notation implies that ‘x’, ‘label’, and ‘data’ are attributes of ‘g’ – that’s entirely correct.

Groups have 1 builtin property – `__name__` which holds a name for the Group. If not specified, it will be set to a hexidecimal value. Groups have no other builtin properties or methods. Since they’re objects, you can use the `dir()` function as above:

    larch> dir(g)
    ['data', 'label', 'x']

(Note that the order shown may vary). You can also use the builtin `show()` function to get a slightly more complete view of the group’s contents:

    larch> show(g)
    == Group 0x1b8cbfb0: 3 symbols ==
      data: array<shape=(100,), type=dtype('int32')>
      name: 'here is a string'
      x: 1002.8

(The ‘0x1b8cbfb0’ is the default name, discussed in more detail below in Object identities, copying, and equality vs. identity). The `group()` function can take arguments of attribute names and values, so that this group could have been created with a single call:

    larch> g = group(x=1002.8, name='here is a string', data=arange(100))

Many Larch functions act on groups, either returning groups, expecting groups as certain arguments, or taking a ‘group’ argument to write data into. For example, the built-in functions that read data from an external files will likely organize that data into a group and that group perhaps something like:

    larch> cu = read_ascii('cu_150k.xmu')

### 10.2.2.3. Builtin Larch Groups

Larch starts up with several groups, organizing builtin functionality into different groups. The top-level ‘_main’ group begins with 3 principle subgroups, ‘_builtin’, ‘_sys’, and ‘_math’ for basic functionality. For almost all uses of Larch, several additional groups are created for more specific functionality are created on startup by Larch plugins. The principle starting groups are describe in Table of Basic Larch Groups

> > Table of Basic Larch Groups. These groups are listed in order of how they will be searched for functions and data.

> Group Name | description
> --- | ---
> _builtin | basic builtin functions.
> _math | mathematical and array functions.
> _sys | larch system-wide variables.
> _io | file input/output functions.
> _plotter | plotting and image display functions.
> _xafs | XAFS-specific functions.

The functions in ‘_builtin’ are mostly inherited from Python’s own built-in functions. The functions in ‘_math’ are mostly inherited from Numpy, and contain basic array handling and math.

### 10.2.2.4. How Larch finds variable names

With several builtin groups, and even more groups created to store your own data to be processed, Larch ends up with a complex heirarchy of data. This gives a good way of organizing data, but it also leads to a question of how variable names are found. Of course, you can always access a function or data object by its full name:

    larch> print(_math.sin(_math.pi/2))
    1.0

but that’s too painful to use, and of course, one needs to be able to do:

    larch> print(sin(pi/2))
    1.0

and have Larch know that when you say `sin()`, you mean `_math.sin()`. The way this look-up of names works is that Larch keeps a list of groups that it will search through for names. This list is held in the variable `_sys.searchGroups`, and can be viewed and modified during a Lach session. On startup, this list has the groups listed in Table of Basic Larch Groups, in the order shown. To be clear, if there was a variable named `_sys.something` and a `_math.something`, typing ‘something’ would resolve to `_sys.something`, and to access `_math.something` you would have to give the full name. For the builtin functions and variables, such clashes are not so likely, but they are likely if you read in many data sets as groups, and want to access the contents of the different groups.

## 10.2.3. More Complex Data Structures: Lists, Arrays, Dictionaries

Larch has many more data types built on top of the primitive types above. These are generally useful for storing collections of data, and can be built up to construct very complex structures. These are all described in some detail here. But as these are all closely related to Python objects, further details can be found in the standard Python documentation.

### 10.2.3.1. Lists

A list is an ordered sequence of other data types. They are heterogeneous – they can be made up of data with different types. A list is constructed using brackets, with commas to separate the individual:

    larch> my_list1 = [1, 2, 3]
    larch> my_list2 = [1, 'string', sqrt(7)]

A list can contain a list as one of its elements:

    larch> nested_list = ['a', 'b', ['c', 'd', ['e', 'f', 'g']]]

You can access the elements of a list using brackets and the integer index (starting from 0):

    larch> print(my_list2[1])
    'string'
    larch> print(nested_list[2])
    ['c', 'd', ['e', 'f', 'g']]
    larch> print(nested_list[2][0])
    'c'

Lists are mutable – they can be changed, in place. To do this, you can replace an element in a list:

    larch> my_list1[0] = 'hello'
    larch> my_list1
    ['hello', 2, 3]

As above, lists are python objects, and so come with methods for interacting with them. For example, you can also change a list by appending to it with the ‘append’ method:

    larch> my_list1.append('number 4, the larch')
    larch> my_list1
    ['hello', 2, 3, 'number 4, the larch']

All lists will have an ‘append’ method, as well as several others:

> - append – add an element to the end of the list

> - count – to return the number of times a particular element occurs in the list

> - extend – to extend a list with another list

> - index – to find the first occurance of an element

> - insert – to insert an element in a particular place.

