Tuples

Tuples are ordered, nonuniqued collections. In this course, we will use tuples to model words, phrases, and sentences. We will refer to these objects generically as strings.

Tuples are often represented using the notation \(\langle \cdot, \cdot, \ldots \rangle\). For instance, we might represent the phonological word ruder as:

\[\mathbf{w} \equiv \langle \text{ɹ,u,d,ə,ɹ} \rangle\]

In Python, there are multiple ways to represent a tuple: as a str, as a tuple, or as a list.

w_str = "ɹud"
w_tuple = ("ɹ", "u", "d")
w_list = ["ɹ", "u", "d"]

A tuple with \(n\) elements is called an \(n\)-tuple. So \(\mathbf{w}\) is a 3-tuple. We can assess what kind of \(n\)-tuple we have using the len() function.

len(w_str), len(w_tuple), len(w_list)

(3, 3, 3)

Why would we use a tuple or a list to represent a string, when we have str available? Well. Many times, the elements string are themselves complex. So for instance, if we want to represent the morphological word ruder, we might want to represent the morpheme \(\langle \text{ɹ,u,d,ə,ɹ} \rangle\) as a separate element from the morpheme \(\langle \text{ə,r} \rangle\).

\[\bar{\mathbf{w}} \equiv \langle \langle \text{ɹ,u,d} \rangle, \langle \text{ə,r} \rangle \rangle\]

w_rude_tuple = ("ɹ", "u", "d")
w_er_tuple = ("ə", "r")
w_bar_tuple = (w_rude, w_er)

print(w_bar_tuple)

(('ɹ', 'u', 'd'), ('ə', 'r'))

We commonly refer to the elements of a tuple using the notation \(w_i\). So for instance, \(w_1 = \text{ɹ}\), \(w_2 = \text{u}\), and \(w_3 = \text{d}\). This notation corresponds directly to indexation in Python, but unlike in Python, we will often use 1-indexation (as above).

for i in range(len(w_str)):
    print(f"w_{i+1} = {w_str[i]}")

w_1 = ɹ
w_2 = u
w_3 = d

You’ll note that I am using bolded \(\mathbf{w}\) to represent a tuple, but italic \(w\) when indexing its elements. This is a common convention for tuples.¹

Footnotes

1. If you have taken linear algebra, you may be familiar with this notation.