Functional Programming Language

The applied intersection of Programming Language Theory, Category Theory, and Logic to Computation. Designing a Program around pure functions and immutable data. Essentially, the mathematical way of programming, where functions behave like they do in math, and data consists of mathematical objects that have a single identity, not a changing one. Instead of changing the state of objects, data is transformed by being passed through a composition of functions.

Algebraic Pillars

The function paradigm consists of two pillars of algebraic computation.

• Structural Algebra
  • Describes the shape of algebraic types
    • Algebraic Type + Shape = Algebraic Data Type
      • Sum Type
        • Traffic light signal. Red or Yellow or Green.
      • Product Type
        • Coordinate. x and y and z.
• Operational Algebra
  • Describes the behavior of algebraic types
    • An algebraic type that has a particular behavior (e.g. operations and laws) is an Algebraic Structure
      • Monoid
        • Booleans under AND
      • Functor
        • Doubling every value in a Tree
      • Monad
        • Monadic Chaining