![]() It also helps impose referential transparency. If the expression has no normal form or it is not a valid. this helps prevent cheating and defining recursive functions. 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 free variables and produces as its output the expression's normal form (or an expression alpha-congruent to it). 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. They terminated when they reached an answer in Weak Head Normal Form. ![]() In lecture, we wrote several interpreters for the Lambda Calculus. Since the language is based on the lambda calculus, it will need to include a constructor for functions. A Normal Order Normal Form Interpreter for the Lambda Calculus Now, we will describe the actual homework. Λ: not := \b.b false true - Lambda Light allows you to create functions with named functions. Value type You’ll need a type to represent the values your language works on, a sum of all the types of values you want to work with. Λ: false := \x.\y.y - Lambda Light supports bindings to a global namespace. beta - (App (Abst var body) env) -> (Sub body var env) - eta - (Abst var (App body var')) -> body - alpha - (Sub (Var var) var env) -> env - (Sub (Var var') var env) -> (Var var') - (Sub (Abst var body) var env. Λ: true := \x.\y.x - Lambda Light supports binding names to expressions. This code is a representation of lambda calculus using an AST instead of text. Λ: (λx.x x) (λx.x) - Lambda Light supports function application. Λ: \x.x - Lambda Light supports the creation lambda expressions using \ and the unicode λ character. Λ: x - Lambda Light supports creating arbitrary variables. isFree takes a variable name, and returns a function that takes an expression and. Λ: - Lambda Light supports Haskell-like single line comments In Haskell, all signatures are curried, i.e., they take just one argument.
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