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HPM Education - Haskell
  • Introduction to Haskell
  • Introduction
    • Functions
    • Functional Programming vs Imperative Programming
    • Installing Haskell
    • Haskell Modules
    • Loading Modules into GHCi
    • Expressions
    • Laziness
    • Immutability
  • Types in Haskell
    • Introduction
    • Basic Types
    • Static Type Check
    • Polymorphic and Overloaded Types
    • Data Structure Types
      • Lists
        • List Functions
      • Tuples
    • Function Types
      • Curried Functions
      • Partial Application
  • Defining Functions / Working with Functions
    • The Layout Rule
    • Local Definitions
    • The Infix Operator
    • Conditionals
      • If-then-else Statements
      • MultiWayIf
      • Guarded Equations
      • Case-of Statements
    • Pattern Matching
      • Tuple Patterns
      • List Patterns
    • Lambda functions
    • Function Operators
  • List Comprehensions
    • List Comprehensions
  • Higher-order Functions
    • Introduction
    • The map Function
    • The filter Function
  • Recursion
    • Introduction
    • 4 Steps to Defining Recursive Functions
    • Recursion Practice
    • Folds
      • Fold Right (foldr)
      • Fold Left (foldl)
  • Cutom Types
    • Declaring Types
      • Type Synonyms
      • Data Declarations
      • Newtype declarations
  • Type Classes
    • Introduction
    • Basic Classes
      • Eq – Equality Types
      • Ord – ordered types
      • Show – Showable Types
      • Read – readable types
      • Num – Numeric Types
      • Integral – Integral Types
      • Fractional – Fractional Types
      • Enum – Enumeration Types
    • Derived Instances
    • Exercise – Making a Card Deck Type
  • Interactive Programming
    • Introduction
    • Input / Output Actions
    • Sequencing Actions
    • Exercise - Numbers Guessing Game
  • Functors, Applicatives and Monads
    • Introduction
    • Functors
    • Applicative Functors
    • Monads
      • Maybe Monad
      • List Monad
      • Monad Laws
  • References / Further Reading
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  1. Recursion

4 Steps to Defining Recursive Functions

A good set of steps to follow when defining recursive functions is:

  1. Define the function type

    Thinking about function types is very helpful when defining functions, and explicitly

    defining the function type is good practice.

  2. Enumerate different cases

    Considering the general cases we expect allows us to create the function structure that we can then fill out gradually. For example, two standard cases for lists are empty and non-empty lists.

  3. Take care of the simple cases first (usually base cases)

    The simple cases are usually straightforward so it's easier to define them. For example, our

    sumN 0 = 0 is a simple case and also the base case.

  4. Define the other cases

    Here, we have to think about how to calculate the wanted result using both the recursive call

    on the function itself and any other functions we might need. For example, in sumN x = x sumN (x - 1) we used both the (+) and (-) functions.

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Last updated 2 years ago

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