Lambda Calculus FAQs

Lambda calculus is a formal system in mathematical logic for expressing computation through function abstraction and application. It forms the theoretical foundation for functional programming languages like Haskell and Lisp. Our interactive tools let you explore reductions, combinators, and recursive functions visually.

Begin with our Basics tutorial covering lambda expressions, beta reduction, and combinator examples. After that, explore advanced topics like the Y-combinator or tiling algorithms. Our interactive simulators let you test reductions in real-time. We recommend completing the sequence from simple abstractions to complex type systems for optimal understanding.

SKI combinators are three fundamental combinators that form a complete basis for combinatorial logic.

• S = λx.λy.λz.x z (y z)
• K = λx.λy.x
• I = λx.x

These combinators can replace any lambda expression using substitution rules. Our advanced tools let you convert lambda terms to SKI representations interactively.

Type inference algorithms like Hindley-Milner use the principle of "let definitions" and unification to derive type signatures for expressions. Our visualizer shows constraint propagation and type derivation trees step-by-step. You can input expressions and see how the type system infers polymorphic signatures automatically.

Simulations interpret lambda expressions as function applications and maintain reduction order tracking. The visualizer shows alpha conversions, beta reductions, and eta equalities through animated transitions. You can pause, step through, or auto-play reductions while observing the transformation of expressions.

Yes! Use the "Export" button on any simulator view to download:

• SVG diagrams of reductions
• Textual derivation traces
• JSON of state machines

This lets you save progress, share findings, or include in academic work.

Per our Terms of Service, you may:

• Use tools for non-commercial education
• Share outputs with attribution

Commercial redistribution requires written permission from the Lambda Calculus Foundation. All content remains under copyright protection.