Values and types: why 1 is not "1"

A program is a pile of values that get moved around. A number, a piece of text, a yes or no, a shopping list of scores. Everything else in this lesson is about one question: what kind of thing is this value, and what is allowed to happen to it.

In logic:1 a type was just a set. The boolean set has exactly two members: true and false. The integer set holds whole numbers. The string set holds text of any length, including the empty string. Saying that a value has a type means saying which set it came from. Every operation you write is a claim about sets: addition wants two numbers, joining text wants two strings.

bool   = { true, false }
int    = { ..., -2, -1, 0, 1, 2, ... }
string = any sequence of characters

age + 1   needs a value from int
"1" + 1   mixes a value from string with a value from intA type is a set of values, and an operation is a claim about sets.

Here is the same handful of values written in three languages. Do not try to memorise this. Read it the way you would read the same sentence in three accents: the words change, the meaning does not.

name = "Ada"
age = 36
tall = True
scores = [90, 85, 77]
prices = {"soup": 2.50, "juice": 1.90}Python: no type written by hand, the value decides.

const name = "Ada";
const age = 36;
const tall = true;
const scores = [90, 85, 77];
const prices = { soup: 2.50, juice: 1.90 };JavaScript: const for a name that will not be reassigned.

var name string = "Ada"
var age int = 36
var tall bool = true
scores := []int{90, 85, 77}
prices := map[string]float64{"soup": 2.50, "juice": 1.90}Go: the type is written next to the name, and the compiler checks it.

Now the classic beginner disaster. A signup form asks for your age. The form sends text, because everything a form sends is text. Your code then tries to add one to it.

form sends: age = "16"
8 + 1  = 9
"16" + 1 = ?Eight plus one is nine. What is the text "16" plus one?

The last idea is mutability, and it costs people more debugging hours than anything else in this lesson. A list is one object that many names can point at. Change the list through one name and every other name sees the change, because there was only ever one list.

scores = [90, 85]
same = scores
same.append(77)
print(scores)

[90, 85, 77]Two names, one list. The change is visible through both.

Collections also carry the Big-O idea from logic:1. Choosing the right collection is often worth more than rewriting your loops. A list is for order and for walking through everything. A map is for looking things up by key. The cost table below is the whole justification for maps existing.

list.append(x)      O(1)
map[key]            O(1) average
x in list           O(n)
x in map            O(1) averageThe cost of an operation is the cost of the collection that holds the values.