> - pop – to remove and return the last element (or other specified index).

> - remove – remove a particular element

> - reverse – reverse the order of elements

> - sort – sort the elements.

Note that the methods that change the list do so IN PLACE and return `None`. That is, to sort a list (alphabetically by default, or with an optional custom comparison function passed in), do this:

    larch> my_list.sort()

but not this:

    larch> my_list = my_list.sort()  # WRONG!!

as that will sort the list, then happily set ‘my_list’ to None.

You can get the length of a list with the built-in `len()` function, and test whether a particular element is in a list with the in operator:

    larch> my_list = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']
    larch> print(len(my_list))
    10
    larch> 'e' in my_list
    True

You can access a sub-selection of elements with a slice, giving starting and ending indices between brackets, separated by a colon. Of course, the counting for a slice starts at 0. It also excludesthe final index:

    larch> my_list[1:3]
    ['b', 'c']
    larch> my_list[:4]   # Note implied 0!
    ['a', 'b', 'c', 'd']

You can count backwards, and using ‘-1’ is a convenient way to get the last element of a list. You can also add an optional third value to the slice for a step:

    larch> my_list[-1]
    'j'
    larch> my_list[-3:]
    ['h', 'i', 'j']
    larch> my_list[::2]  # every other element, starting at 0
    ['a', 'c', 'e', 'g', 'i']
    larch> my_list[1::2]  # every other element, starting at 1
    ['b', 'd', 'f', 'h', 'j']

A final important property of lists, and of basic variable creation in Larch (and Python) is related to the discussion above about variable creation and assignment. There we said that ‘creating a variable’:

    larch> my_list = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j']

was best thought of as creating a value (here, the literal list “[‘a’, ‘b’, …, ‘j’]”) and then assigning the name ‘my_list’ to point to that value. Here’s why we make that distinction. If you now say:

    larch> your_list = my_list

the variable ‘your_list’ now points to the same value – the same list. That is, it does not make a copy of the list. Since the list is mutable, changing ‘your_list’ will also change ‘my_list’:

    larch> your_list[0] = 500
    larch> print(my_list[:3])
    [500, 'b', 'c']                # changed!!

You can make a copy of a list, by selecting a full slice:

    larch> your_list = my_list[:]
    larch> your_list[0] = 3.2444
    larch> print(my_list[:3])
    [500, 'b', 'c']                 # now unchanged

    larch> your_list[0] == my_list[0]
    False

Note that this behavior doesn’t happen for immutable data types, including the more primitive data types such as integers, floats and strings. This is essentially because you cannot assign to parts of those data types, only set its entire value.

As always, consult the Python documentation for more details.

### 10.2.3.2. Tuples

Like lists, tuples are sequences of heterogenous objects. The principle difference is that tuples are immutable – they cannot be changed once they are created. Instead, tuples are a simple ordered container of data. The syntax for tuples uses comma separated values inside (optional!) parentheses in place of brackets:

    larch> my_tuple = (1, 'H', 'hydrogen')

Like lists, tuples can be indexed and sliced:

    larch> my_tuple[:2]
    (1, 'H')
    larch> my_tuple[-1]
    'hydrogen'

Due to their immutability, tuples have only a few methods (‘count’ and ‘index’ with similar functionality as for list).

Though tuples they may seem less powerful than lists, and they are actually used widely with Larch and Python. In addition to the example above using a tuple for a short, fixed data structure, many functions will return a tuple of values. For this case, the simplicity an immutability of tuples is a strength becaues, once created, a tuple has a predictable size and order to its elements, which is not true for lists. That is, if a larch procedure (which we’ll see more of below) returns two values as a tuple:

    larch> def sumdiff(x, y):
    .....>     return x+y, x-y
    .....> enddef
    larch> x = sumdiff(3, 2)
    larch> print( x[0], x[1])
    5 1

Because the returned tuple has a fixed structure, you can also assign the it directly to a set of (the correct number of) variables:

    larch> plus, minus = sumdiff(10, 3)
    larch> print(plus, minus)
    13 7

### 10.2.3.3. A second look at Strings

Though discussed earlier in the basic data types, strings are closely related to lists as well – they are best thought of as a sequence of characters. Like tuples, strings are actually immutable, in that you cannot change part of a string, instead you must create a new string. Strings can be indexed and sliced as with lists and tuples:

    larch> name = 'Montaigne'
    larch> name[:4]
    'Mont'

Strings have many methods – over 30 of them, in fact. To convert a string to lower case, use its `lower()` method, and so on:

    larch> 'Here is a String'.lower()
    'here is a string'
    larch> 'Here is a String'.upper()
    'HERE IS A STRING'
    larch> 'Here is a String'.title()
    'Here Is A String'

This aslo shows that the methods are associated with strings themselves – even literal strings, and simply with variable names.

Strings can be split into words with the `split()` method, which splits a string on whitespace by default, but can take an argument to change the character (or substring) to use to split the string:

    larch> 'Here is a String'.split()
    ['Here', 'is', 'a', 'String']

    larch> 'Here is a String'.split('i')
    ['Here ', 's a Str', 'ng']

As above, this is really only touching the tip of the iceberg of string functionality, and consulting standard Python documentation is recommended for more information.

### 10.2.3.4. Arrays

Whereas lists are sequences of heterogeneous objects that can grow and shrink, and included deeply nested structures, they are not well suited for holding numerical data. Arrays are sequences of the same primitive data type, and so are much closer to arrays in C or Fortran. This makes them much more suitable for numeric calculations, and so are extremely important in Larch. There are many ways to create arrays, including the builtin `array()` function which will attempt to convert a list or tuple of numbers into an Array. You can also use the builtin `arange()` function to create an ordered sequence of indices ([1, 2, 3, …]), or one of several other methods to create arrays.

Arrays are so important for processing numerical data that the next section is devoted to them.

### 10.2.3.5. Dictionaries

Our final basic data-structure is the dictionary, which is a container that maps values to keys. This is sometimes called a hash or associative array. Like a list, a dictionary holds many heterogeneous values, and can be altered in place. Unlike a list, the elements of a dictionary have no guaranteed order, and are not selected by integer index, and multiple values cannot be selected by a slice. Instead, the elements of a dictionary are accessed by key, which is normally a string, but can also be an integer or floating point number, or even a tuple or some other objects – any immutable object can be used. Dictionaries are delimited by curly braces, with colons (‘:’) separating key and value, and commas separating different elements:

    larch> atomic_weight = {'H': 1.008, 'He': 4.0026, 'Li': 6.9, 'Be': 9.012}
    larch> print(atomic_weight['He'])
    4.0026

You can also add more elements to a dictionary by assigning to a new key:

    larch> atomic_weight['B']  = 10.811
    larch> atomic_weight['C']  = 12.01

Dictionaries have several methods. These include

> - clear – remove all elements from a dictionary.

> - copy – make a copy of a dictionary.

> - get – get an element by name.

> - has_key – return whether a dictionary has a key.

> - items – return a list of (key, value) tuples

> - keys – return a list of keys.

> - values – return a list of values.

> - pop – remove an element by key, return the value.

> - popitem – remove the “next” item, return (key, value)

> - update – add or overwrite items from another dictionary.

For example:

> larch> atomic_weight.keys() [‘Be’, ‘C’, ‘B’, ‘H’, ‘Li’, ‘He’] larch> atomic_weight.values() [9.0120000000000005, 12.01, 10.811, 1.008, 6.9000000000000004, 4.0026000000000002]

Note that the keys and values are not in the order they were entered. If you add more elements to the dictionary, the new order can be unrelated to the old order. What is guaranteed is that the order of the list of keys will always match the order of the list of values.

As with lists, dictionaries are mutable, and the values in a dictionary can be any object, including other lists and dictionaries, so that a dictionary can end up with a very complex structure. Dictionaries are quite useful, and are in fact used throughout python.

## 10.2.4. Object identities, copying, and equality vs. identity

OK, this may be a bit advanced for a section in a tutorial, but there are a few important topics we need to make about objects, groups, and the idea of mutability discussed above. Though it may at first pass seem surprising, these points are all related, and will come up several times in this document and in your use of Larch. Those familiar with Fortran, C, or Java programming may need to read this more carefully, as Larch and Python actually work quite differently from those languages. What we’re aiming to cover here includes:

> - what variable assignment really means.

> - mutable and immutable objects.

> - object identity.

> - the difference between equality and identity.

