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The Little Typer (Paperback)
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The Little Typer (Paperback)
Series: The MIT Press
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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.
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