Translating math into code with examples in Java, Racket, Haskell and Python

Abstraction: Mapping discrete math structures to immutable functional code patterns

Key points:

• Mathematics has no side effects; correct code translation must use immutable data structures — mutable structures are a fatal mistake
• Sets map to types, sorted tree-backed collections, or predicates depending on whether membership is static, runtime-computed, or structural
• Disjoint union (sum types) maps to class inheritance in Java or algebraic data types in Haskell
• Sequences map to linked lists; vectors to arrays (never mutated); infinite sequences to lazy streams in Haskell or Racket
• Functions as finite maps should use immutable red-black trees or shallow-copy dict wrappers, not Python dicts or Java TreeMap directly
• Relations can be encoded as collections of tuples, as functions (A → P(B)), or as predicates

Connections: Haskell · Functional Programming · Discrete Mathematics · Type Theory

Source: http://matt.might.net/articles/discrete-math-and-code/