Brainfuck interpreter in an extended lambda calculus. Denotational semantics - Wikipedia. Programming Computable Functions. In computer science, Programming Computable Functions,[note 1] or PCF, is a typed functional language introduced in an unpublished 1969 manuscript by Dana Scott.

It can be considered to be an extended version of the typed lambda calculus or a simplified version of modern typed functional languages such as ML. A fully abstract model for PCF was first given by Milner (1977). However, since Milner's model was essentially based on the syntax of PCF it was considered less than satisfactory (Ong, 1995). The first two fully abstract models not employing syntax were formulated during the 1990s. These models are based on game semantics (Hyland and Ong, 2000; Abramsky, Jagadeesan, and Malacaria, 2000) and Kripke logical relations (O'Hearn and Riecke, 1995). Syntax[edit] The types of PCF are inductively defined as. Logic of Computable Functions - Wikipedia. From Wikipedia, the free encyclopedia Logic of Computable Functions (LCF) is a deductive system for computable functions proposed by Dana Scott in 1969 in a memorandum unpublished until 1993.[1] It inspired: Jump up ^ Dana S.

Scott. "A type-theoretical alternative to ISWIM, CUCH, OWHY". Theoretical Computer Science, 121:411–440, 1993. 9780857290755 c2. RNC3. PCF and LCF. LCF. LCI - A lambda calculus interpreter. LCI is an interpreter for the lambda calculus.

It supports many advanced features such as recursion, user-defined operators and multiple evaluation strategies, all based on the pure calculus. It is free software licenced under the GNU General Public Licence (GPL). Install From source The latest version (v0.6) is available here. . It is recommended to install the readline library (and development files) before compiling. You can also checkout the code from github. Using Homebrew on OSX Install Homebrew and run brew install lci. Binaries for Windows Windows binaries are available here.

Documentation LCI's documentation covers most of the program's features and explains various topics concerning the lambda-calculus View documentation online.Download documentation (pdf) Church-encoded numbers, lists, booleans, conditionals with fixed-point recursion in Scheme. When prototyping a new language or a new static analysis, Church encodings become practical.

Since any language construct may be desugared into a pile of lambdas, a researcher can bring the language down to the interpreter/analysis, rather than the interpreter/analysis to the language. The Church encoding philosophy also allows practicing programmers to extend a language with new features from with the language itself, so long as that language contains anonymous functions. ;; A demonstration of Church encodings. Lambda pur. Lambda pur. 7 lines of code, 3 minutes: Implement a programming language. A small (yet Turing-equivalent) language The easiest programming language to implement is a minimalist, higher-order functional programming language known as the lambda calculus.

The lambda calculus actually lives at the core of all the major functional languages--Haskell, Scheme and ML--but it also lives inside JavaScript, Python and Ruby. It's even hiding inside Java, if you know where to find it. Memoizing recursive functions via the fixed-point Y combinator: Applying functional programming techniques to Javascript. If you like the article below, you might also enjoy: Recursion as fixed points Students of algebra are already familiar with recursion and fixed points.

They just don't realize it. Show HN: Caramel – a modern syntax for the lambda calculus. Decorators in Python are basically special syntax for higher-order functions, so I don't think there's much there to evaluate.

The lambda calculus is usually used when you want to ignore syntax. Introductory resources on programming language theory usually have examples, after giving you a thorough grounding in the basic untyped lambda calculus. In particular, this is how they usually introduced type system features, but there are interesting things like continuations that don't necessarily involve types. Types and Programming Languages by Benjamin Pierce is a great resource, but you can probably find free lecture notes to the same effect. MaiaVictor/caramel: A modern syntax for the λ-calculus. Haskell - How to model the output of the binary lambda calculus? Tadeuzagallo/lc-js: A λ-calculus interpreter written in JavaScript. Blc. Uni. Tromp. Code golf - Write an interpreter for the untyped lambda calculus.

Newest: I've squeezed it down to 644 chars, I factored parts of cEll into cOpy and Par; cached calls to cell and cdr into temporary local variables, and moved those local variables to globals in "terminal" (ie. non-recursive) functions.

Also, decimal constants are shorter than character literals and this nasty business ... atom(x){ return m[x]>>5==3; } ... correctly identifies lowercase letters (assuming ASCII), but also accepts any of `{|}~. (This same observation about ASCII is made in this excellent video about UTF-8.) Et viola:| Earlier: Can I get a few votes for effort? And after all that, it's not even close to the winning entry! I'm not sure how to make this any shorter; and I've used all the dirty tricks I can think of! With some generosity in the counting (the first chunk takes a string and prints out the result), it's 778 770 709 694 chars. So, alas, here it is: Here's the block just before the final reductions. LC. John's Combinatory Logic Playground. Pictured above you can see on the left the 206 bit binary lambda calculus (blc) self-interpreter in graphical notation, and on the right a 167 bit primes program, in both binary and graphical notation, together with the first 300 bits of output.

You can run this right away by feeding primes.blc into the tiny blc interpreter in perl with. Most functional. John Trompjohn.tromp@gmail.

A λ-calculus interpreter - Blog by Tadeu Zagallo. Recently I tweeted about falling in love with Lambda Calculus, and how simple and powerful it is. Of course I had heard of λ-calculus before, but it wasn’t until I read the book Types and Programming Languages that I could really see the beauty in it. There are many compiler/parser/interpreter tutorials out there, but most won’t guide you through the complete implementation of a language, since implementing full language semantics is usually lot of work, but in this case, λ-calculus is so simple that we can cover it all! First of all, what is λ-calculus? Here’s the Wikipedia description: Most functional. A □-calculus interpreter. Recently I tweeted about falling in love with Lambda Calculus, and how simple and powerful it is. Of course I had heard of λ-calculus before, but it wasn’t until I read the book Types and Programming Languages that I could really see the beauty in it.

There are many compiler/parser/interpreter tutorials out there, but most won’t guide you through the complete implementation of a language, since implementing full language semantics is usually lot of work, but in this case, λ-calculus is so simple that we can cover it all! First of all, what is λ-calculus? Here’s the Wikipedia description: Compiling up to the λ-calculus: Church encodings and the Y combinator. The λ-calculus The λ-calculus is a language with three expression forms: variable reference, e.g., v, foo; function application, e.g., (f x), (f (g x)); and anonymous functions, e.g., (λ (v) (+ v 1)).