Comments by "xybersurfer" (@xybersurfer) on "Lambda Calculus - Computerphile" video.

  1. it's the truth though. Lambda Calculus is normally used, to formally explain how a function applied to some arguments, is transformed into a function with fixed parameters. it's basically just a way of explaining partial function application in functional programming. partial application is used all over the place in most functional languages. Haskell's "map" function is one of the best examples. it takes 2 parameters: - a function - a list if you give it both parameters, then it takes your function (first parameter) and applies it to each value in your list (second parameter). it gives you a list of the results. but if you only give the first parameter (fix the first parameter), then you get a "new" function. this new function takes a list (the remaining parameter for "map") and gives you a list of the results. Lambda Calculus could help you figure out what the input and output of such a new function is. but it is normally used for more theoretical things. i think functional languages have a huge advantage over imperative languages. you can quickly create more specialized functions, by just applying already existing functions on parameters
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  2. ALL ONE because the right side results in a function and functions take inputs. when not all inputs are given, then the result is a function that expects the remaining inputs (so functions can output functions). passing around functions like any other value is one of the strengths of functional programming ("normal" values are simply functions that don't take any inputs) technically these functions actually only take 1 input at a time (every lambda is the start of a function). so when you see 2 inputs. it's actually a function that takes 1 input and produces a function that takes the other input. this is called "currying"
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  3. great idea. i would love to see an explanation of that thing
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  4. TRUE = λx. λy. x FALSE = λx. λy. y NOT = λb. b FALSE TRUE AND = λx. λy. x y FALSE OR = λx. λy. x TRUE y
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  5. great video by the way
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