x is easier to read and write than Lam 'x' (Lam 'y' (Var 'x'))) and secondly, it lets us write lambda calculus outside of Haskell, which comes in handy when we're building our interpreter later. The original interpreter of Poly is slow because it emulates beta reduction on top of Haskell, but our implementation avoids this overhead by utilizing the host system’s support for beta-reduction. Having a parser serves a few purposes: first, it lets us use a better format for our lambda calculus code ( \ x y. The key idea is to replace Lam and Ap constructors with Haskell’s built-in lambda and application constructs. This code is a representation of lambda calculus using an AST instead of text. The next step is to compile expressions into a fixed, finite combinators. (Note that $IF can be a function because we piggy back on the lazy evaluation of the host language, Haskell.) Compilation to SKI combinators $IF, $FIX, $ADD, $SUB, $MUL, $EQL will be provided as primitive functions. A typed one is, for example, Haskell, while an untyped language is Scheme. If, Fix are Op are desugared into function applications. The functional programming languages can be typed or untyped. N = case op of Add -> "$ADD" Sub -> "$SUB" Mul -> "$MUL" Eql -> "$EQL"ĭesugar function converts let x = e in body into (\x -> body) e. I haven't actually learned or used it yet, although I intend to, but I just thought I'd share this information with you, as it might interest you, since you share my appreciation for Ruby's syntax - Crystal may be worth checking out.Desugar ( App fun arg) = App (desugar fun) (desugar arg)ĭesugar ( Lam x body) = Lam x (desugar body)ĭesugar ( Let x e body) = App ( Lam x (desugar body)) (desugar e)ĭesugar ( If cond tr fl) = foldl App ( Var "$IF") argsĭesugar ( Fix e) = App ( Var "$FIX") (desugar e)ĭesugar ( Op op a b) = foldl App ( Var n) args I also appreciate that it's statically typed (in Python I had to use type notation together with a language server like PyLance in strict typing mode, to stimulate a type system, which is far from ideal).Ĭrystal isn't as widely adopted as Ruby, but it's gaining popularity it's relatively new for a programming language, usually it takes a decade or more before a language starts being adopted in the industry, and Crystal only came out in 2014. I made a more basic site a while ago that also reduces lambda calculus step-by-step, but also handles substitution correctly, and handles infinite recursion by displaying reductions steps asynchronously: Basic infinite recursion for your site: (Lx.x x)(Ly. Though Crystal has renewed hope in me, since it addresses the issues I had with Ruby, and its syntax is equally glorious. Lambda calculus interpreter in Haskell Ask Question Asked 6 years, 10 months ago Modified 6 years, 10 months ago Viewed 1k times 3 This code is a representation of lambda calculus using an AST instead of text. I ended up dropping Ruby, despite its glorious syntax, since my use cases for it overlap with Python, and in the end I chose Python due to greater support and a faster interpreter, even though I prefer Ruby as a language. Computer Society Press, Washington, DC (1987) Mu, S.-C.: Typed -Calculus Interpreter in Agda (2008). There are probably ways to bundle an interpreter and turn a Ruby program into a native executable, but there's always a cost. Haskell's take on the Expression Problem (2010). I love Ruby's syntax, but the main issue I had with it was the slow interpreter, and the fact that Ruby interpreters aren't common on most systems (I might be wrong on this, but MacOS and a lot of Linux distros ship with a Python interpreter, but not a Ruby interpreter), making Ruby programs harder to share without going through additional hoops. I mention it to you since if you like Ruby, you might very much like Crystal as well. Unlike Ruby, it's statically typed and compiled rather than dynamically typed and interpreted. If the expression has no normal form or it is not a valid. I have written all of the other functions but this one is really giving me trouble because it needs to return either Just Expr or Nothing and I'm not sure how to propogate this through the recursion: A single step. Have you heard of the programming language Crystal? It's very Ruby-like in syntax, almost identical in fact with some differences here and there due to new language features. 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). I am implementing a lambda calculus interpreter and one of the functions I have to write is specified as follows.
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