How deeply does Learn Haskell by Example cover associativity?

Defines the equality law, distinguishes grouping from operand order, and notes that the compiler does not verify it.

Associativity

As explained in Learn Haskell by Example

An associative function is a binary operation whose grouping does not affect the result.

Associativity means that regrouping a sequence of applications does not change its result: a <> (b <> c) == (a <> b) <> c. The operands remain in the same order; only the grouping changes. section 7.3.1

Appending three CSV values illustrates the property. Both appendCsv a (appendCsv b c) and appendCsv (appendCsv a b) c produce the same result when appendCsv is associative. Haskell does not prove this law, so the implementer must verify it. section 7.3.1

In Haskell, associativity supports reusable combination APIs:

Semigroup provides the binary associative operation <> for a type. section 7.3.1 section 7.5
Monoid extends Semigroup with mempty, a neutral element, and mconcat for combining a list of values. section 7.3.1
Associativity does not imply commutativity: changing a <> b to b <> a can change the required result. section 7.3.1

How Learn Haskell by Example covers it

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Also explained in

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Functional Programming in Scala, Second EditionThe algebraic law stating that regrouping repeated applications of a binary operation does not change the result.
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Clojure: The Essential ReferenceAssociativity is the property that the grouping of operands does not affect the result of repeatedly applying a binary operation.
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100 Java Mistakes and How to Avoid ThemAssociativity is the property that the grouping of operands does not change the result of an operation.
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Advanced Algorithms and Data StructuresAn associative operation gives the same result regardless of how operands are parenthesized, so regrouping intermediate results does not change the outcome.

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Related concepts

monadused by · A monad is a functional abstraction that encapsulates computational context and provides operations for composing computations while preserving that context.
reduction operationused by · A reduction operation combines multiple input values or partial results according to a combining rule to produce fewer results, often a single aggregate.
floating-point arithmeticcontrasts with · Floating-point arithmetic is computation using finite-precision representations of real numbers, which can introduce rounding and range errors.
applicative functoruses · An applicative functor is an abstraction that applies functions within a computational context to context-wrapped values while combining their contexts.

This explainer was generated by Manning's knowledge graph from the text of Learn Haskell by Example. The section links point to the parts of the book it draws on.