As mentioned above, each named quantity in Larch is simply a Python object (for the C, C++, and Java programmers, every variable is reference or pointer). Assignment to a Larch variable as with:

    larch> w = 1 + 2
    larch> x = 'a string'
    larch> y = ['a', 'b', 'c', 'd']
    larch> z = some_function(3)

first determines the value from the right-hand-side of the expression (1+2, ‘a string’, a list, and the return value of some_function()) then assigns the variable name (w, x, y, z) to point to the corresponding value. Larch doesn’t pre-assign variable names so that ‘w’ there can only ever hold an integer – you can change not only its value but the type of data its pointing to:

    larch> w = 3.25  # now a floating point number
    larch> w = [1, 2, 3]  # now a list

For this reason, a variable name is best thought of as something very different from the value it points to. Of course, it is obvious when two different variable names are different, because the names are different. It is less clear whether the value the variables hold are different.

Values of simple types (integer, float, string, tuple, and a few other builtin types) are said to be immutable – the value itself cannot change. You can reassign a name to a different value, but:

    larch> w = 3.25
    larch> w = 4.68

doesn’t change the value of 3.25. Assignment to simple types then can be thought of as essentially making a fresh value for the name to point each time an assignment is made. This isn’t exactly true because Python sets pre-allocates small integers so that it is not making a new integer object every time you assign a number to 1, but it’s a reasonable approximation for now.

Several object types such as lists, dictionaries, arrays, and groups, all are meant to changeable after they are created: they are mutable. That is, even after creating a list, you can append an element to it or you can remove an item from it, and so on. These actions changes the value that the object points to. The object just points to a place in memory – this does not have to change just because the value changes.

This is somewhat different than the model for variable in languages such as C or Fortran where variables have fixed memory locations and specific types of data they can hold. In Python and Larch, all objects point to some value. For mutable data types, the value is allowed to change. In addition, what the object points to can also change.

Each object value has a unique memory location – its identity. The builtin `id()` function returns this identity. Two variables are said to be identical if their values have the same identity – the variables point to the same quantitiy. Two variabales are equal if their values are the same, even if these values are held in different memory locations. And, of course, two different variables can point to the same object.

You can test both equality (whether two variables hold equal value) and identity (whether two variables point to the same value). First, the builtin `id()` function will give the identity (essentially, the memory location) of a variable:

    larch> x = [1, 2, 3, 4, 5]
    larch> id(x)
    108444568

(the value shown will be different each time you run Larch). Now if we assign another variable to `x`, we can use `id()` to see why changing the value of one changes the value of the other:

    larch> y = x
    larch> id(y)
    108444568      ### The same as id(x) !!
    larch> y[1] = 'hello'
    larch> print(x)
    [1, 'hello', 3, 4, 5]

Here, `x` changed because it is identical to `y` and is mutable. However, if we make another variable that happens to have the same value:

    larch> z = [1, 'hello', 3, 4, 5]
    larch> id(z)
    108399752

Now changing an element of `z` will not change `x` or `y`. You can test whether two variables have equal values with the boolean operator ==. Similarly, you can test whether two variables are identical with the boolean operator is. So:

    larch> x == y, x is y
    (True, True)
    larch> x == z, x is z
    (True, False)

If you want to make a copy of a mutable object, you can use the builtin `copy()` function:

    larch> q = copy(z)
    larch> q == z, q is z
    (True, False)

Another, and very common way to make copies of lists and arrays is to create a new value that happens to have the same value. For a list, a very common approach is to make a full slice:

    larch> newx = x[:]
    larch> x == newx, x is newx
    (True, False)

and for arrays, you can multiply by 1 or add 0:

    larch> a = array([1., 2., 3., 4., 5., 6.])
    larch> b = a
    larch> c = 1 * a
    larch> a is b, a is c
    (True, False)

Note that doing `a == b` on arrays here would give an array of values, testing the values element-by-element. This will be discussed the next section.

Larch Groups are also mutable objects and so assignment to a group does not make a new copy of the group but another reference to the same group:

    larch> g = group(x=1, text='hello')
    larch> h = g
    larch> h is g
    True

If ask for the group to be printed or run the `show()` function on a group:

    larch> g
    <Group 0x6bf17f0>
    larch> show(g)
    == Group 0x6bf17f0: 2 symbols ==
      x: 1
      text: 'hello'

we see the hexidecimal representation of its memory address:

    larch> id(g), hex(id(g))
    (113186800, '0x6bf17f0')

In practice, this issue is not as confusing as it sounds, and the model for data, variables, and values is generally very easy to deal with. The most important thing to be aware of – the thing most likely to cause trouble – is that assigning a variable to be a mutable object like a list, dictionary, or array does not make a copy of the object, but simply creates another variable that points to the same value.