5 ms·

Well i don't get it can anybody simplify it ?

austincheney 7y ago
I cannot simplify the actual paper presented as I am not a mathematician and cannot read Euler expressions (academic calculus). I can speak to lambda calculus from a programming perspective though. Lambda calculus is the basis of functional programming where a function is a portable black box containing instructions and returning a result. That said, a function is an abstraction such that a container of many instructions may be represented by a single reference. Lambda calculus also accounts for nested functions as a means of expressing layers of abstractions. One such style of layered functions is the notion of creating a new function inside a function and returning that new function, which is called currying. Currying allows for the creation of an abstraction where the computation is not ready at the time of creation, such as awaiting additional input via arguments, but ready once called. In my own code I use nested functions to create a separation of concerns. This allows me to write code where portions are isolated from other portions but available by reference where needed. This separation provides a formal means of internal architecture and organization by which complexity is reduced. A major consideration available from lambda calculus is the concept of lexical scope, which is a concept similar to abstraction layers but applies to reference resolution. * https://en.wikipedia.org/wiki/Lambda_calculus https://en.wikipedia.org/wiki/Lambda_calculus * https://en.wikipedia.org/wiki/Scope_(computer_science)#Lexical_scoping https://en.wikipedia.org/wiki/Scope_(computer_science)#Lexic...
- galaxyLogic 7y ago
  Right I would say and argue that lexical scope is the main thing that makes Functional Programming languages Functional Programming languages. Why? Because it allows a function to create and return a new different instance of a function-skeleton coded in the inner scope, part of which function-instance is the values of the variables in its outer scope which were the values of those variables at the time the outer function returned. That means it is easy to create new function-instances. Function instances are "first class citizens" as much part of the machinery of such language as any data-structure. In this sense the "inner function" coded inside an outer is not a function at all. It is just an encoding, a set of instructions for creating a new function which instructions are executed to create a new function when you execute the outer function. Whereas the outermost function is a function by itself since there can be only one instance of it ever.
  - dreamcompiler 7y ago
    In practice the inner function (the body of a lexical closure) is only compiled once. When a "new function is made" at runtime, a data structure for the new lexical environment is created together with a pointer to the already-compiled closure body. So the executable portion (the actual instructions of the closure) are only allocated once.
- lucasverra 7y ago
  Please don't take as disregarding your probably clear explanation, but if I had to show my grandma a youtube video about this subject, wich one would you choose? I'm regarding this subject as Lambda calculas > lambda functions > serverless > "business logic i can define and upload and let idle in the internets without worrying about managing the computers that actually made that business logic available worldwide behing an URL " I know the HN crowd is skeptical about serverless but as a non developper, it is pretty mindblowing the barriers that AWS + lambda functions are taking down.
  - austincheney 7y ago
    I am not skeptical. All my applications are serverless. I find this makes for extreme portability without many privacy and security concerns.

I cannot simplify the actual paper presented as I am not a mathematician and cannot read Euler expressions (academic calculus). I can speak to lambda calculus from a programming perspective though. Lambda calculus is the basis of functional programming where a function is a portable black box containing instructions and returning a result. That said, a function is an abstraction such that a container of many instructions may be represented by a single reference. Lambda calculus also accounts for nested functions as a means of expressing layers of abstractions. One such style of layered functions is the notion of creating a new function inside a function and returning that new function, which is called currying. Currying allows for the creation of an abstraction where the computation is not ready at the time of creation, such as awaiting additional input via arguments, but ready once called. In my own code I use nested functions to create a separation of concerns. This allows me to write code where portions are isolated from other portions but available by reference where needed. This separation provides a formal means of internal architecture and organization by which complexity is reduced. A major consideration available from lambda calculus is the concept of lexical scope, which is a concept similar to abstraction layers but applies to reference resolution. * https://en.wikipedia.org/wiki/Lambda_calculus https://en.wikipedia.org/wiki/Lambda_calculus * https://en.wikipedia.org/wiki/Scope_(computer_science)#Lexical_scoping https://en.wikipedia.org/wiki/Scope_(computer_science)#Lexic...

galaxyLogic 7y ago
Right I would say and argue that lexical scope is the main thing that makes Functional Programming languages Functional Programming languages. Why? Because it allows a function to create and return a new different instance of a function-skeleton coded in the inner scope, part of which function-instance is the values of the variables in its outer scope which were the values of those variables at the time the outer function returned. That means it is easy to create new function-instances. Function instances are "first class citizens" as much part of the machinery of such language as any data-structure. In this sense the "inner function" coded inside an outer is not a function at all. It is just an encoding, a set of instructions for creating a new function which instructions are executed to create a new function when you execute the outer function. Whereas the outermost function is a function by itself since there can be only one instance of it ever.
- dreamcompiler 7y ago
  In practice the inner function (the body of a lexical closure) is only compiled once. When a "new function is made" at runtime, a data structure for the new lexical environment is created together with a pointer to the already-compiled closure body. So the executable portion (the actual instructions of the closure) are only allocated once.
lucasverra 7y ago
Please don't take as disregarding your probably clear explanation, but if I had to show my grandma a youtube video about this subject, wich one would you choose? I'm regarding this subject as Lambda calculas > lambda functions > serverless > "business logic i can define and upload and let idle in the internets without worrying about managing the computers that actually made that business logic available worldwide behing an URL " I know the HN crowd is skeptical about serverless but as a non developper, it is pretty mindblowing the barriers that AWS + lambda functions are taking down.
- austincheney 7y ago
  I am not skeptical. All my applications are serverless. I find this makes for extreme portability without many privacy and security concerns.