Is $\Gamma \vdash x x : T$ possible in the simply typed lambda calculus?

Is $ \Gamma \vdash x x : T$ possible?

This problem appears on page 104 of Benjamin Pierce’s “Types and Programming Languages”.

My conclusion is that it is was the case then we would get $ x: T_1 \to T_2$ and $ x: T_1$ and by some axiom, these types are not equal.

The problem is identifying this axiom but I fear it might be possible to have this equality…

Any hints?

Is it possible to deduce type from the lambda form?

I was continuing the exploration of lambda world this summer. When I take a look at the simply typed lambda calculus, it looks like there is no use for usual chuch numerals and boolean forms anymore. If types are declared in the environment, how would you actually implement it without referring to the internal types of the implementing language?

Other way of asking it is that if the application ((L x:int x) 1) is replaced with a chuch numeral instead of 1, how would it be possible to determine, if the chuch number is int indeed?

Converting Lambda Calculus functionality to predicate logic syntax

I am trying to validate the simplest possibly notion of a formal system as relations between finite strings. I know that Lambda Calculus has the expressive power of a Turing Machine:

<λexp> ::= < var > | λ . <λexp> | ( <λexp> <λexp> )

I was thinking that it might be possible so somehow convert the functionality of lambda calculus into syntax that is closer to predicate logic by defining named functions that take finite string arguments and return finite string values.

Does anyone here have any ideas on this?

Does type-1 lambda calculus exist?

I’m interested in the intersection of linguistics and computer science, I’ve been reading on Chomsky hierarchy, and would like to know if there exist lambda calculus types that are equivalent to the Chomsky types, especially the type-1 that’s context-sensitive and has the linear-bounded non-deterministic Turing machine as an automation equivalent on the wiki.

MN Lambda student here

Good morning, all! I'm a stay-at-home dad from the balmy state of Minnesota. I'm currently attending Lambda School's Frontend WebDev program, and loving it. I'm an avid reader, movie buff, video game lover, and comic fanatic. I worked as a website support specialist for an ISP some 20+ years ago. Now that my kiddo is school age, I figured I'd delve officially back into my burgeoning love for coding. I'm excited to be a part of this community and can't wait to interact with you all!

LINQ with Lambda expression – Left Join ,GroupBy ,Count

Necesito pasar esta expresion lambda para ser usada en c#, la uso para saber el número de chas por agentes

 SELECT     aa.UserId agent,     COUNT (c.Id) chatsPerAgent FROM     AvailableAgents aa LEFT OUTER JOIN Chat c ON aa.UserId = c.AgentId WHERE     aa.IsAvailable = 1 GROUP BY     aa.UserId  

y obtener algo asi donde la primera columna es el id del agente y la segunda el numero de chats que esta atendiendo

3fde3b78-815a-4c6a-b03c-a2b473ed12d2    3 74ac56eb-b8d6-44d3-914a-8af6386b00e6    0 a2d31e31-7052-445a-94d5-0af47f751c15    2 daeafdb2-52de-4126-a2eb-498346f3d1nh    0  

Lambda y su corte de ejecución JAVA

Tengo una función lambda la cual me genera una excepción. Se ejecuta un proceso muy extenso y es propenso a fallos.

Básicamente se encarga de recorrer una serie de valores y realiza una funciones por cada una de ellas. Esas funciones lanzan una serie de excepciones. El tema es que imaginemos que tenemos 100 valores que recorrer. Si por un casual la vuelta 54 falla. La lamda entera corta su ejecución debido al throw de la excepción y el resto de valores los omite.

Como podría hacer que en caso de fallo no me fallara la lamba y se encargase de ir al siguiente.

un break o un return me valdría? un saludo

Função lambda Python não funciona [pendente]

Fiz um algoritmo em python que converte graus célsius em fahrenheit, porém preciso usar nele a função lambda e não estou conseguindo, alguém consegue me ajudar

Algoritmo em Python sem lambda:

c = float(input('Informe a temperatura em graus celsius:'))  print('A temperatura de {} convertido para fahrenheit fica {:.2f}.'.format(c, ((9 * c) / 5) + 32)) 

Algoritmo em Python com Lambda

c = float(input('Informe a temperatura em graus celsius:'))  print('A temperatura de {} convertido para fahrenheit fica {:.2f}.'.format(c, lambda f: ((9 * c) / 5) + 32)) 

Run a job every hour with Lambda or something else?

I am working on a SaaS project that will have a trial when the trial is ending I get a webhook notification when 3 days are remaining. I do some stuff with this and one of the things is I update user.company.stripe.trialEnd to the value Stripe tells me for the ending time.

When a trial ends I’d like some cron/Lambda job that runs once per hour and updates the correct things for when a trial ends.

Currently, when a payment fails a webhook takes that and marks the user unable to log in properly (redirects to billing) and forces them to stay on that page until they pay so as to prevent them from using the site.

Also when this happens the webhook service sends API calls to my serviceA and serviceB which then do some things like disabling certain things that cost me extra and then updates their user with some new values.

I want pretty much the exact same thing to happen when a trial has ended.

My question comes in how to do this? Currently, I have two thoughts on options,

1) have the lambda call my Consul cluster and then send API calls to the correct services

2) move the logic I need into a Lambda (and remove from the two services) which would then work off a SQS queue where my webhook service would publish a message to the queue and my Lambda would do the work there and only run when needed.

Issues I see with the options…

1)

  • I currently have no clue how to connect Lambda to Consul to get the right IP/port for what I need

  • My other services are running inside Kubernetes

2)

  • Introduces an extra point of failure

  • Potentially increases cost

  • Means I now have to keep my data (mongoose) models up to date in multiple git repos and services which I can see being an issue as I scale.

An option I came up with after typing this was using a Kubernetes cron job that would be in the same cluster and run Node.js like the rest of my microservices. This seems like a simple option but not sure how good it is from a design perspective.

Are the definitions of constructs in terms of lambda terms issues in implementation/design or uses of functional languages?

In Lambda Calculus, natural numbers, boolean values, list processing functions, recursion, if function are defined in terms of lambda terms. For example, natural numbers are defined as Church numerals, and recursion is defined in terms of a fixed point of a function.

Functional languages are said to be based on Lambda Calculus.

Who shall be concerned about the above concepts in terms of lambda terms: the implementer/designer of the languages, and/or programmers in the languages?

  • Do functional programming languages define/implement the above concepts in terms of lambda terms?

  • As programmers in regular functional programming languages (such as Haskell, Lisp, ML), is it correct that the above concepts are always given in the same way as in imperative languages, and we never have to understand or deal with their definitions in terms of lambda terms?

Thanks.