Lecture Notes on Advanced Concepts in Haskell Functions

Introduction

• Recap of previous lecture on basic functions.
• Introduction to advanced concepts related to functions in Haskell.

Curried Functions

• Definition: A function applied to its arguments in a specific manner.
• Example: add function with two arguments behaves as a function taking an int and returning another function.
• Currying Benefits:
  • Allows arguments to be applied one at a time.
  • Implicitly handles additional arguments.
• Haskell defaults to curried functions.
• Uses: Beneficial for higher-order functions.

Uncurried Functions

• Achieved using tuples.
• All arguments must be specified at once.
• Example: add function with arguments grouped into a tuple.

Polymorphism

• Allows functions to operate on various types.
• Example: length function works on lists of any type.
• Type parameter (e.g., a) indicates generalization over types.
• Polymorphic Functions: fst, reverse, head, map.
  • fst: Takes a tuple and returns the first element.
  • reverse: Reverses a list while maintaining type.
  • head: Returns the first element of a list.
  • map: Applies a function to each element of a list, transforming types.

Function Composition

• Operator: Dot operator . used for composing functions.
• Example: last function using head and reverse.
• Implicit arguments in composed functions.

Dollar Sign Operator

• Simplifies expressions by reducing parentheses.
• Acts as a parenthesis ending till the expression's end.

Type Classes

• Extend polymorphism to functions with different implementations.
• Methods: Functions defined within type classes (e.g., eq for equality).
• Instance: Specific type implementing a type class.
• Common Type Classes:
  • Eq: Equality operations.
  • Ord: Orderable operations, dependent on Eq.
  • Num: Basic arithmetic operations.
  • Fractional: Division operations.

Overloaded Functions

• Type constraints based on type classes.
• Example: sum function uses Num type class for addition.

Lambda Expressions

• Anonymous functions without names.
• Useful for writing concise functions directly where needed.
• Compatible with functions like map.

Recursion Introduction

• Definition: Functions using their own definition within their implementation.
• Example: Recursive definition of map.
  • Pattern matching on list to process head and tail.

Conclusion

• Recap of complex concepts covered.
• Importance of understanding foundational concepts for advanced topics.
• Next topic: Recursion in depth.