For students, it is a tool to learn lambda-calculus and intuitionistic logic by coding. The environment, however, is populated only when evaluating a lambda, which will insert the values v, g above in the environment. Mikrokosmos is an educational untyped and simply typed lambda-calculus interpreter. This ensures that no unevaluated thunks are fed to a function, unless they are already in the environment. Your mission, should you choose to accept it, is to write an interpreter which takes as its input an expression of the untyped lambda calculus containing no. To get an eager (CBV) semantics, we can force the argument before the call: interpret env (App e1 e2) = case interpret env e1 of This interpreter is capable of finding the (beta-eta) reduced normal form of any expression in the untyped lambda calculus, as well as using a lazy reduction. (As luqui states, operationally GHC would reduce this in a call-by-need fashion). The simply typed lambda calculus (), a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor that builds function types. In my implementation I needed a parser, an. There are several steps of the process that are missed because they are built into the Racket language. I decided I would try to implement it in Haskell instead of Racket. This whole project is based on this post by Matt Might. Since Haskell is lazy, the code interpret env (App e1 e2) = case interpret env e1 of Compiling and Interpreting the Lambda Calculus in Haskell. Of course eager corresponds to CBV, and lazy to CBN. In a denotational-style interpreter like the posted one, I'd speak of eager vs lazy semantics, instead of CBV/CBN. In an operational-style interpreter which reduces terms representations, you can properly speak of CBV/CBN. The Mathematics of Functional Programming: Lambda Calculus Lambda calculus. related to the choice of redex in lambda term reduction. In a recent meeting I talked to my assistants about using dependent type to guarantee that, in an evaluator for. then a Haskell interpreter will respond as follows when we try to display or. Alternatively, one could compile with and use simple lambdas and applications instead instead of the above machinery.ĬBV/CBN are concepts related to the evaluation strategy of the lambda calculus, i.e. Now, instead of storing a thunk in the environment, we store a partial application object, and then evaluate it separately at different call sites.įorce and delay are required to prevent GHC from floating out function bodies, thereby recovering sharing. Interpret env (App e1 e2) = delay (case force (interpret env e1) of Interpret env (Lam x e) = delay (F (\v -> force (interpret ((x, v):env) e))) Interpret env (Var x) = delay (case lookup x env of We could modify the data definition: data Value a = V a | F ((() -> Value a) -> Value a)Īnd also have the interpreter return explicit thunks: interpret :: -> Expr -> () -> Value a F (Value a -> Value a) has Value a as argument, so we have no choice but to pass in some already interpreted value, and it'll be call-by-need under Haskell reduction behaviour. We write a rather small lambda calculus expression parser, evaluator, and repl in Haskell. Thus our interpreter actually runs more than plain lambda. It also helps impose referential transparency.I don't think proper call-by-name is possible with the original data definition. These on-demand lookups and the way we update env means recursive let definitions are possible. this helps prevent cheating and defining recursive functions. All definitions in the language are immutible. Once something is defined, it cannot be changed. This is called lazy evaluation or normal order evaluation, as opposed to eager or applicative order evaluation. The last line returns true because Lambda Light substitutes a variable for it's relevant binding only when it is being called, instead of when it is an argument to a function. Λ: not := \b.b false true - Lambda Light allows you to create functions with named functions. Λ: false := \x.\y.y - Lambda Light supports bindings to a global namespace. Λ: true := \x.\y.x - Lambda Light supports binding names to expressions. Λ: (λx.x x) (λx.x) - Lambda Light supports function application. GitHub - txyyss/Lambda-Calculus: An introduction to lambda calculus in Chinese, including an interpreter in Has. Λ: \x.x - Lambda Light supports the creation lambda expressions using \ and the unicode λ character. An introduction to lambda calculus in Chinese, including an interpreter in Haskell. Λ: x - Lambda Light supports creating arbitrary variables. Λ: - Lambda Light supports Haskell-like single line comments
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