When you enter a term in the REPL, the interpreter prints the inferred type, and then reduces the term to normal form. | add | sub | mul | div | mod : Int → Int → Int My implementation includes the following type constants (ι) and term constants (k): ι ::= Int | Bool Therefore, booleans, numbers, and data structures cannot be encoded in the usual way, and must be built in to the calculus itself. Universal quantifiers are not allowed within function types. Terms (e) and types (τ) are constructed as follows: e ::= k constant Hindley-Milner is a type system that allows a restricted form of parametric polymorphism while not requiring any type annotations the type of an expression can always be inferred. You can also define type synonyms using ~. You can also create local variables using the syntax before all succeeding inputs. In the REPL, you can use \, ->, and ? instead of λ, →, and ∀ respectively. There are separate syntaxes for terms (e) and types (τ): e ::= x variable System F is a typed lambda calculus with universal quantifiers. Variables are limited to a single character, so you don't need to put spaces between them. sxyz reduces to xz(yz), and kxy reduces to x (where x, y, and z stand for any terms). There are two variables with a special meaning: s and k. It has variables and application, but no λ-abstraction. SK combinator calculus is a restricted version of lambda calculus. For example, x, 0, Abc, and add1 can all be used as variables. x).Īny sequence of basic latin letters and/or digits is a valid variable. In the example above, when the user types and true false, the interpreter evaluates the expression (λtrue. When you define a constant, it is added as an argument to all succeeding inputs. You can also define named constants using =. You can use \ instead of λ for abstractions. When you enter a term, the interpreter will reduce it to βη-normal form if possible, and display the result. For more information, see the manual below. You can access the different REPLs by passing an argument to the executable: "lambda", "sk", "systemf", "hm", or "coc". Currently, the following languages are supported: A collection of interpreters, type checkers, and REPLs implemented in Haskell.
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