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Part I: Functional Principles
● First-Class and Higher-Order Functions
● Referential Transparency and Equational Reasoning
● Immutability
● Lazy Evaluation
● Totality: Guaranteed Termination Through Substructural Recursion
Part II: Abstract Algebra
● Magma (Integral Sum)
● Semigroup (Integral Sum, Integral Product, All, Any, Min, Max)
● Monoid (Integral Sum, Integral Product, All, Any, List Concatenation, Set Union)
● Group (Integral Sum, Rational Product, Modular Arithmetic, Square Symmetry)
● Abelian Group (Integral Sum)
Part III: Category Theory
● Category
● Arrow
● Homomorphism
● Functor
● Applicative
● Monad