Denotational-Semantics

Every trait in your hexagonal architecture is a tagless-final algebra. Every impl is an interpreter. You have been writing denotational semantics without knowing it. We trace the connection from Kiselyov’s paper through Scala’s Cats-Effect to Rust’s port traits, and show why the pattern that academics call ‘finally tagless’ is the same pattern that practitioners call ‘dependency injection.’

Your match expression is operational semantics. Your pure function is denotational semantics. Rust’s borrow checker is axiomatic semantics. Three formal frameworks, three ways to assign meaning to code, and you have been using all of them without knowing it.