![]() As you will see, the Lambda Calculus can compute everything that can be computed, just with a very simple cut and paste.Ī line of symbols is called an expression. All it ever does is taking a line of letters (or symbols), and performing a little cut and paste operation on it. ![]() Don’t be intimidated by the word “calculus”! It does not have any complicated formulae or operations. The Lambda Calculus has been invented at roughly the same time as the Turing Machine (mid-1930ies), by Alonzo Church. And if you understood it, you might end up with a much better intuition of computation. It might look frighteningly mathematical from a distance (it has a greek letter in it, after all!), so nobody outside of academic computer science tends to look at it, but it is unbelievably easy to understand. The Lambda Calculus does exactly the same thing, but without wheels to cloud your vision. (A Turing Machine, doing more harm than good. Many may have heard of Turing Machines, but these things tend to do more harm than good, because they leave strong intuitions of moving wheels and tapes, instead of what it really does: embodying the nature of computation. Unfortunately, most people outside of programming and computer science don’t know exactly what computation means. If the universe/the mind/the brain/bunnies/God is explicable in a mechanical way, then it is a computer, and vice versa. The term computation does just this: it defines exactly what machines can do, and what not. For millennia, philosophers have struggled when they wanted to express or doubt that the universe can be explained in a mechanical way, because it is so difficult to explain what a machine is, and what it is not. Why is it so important? Because computationalism is the new mechanism. If there is one highly underrated concept in philosophy today, it is computation. Parenthesisation.The Lambda Calculus for Absolute Dummies (like myself) Syntax tree, and thus encodes parsing precedences and Supervisions, as it is the concrete syntax tree, not the abstract This grammar is more complex than the one given in IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS // BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN // ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN // CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE // SOFTWARE.įirst we need to parse the expression, using the grammar givenīelow. // THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, // EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF // MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND // NONINFRINGEMENT. Copyright 2019 by Robert Kovacsics // // Permission is hereby granted, free of charge, to any person // obtaining a copy of this software and associated documentation // files (the "Software"), to deal in the Software without // restriction, including without limitation the rights to use, copy, // modify, merge, publish, distribute, sublicense, and/or sell copies // of the Software, and to permit persons to whom the Software is // furnished to do so, subject to the following conditions: // // The above copyright notice and this permission notice shall be // included in all copies or substantial portions of the Software. Let _loop_ (fn loop => fn n => if (eq0 n) To completion isn't as useful as just iterating a couple of steps, Will end up evaluating (pred 2) and (pred (pred 2)) rather than Chosing the non-strict strategyĪlways reduces to beta-normal form, but you might want to eagerlyĮvaluate the predecessor function when you see it, otherwise you Here you have to be careful about the order of the evaluation, Let pred2 (fn n f x => n (fn g h => h (g f)) (fn u => x) (fn u => u)) ![]() ![]() Let pred (fn n => snd (n (fn p => pair (succ (fst p)) (fst p)) (pair 0 0)))Īnd here is a faster predecessor, try it out to see how it works: ![]() Let add (fn n m => fn f x => n f (m f x)) Re-computation of the parse tables which is laborious, and it is notĪ high priority problem, as Poly/ML and GHC have the same parsing Yet, as it would require a change to the grammar, and hence a pred is fn n f x => n (fn g h => h (g f)) (fn u => x) (fn u => u)Īnd the special built-in let variable value.Įven though both of them are equally unambiguous.map is fn f l => fn g init => l (compose g f) init.cons is fn x y => fn f init => f x (y f init).Y is fn f => (fn x => f (x x)) (fn x => f (x x)).Note, it uses space-based lexing (though you don't need to put spacesĪround parentheses), and only implements the following prefix x fn x => x Maximum single steps Evaluation strategy Strict/Eager Non-strict/Call-by-name Also have a look at the examples section below, where you canĬlick on an application to reduce it (e.g. Type an expression into the following text area (using the fn x =>īody synatx), click parse, then click on applications to evaluate ![]()
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