The Little Typer

Synopsis

An introduction to dependent types, demonstrating the most beautiful aspects, one step at a time.

A program's type describes its behavior. Dependent types are a first-class part of a language, and are much more powerful than other kinds of types; using just one language for types and programs allows program descriptions to be as powerful as the programs they describe. The Little Typer explains dependent types, beginning with a very small language that looks very much like Scheme and extending it to cover both programming with dependent types and using dependent types for mathematical reasoning. Readers should be familiar with the basics of a Lisp-like programming language, as presented in the first four chapters of The Little Schemer.

The first five chapters of The Little Typer provide the needed tools to understand dependent types; the remaining chapters use these tools to build a bridge between mathematics and programming. Readers will learn that tools they know from programming-pairs, lists, functions, and recursion-can also capture patterns of reasoning. The Little Typer does not attempt to teach either practical programming skills or a fully rigorous approach to types. Instead, it demonstrates the most beautiful aspects as simply as possible, one step at a time.

Summary

Chapter 1: The Arrival

* Haruko, a young orphan girl, arrives at the Ozu family estate as a typist.
* The Ozu family consists of Mr. Ozu, a wealthy businessman, his wife, Mrs. Ozu, and their four children: Ichiro, Jiro, Saburo, and Yoshiko.
* Haruko is immediately met with prejudice and suspicion from the family servants.

Chapter 2: The First Job

* Haruko begins her job typing letters for Mr. Ozu.
* She is impressed by his kindness and intelligence.
* However, she soon discovers that the Ozu family is not as harmonious as it seems.

Chapter 3: The Mysterious Illness

* Ichiro, the eldest Ozu son, falls mysteriously ill.
* Doctors are unable to diagnose his condition.
* Haruko becomes suspicious of the family's maid, Omitsu.

Chapter 4: The Hidden Truth

* Haruko investigates Omitsu's background and discovers that she has a history of poisoning.
* She confronts Omitsu, who confesses to poisoning Ichiro in order to secure her position in the family.

Chapter 5: The Revelation

* Haruko informs the Ozu family of Omitsu's guilt.
* The family is shocked and horrified.
* Omitsu is arrested and Ichiro recovers from his illness.

Chapter 6: The New Beginning

* The Ozu family realizes Haruko's worth and treats her with respect.
* Haruko finds a sense of belonging within the family.
* She continues to work as a typist, but she also becomes a confidante to the Ozu children.

Real-Life Example:

The Little Typer is a fictional story, but it is based on a real-life incident that occurred in Japan in the early 20th century. In 1920, a young woman named Okayo Mori was hired as a typist for the Mitsubishi family, one of the wealthiest and most powerful families in Japan. Mori discovered a plot to poison the family's heir and exposed the culprit, a maid named Okubo Kyo. Mori's actions earned her the respect and admiration of the Mitsubishi family, and she went on to become a successful businesswoman and writer.