Keywords: Domain Specific Language Interpreter Lambda calculus 1. With memoization this might not be so bad. In Haskell, existing techniques that address this problem, such as Typeable and. denotational semantics for a simply-typed call-by-value lambda calculus with. The evalWhile function also seems like a poor way to check if we've reached normal form, though I have seen other code that does this. ming resumption-based interpreters for interactive programs in Haskell. There are several steps of the process that are missed because they are built into the Racket language. If the expression has no normal form or it is not a valid. I decided I would try to implement it in Haskell instead of Racket. 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 expressions normal form (or an expression alpha-congruent to it). Perhaps there is a better way to do this. Compiling and Interpreting the Lambda Calculus in Haskell This whole project is based on this post by Matt Might. The eval function feels particularly awkward to me, as every type in Expr is preceded by it's equivalent function. GULCII is an untyped lambda calculus interpreter supporting interactive modification of a running program with graphical display of graph reduction. S = Abst "x" (Abst "y" (Abst "z" (App (App (Var "x") (Var "z")) (App (Var "y") (Var "z")))))įor instance: λ> evalWhile (App (App (App s k) k) k) Here are a few applicative combinators for debugging. GitHub - txyyss/Lambda-Calculus: An introduction to lambda calculus in Chinese, including an interpreter in Has. Sub (Sub (App a b) var env) = (App (Sub a var env) (Sub b var env))Įval a b c) = sub (Sub (eval a) b (eval c)) An introduction to lambda calculus in Chinese, including an interpreter in Haskell. | otherwise = (Abst var' (Sub body var env)) Let's write a programming language interpreter for the simple. module Eval whereĪpp (App (Abst var body) env) = (Sub body var env) The lambda calculus is an amazingly powerful and simple mathematical model. This project consists of a lambda calculus expression parser using Parsec, and an eval-apply interpreter. This code is slower than many other interpreters, and if there is a way to make the code more efficient while still conveying the reduction rules clearly, that would be an improvement. An Untyped Lambda Calculus Interpreter in Haskell. import qualified as Map data Val Num Integer Fun (Val -> Val) Wrong data Term Cons Integer Var String Lam String Term App Term Term Add Term Term type Env Map.Map String Val add :: Val -> Val -> Val add (Num x) (Num y) Num (x+y) add Wrong apply :: Val -> Val -> V. My goal is to represent the transformation rules listed here accurately and explicitly. (Sub (App a b) var env) -> (App (Sub a var env) (Sub b var env)) (Sub (Abst var' body) var env) -> (Abst var' (Sub body var env)) The lambda calculus is a formal mathematical system for expressing the notion of computation. (Sub (Abst var body) var env) -> (Abst var body) (App (Abst var body) env) -> (Sub body var env) We’ve ended up with a weird constraint on our m, though: (MonadReader m).This code is a representation of lambda calculus using an AST instead of text. The Mathematics of Functional Programming: Lambda Calculus Lambda calculus. So we just want a normal catamorphism which computes monadic values. then a Haskell interpreter will respond as follows when we try to display or. Take the un-evaluated computation for the body of an abstraction and save it to evaluate later in a differentĮnvironment. But this is not what we want, because we want to Us to automatically evaluate all the monadic computations for sub-terms before evaluating the With monadic catamorphisms the idea is that the Traversable constraint allows the formal definition of capture avoiding substitution to execute by hand -calculus programs according to its operatial semantics how our Haskell. Initially I thought that I would want to write this as a monadic Later, when evaluating anĪpplication we can just fish out the monadic computation and evaluate it in the Which we can just put into the closure value. This is pretty neat - the body of an abstraction has been evaluated to a m (Value m), Type Algebra f a = f a -> a - specialisation of the real signature - cata :: Algebra f a -> Fix f -> a - note the weird contstraint evalAlgebra :: ( MonadReader m ) => Algebra LambdaF ( m ( Value m )) evalAlgebra term = case term of Index i -> do e do - capture the environment e do - this will cause pattern match failures if the term - isn't well-typed Clos ctx t ( c : ctx )) t
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