The big result in theoretical computer science is that these can all do the same thing, in the sense that if you can express a calculation in one, you can express it in any other. Lisp, a human-friendly axiomatisation of computation that accidentally became an extremely good and long-lived programming language.the projection functions, defined for all natural numbers a and b such that a \geq b as taking in a arguments and returning the bth one.a successor function that takes a number and returns that number plus 1 and.the zero functions, that take some number of arguments and return 0.The partial recursive functions, constructed by function composition, primitive recursion (think bounded for-loops), and minimisation (returning the first value for which a function is zero) on three basic sets of functions:.The lambda calculus ( λ-calculus), a formal system that has expressions that are built out of an infinite set of variable names using λ-terms (which can be thought of as anonymous functions) and applications (analogous to function application), and a few simple rules for shuffling around the symbols in these expressions.moves one cell left or right on the tape. ![]() transitions to some some state (possibly the same it is already in), and.writes some symbol on the tape (possibly the same that was already there),.given a combination of current state and current symbol on the tape, always does an action consisting of three things:.has some set of states it can be in, some of which are termed "accepting" and one of which is the starting state and.works on an infinite tape of cells from which a finite set of symbols can be read and written, and always points at one of these cells.The Turing machine – that is, a machine that:.At the end we will see a lambda calculus interpreter written in the lambda calculus, and realise that we're most of the way to Lisp.īut first, why care about lambda calculus? Consider four different systems: The goal is not to do maths with it, but rather to build up definitions within it so that we can express non-trivial algorithms easily. It is most useful if you want to get some intuition for the lambda calculus, or more generally for how simple axiomatisations of computation actually let you express anything. They don't "expand" the set of programs you can write, but they can make writing them a hell-of-a-lot easier.Īs for the claim "there is a “full theory of lambda calculus”," it essentially means, that the function definition and composition in this language is Turing complete right out of the box.This is a linkpost that I'm posting in response to a request to share more of the archive of my personal blog on LessWrong. In fact, you can create hybrid languages which combine the features of both and still compile to machine code for whichever computer you like. Because the computational models are equivalent, you can pick whichever is more appropriate and "compile" it into the other. Others are more natural as series of instructions. ![]() Why does this matter? Some algorithms are more natural to express in terms of functions. They are equivalent - you can program a simulation of arbitrary Turing machine in lambda calculus / RAM machine and vice versa. That means, in each of these models, it is possible to write a program, that can accept code of any other program and execute it. They are powerful enough to create a universal programable computer. It is an alternative to Turing machine and RAM machine. Lambda calculus is a mathematical model of computation, that's entirely made of composing and applying functions. We'll do our best to keep these links up to date, but if we fall behind please don't hesitate to shoot us a modmail. This is not an official Rust forum, and cannot fulfill feature requests. Err on the side of giving others the benefit of the doubt.Īvoid re-treading topics that have been long-settled or utterly exhausted. Please create a read-only mirror and link that instead.Ī programming language is rarely worth getting worked up over.īe charitable in intent. If criticizing a project on GitHub, you may not link directly to the project's issue tracker. ![]() Post titles should include useful context.įor Rust questions, use the stickied Q&A thread.Īrts-and-crafts posts are permitted on weekends.Ĭriticism is encouraged, though it must be constructive, useful and actionable. For content that does not, use a text post to explain its relevance. Posts must reference Rust or relate to things using Rust. ![]() We observe the Rust Project Code of Conduct. Strive to treat others with respect, patience, kindness, and empathy. Please read The Rust Community Code of Conduct The Rust Programming LanguageĪ place for all things related to the Rust programming language-an open-source systems language that emphasizes performance, reliability, and productivity.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |