Design Principles
Functional languages derive their core paradigms from lambda calculus abstractions. This research explores how pattern matching, immutability, and higher-order functions emerge from pure calculus foundations.
Immutability
Lambda calculus expressions are inherently immutable, forming the basis for pure functional state management.
Type Systems
Hindley-Milner and dependent types evolve from λ-encoding techniques to ensure program correctness.
Recursion
The Y-combinator provides recursion without explicit named functions, fundamental to functional iteration.
Case Studies
Haskell
Demonstrates currying, type classes, and lazy evaluation derived from λ-calculus principles.
factorial :: (Num a, Ord a) => a -> a
factorial n = if n <= 0 then 1 else n * factorial (n-1)
OCaml
Utilizes algebraic data types and pattern matching rooted in lambda calculus encoding.
type list =
| Nil
| Cons of int * list
let rec sum = function
| Nil -> 0
| Cons (x, xs) -> x + sum xs
Implementation Patterns
Combinator-Based Design
SKI combinators form the basis for minimal functional cores in languages like Unlambda.
S = λx.λy.λz.x z (y z)
K = λx.λy.x
I = λx.x
Continuation Passing Style
Transforms direct recursion into continuation chains for explicit control flow.
factorialcps n k =
if n == 0 then k 1
else factorialcps (n-1) (λr → k (n*r))
Language Feature Comparison
| Concept | Haskell | Rust (Functional) | OCaml |
|---|---|---|---|
| Immutability | Default pattern | Requires [&] syntax |
Value restriction |
| Recursion | Recursive by default | Requires loop keywords |
Tail call optimized |
| Type Inference | Hindley-Milner | Rust's Chalk | Class-based |