🔦 Theory

Theory explores the mathematical ideas that let us define, reason about, and reuse computer programs.

• 🪨 Lambda Calculus serves as the logic that forms the core of computation.
• 🌿 Haskell is a typed, lazy, purely functional $\lambda$‑calculus with syntax, types, and a rich standard library.
  • ✏️ Syntax & Equations involve function equations, patterns, guards, where/let scope.
  • 🛡️ Type System allows for polymorphism, type annotations, type inference, etc.
  • 🔄 Recursion & Pattern Matching involves structural recursion, mutual recursion, and tail recursion.
  • 📜 Lists & Comprehensions give us built‑in list syntax, ranges, comprehensions, library helpers.
• 🌲 Algebraic Data Types are user‑defined product, sum, recursive and polymorphic types that include tuples & lists.
  • 📦 Product Types include “and” data (records/tuples), pattern matching, and field labels.
  • 🔀 Sum Types cover “either/or” data, tagged unions, exhaustive case analysis.
  • 🌳 Recursive Types cover lists, trees, and structural induction.
  • 🌀 Polymorphic Data covers type constructors & parametric data (e.g. List a, Tree a).
• 🔧 Higher‑Order Functions bottles common iteration patterns.
  • 🚿 Map applies a transformation to every element.
  • 🔍 Filter selects elements that satisfy a predicate.
  • 📐 Foldr & Foldl reduce a list right‑ or left‑associatively (sums, cats, reversals).
  • ➡️ Function Combinators such as flip, (.) provide eta‑conversion & point‑free style.
• 🔒 Closures are the key mechanism that enforces static scoping.
• 🎛️ Type Classes enable ad-hoc polymorphism.
• 📜 Parsers convert raw input into a structured value like an AST.
• 🌀 Monads let you chain actions while preserving context.