From Simple IO to Monad Transformers

By J Adrian Zimmer

From Simple IO to Monad Transformers is written for you if you know some Haskell, have seen a description or example of Haskell’s monads, and are not yet comfortable with the concept. You are also expected to have enough math background
to understand that function composition makes up some kind of algebraic system.

This ebook’s objective is to help you develop an intuitive notion of monad that is accurate enough to be useful. You may have found this difficult to achieve because the concept is abstract and explanations are often aimed at the mathematically sophisticated. When they are not, they tend to be of the “See how to do this! Wasn’t that easy?” variety.

Neither approach works very well. What you need is help understanding how abstractions organize details. Contrary to popular opinion, we cannot create abstractions by ignoring details. What abstractions do is control the time and place for such thinking. Edsger Dijkstra once reacted to the top-down programming movement–which he helped start–by writing that he himself did not create programs purely from the top down. He merely organized them that way for clarity and correctness.

Here the author discusses monads by looking at them from both the outside in and the inside out. The focus is on building understanding. Functors and applicative types are omitted. Those concepts can be stepping stones on the way to understanding monads but they are unnecessary with shorter approach I have chosen to use.

In prioritizing clearer explanations over content the author has also omitted almost all of the monads included with Haskell. You will find plenty of documentation online for those. The monads the author has chosen to present will give you a mental model for making
sense of that documentation.

Most sections have one worked exercise. It is OK if you cannot work it. Just pausing to think about it will give you a better understanding than merely reading through an example would.

Version 1.2 has expanded material on the List and State monads as well as on monad transformers. A few small errors have also been corrected. See the books website at BonsaiReads.com for an errata list.

• Language: English
• Publisher: J Adrian Zimmer
• Release date: May 31, 2014
• ISBN: 9780990451501

J Adrian Zimmer

I was raised in Nebraska but have lived in the eastern, southern, and midwestern U.S., Canada, Denmark, and Iran. Educated through a postdoc in mathematics, my publications include three books. I recently retired knowing more about computer science than mathematics.

Book preview

cover.jpg

Title Page

Copyright Page

Annotated List of Keywords

Annotated List of Sections

Preface

I. Pure Versus Impure

Ia Scope Example

Ib Impure Code

II. Functional Programming and the Real World

IIa Decomposed Haskell Program

IIb Question

IIc Answer

III. Monads and the (>>=) Combinator

IIIa Question

IIIb Answer

IV. The return Function

IVa getInt

IVb ask

IVc return_or_recurs

IVd Question

IVe Answer

V. Mimicking Composition of Functions

Va Question

Vb Answer

VI. The do Block

VIa Scoping In do Block

VIb Java-like Scoping

VIc Equivalent Monadic Expression

VId Substitution 1

VIe Substitution 2

VIf Substitution 3

VIg Monadic Expression Equivalent to do Block

VIh Equivalence Step 1

VIj Equivalence Step 2

VIk Equivalence Step 3

VIl Equivalence Step 4

VIm Equivalence Step 5

VIn Question

VIo Answer

VII. The List Monad

VIIa Nested do Block Loop

VIIb Defining pairs I

VIIc Defining pairs II

VIId Defining pairs III

VIIe Question

VIIf Answer

VIIg Program Testing pairs

VIII. Introduction to Monad Transformers

VIIIa 'Hello World'

VIIIb 'Hello World' Using LisT

VIIIc A Bit About GHCI

VIIId GHCI Example

VIIIe Nonloop Example

VIIIf Question

VIIIg Answer

IX. Intro to the State Monad

IXa State Monad (>>=)

IXb Question

IXc Answer

X. More About the State Monad

Xa Deriving >> for the State monad

Xb Testing get and put

Xc Question

Xd Answer

XI. A StateT Example.

XIa Repeated next_coins

XIb Definition of recurs

XIc Definition of dispense

XId Question

XIe Answer

XII. Monads

XIIa Definition of Monad

XIIb Monadic Axioms

XIIc Question

XIId Answer

About the Author

From Simple IO to Monad Transformers

by J Adrian Zimmer

Reader discussion encouraged at this ebooklet's web page.

Published by Bonsai Reads and distributed by Amazon.

Cover Design: Jennifer Melot

Copyright 2014 by J Adrian Zimmer

All rights reserved. Permission to copy is granted to the purchaser for personal use provided purchaser takes reasonable steps to prohibit further copying by others.

This is version 1.2. See for differences between versions.

There are two tables of contents. One is an annotated list of sections. The other has a listing for every major code segment.

Annotated List of Keywords

monad

Establishing a mindset for understanding Haskell's monads is the purpose of this publication.

Haskell

Readers are expected to know how to write simple recursive programs in the Haskell programming language.

functional programming

Functional and imperative programming are compared.

IO

Some examples involve console IO in Haskell.

list monad

Haskell's

List

monad is described.

state monad

Haskell's

State

monad is described.

monad transformer

Examples of monad transformers are given.

small screen

This monograph has been formatted for paging readers on small or large screens. Many code examples are hard coded into their own pages. Haskell source code has been kept to short line lengths.

Annotated List of Sections

I. Pure Versus Impure

Mathematical functions versus side-effects in computer programs.

II. Functional Programming and the Real World

Haskell's way