Theory of computation | Lambda calculus | Type theory

Simply typed lambda calculus

The simply typed lambda calculus, a formof type theory, is a typed interpretation of the lambda calculus with only one type constructor that builds function types. It is the canonical and simplest example of a typed lambda calculus. The simply typed lambda calculus was originally introduced by Alonzo Church in 1940 as an attempt to avoid paradoxical use of the untyped lambda calculus. The term simple type is also used to refer extensions of the simply typed lambda calculus such as products, coproducts or natural numbers (System T) or even full recursion (like PCF). In contrast, systems which introduce polymorphic types (like System F) or dependent types (like the Logical Framework) are not considered simply typed. The simple types, except for full recursion, are still considered simple because the Church encodings of such structures can be done using only and suitable type variables, while polymorphism and dependency cannot. (Wikipedia).

Video thumbnail

Python Programming Tutorial - 40 - Lamdba

Source Code: https://github.com/thenewboston-developers Core Deployment Guide (AWS): https://docs.google.com/document/d/16NDHWtmwmsnrACytRXp2T9Jg7R5FgzRmkYoDteFKxyc/edit?usp=sharing

From playlist Python 3.4 Programming Tutorials

Video thumbnail

LambdaConf 2015 - Introduction to Typed Racket Mark Farrell

This workshop will give an introduction to Typed Racket. We will give an overview of the features of its type system, go over some examples of typing old untyped Racket code and provide some accompanying typing exercises for people to try. We will also discuss some current issues trusting

From playlist LambdaConf 2015

Video thumbnail

Lambda Expressions & Anonymous Functions || Python Tutorial || Learn Python Programming

Lambda expressions - also known as “anonymous functions” - allow you to create and use a function in a single line. They are useful when you need a short function that you will only use once. For example, when using the map, filter and sort methods. Please SUBSCRIBE: http://bit.ly/Socra

From playlist Python Programming Tutorials (Computer Science)

Video thumbnail

Anonymous Functions - What's in a name? - Socratica #Shorts

Find our programming playlists here: Python: http://bit.ly/PythonSocratica SQL: http://bit.ly/SQL_Socratica Python instructor: Ulka Simone Mohanty (@ulkam on Twitter) Written & Produced by Michael Harrison #Python #Coding #Shorts

From playlist Python Programming Tutorials (Computer Science)

Video thumbnail

LAMBDA Functions: Powerful And Elegant Abstractions

Python’s lambda, a tiny anonymous function, can be useful in a pinch when you’re feeling too lazy to type that extra d-e-f. But did you know that behind this little lambda is actually one of the most powerful & elegant abstractions in the history of computer science? The lambda calculus,

From playlist Functional Programming

Video thumbnail

C++ Tutorial 9 : Lambda Expressions

Code & Transcript : http://bit.ly/cplusplus9 Best C++ Book : https://amzn.to/2GPb7do https://www.patreon.com/derekbanas This part of my C++ tutorial provides numerous examples of what you can do with Lambda Expressions. We'll cover how to Sort, Filter, Sum, Edit and Generate Lists based o

From playlist C++ Tutorial

Video thumbnail

Lambda Expressions in Java | Java Lambda Tutorial | Java Certification Training | Edureka

**** Java Certification Training: https://www.edureka.co/java-j2ee-training-course **** This Edureka tutorial on “Lambda Expressions in Java” will introduce you to a new Java feature called Lambda Expressions. It will also talk about the functional interface in Java. Through this tutorial

From playlist Java Tutorial For Beginners | Edureka

Video thumbnail

Lecture 2: The Curry-Howard correspondence

This talk gives an elementary introduction to some central ideas in the theory of computation, including lambda calculus and its relation to category theory. The aim was to get to the statement of the Curry-Howard correspondence, but we ran out of time; at some point there will be another

From playlist Topos theory seminar

Video thumbnail

Shadows of Computation - Lecture 5 - What is Computation?

Welcome to Shadows of Computation, an online course taught by Will Troiani and Billy Snikkers, covering the foundations of category theory and how it is used by computer scientists to abstract computing systems to reveal their intrinsic mathematical properties. In the fifth lecture Will sp

From playlist Shadows of Computation

Video thumbnail

Stanford Seminar - Propositions as Types

"Propositions as Types" - Philip Wadler of University of Edinburgh About the talk: The principle of Propositions as Types links logic to computation. At first sight it appears to be a simple coincidence---almost a pun---but it turns out to be remarkably robust, inspiring the design of the

From playlist Engineering

Video thumbnail

Proof synthesis and differential linear logic

Linear logic is a refinement of intuitionistic logic which, viewed as a functional programming language in the sense of the Curry-Howard correspondence, has an explicit mechanism for copying and discarding information. It turns out that, due to these mechanisms, linear logic is naturally r

From playlist Talks

Video thumbnail

Shadows of Computation - Theorems for Free (Discussion)

Welcome to Shadows of Computation, an online course taught by Will Troiani and Billy Snikkers, covering the foundations of category theory and how it is used by computer scientists to abstract computing systems to reveal their intrinsic mathematical properties. In this video, Billy and Wil

From playlist Shadows of Computation

Video thumbnail

LAMBDA Excel Function. LET & LAMBDA together to make Single Cell Reports. Excel Magic Trick 1706

Introduction to LAMBDA Excel Function. LET & LAMBDA together to make Single Cell Reports. EMT 1706. Download Excel File: https://excelisfun.net/files/EMT1706.xlsx Learn about the new LAMBDA Excel worksheet function that allows us to create a re-usable function with variable inputs that we

From playlist Single Cell Formula Reporting in the Excel Worksheet

Video thumbnail

"Magnetic Edge and Semiclassical Eigenvalue Asymptotics" by Dr. Ayman Kachmar

What will be the energy levels of an electron moving in a magnetic field? In a typical setting, these are eigenvalues of a special magnetic Laplace operator involving the semiclassical parameter (a very small parameter compared to the sample’s scale), and the foregoing question becomes on

From playlist CAMS Colloquia

Video thumbnail

FEM@LLNL | Unifying the Analysis of Geometric Decomposition in FEEC

Sponsored by the MFEM project, the FEM@LLNL Seminar Series focuses on finite element research and applications talks of interest to the MFEM community. On March 22, 2022, Tobin Isaac of Georgia Tech presented "Unifying the Analysis of Geometric Decomposition in FEEC." Two operations take

From playlist FEM@LLNL Seminar Series

Video thumbnail

Paul Zinn-Justin: "Schubert calculus and quantum integrability"

Asymptotic Algebraic Combinatorics 2020 "Schubert calculus and quantum integrability" Paul Zinn-Justin - University of Melbourne Abstract: We report on recent progress in the field of Schubert calculus and its recently uncovered relation to quantum integrable systems. We shall see how th

From playlist Asymptotic Algebraic Combinatorics 2020

Video thumbnail

Univalent Foundations Seminar - Steve Awodey

Steve Awodey Carnegie Mellon University; Member, School of Mathematics November 19, 2012 For more videos, visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Lambda in Python - Advanced Python 08 - Programming Tutorial - Map Filter Reduce

Lambda in Python - Advanced Python 08 - Programming Tutorial - Map Filter Reduce In this Python Advanced Tutorial, we will be learning about Lambda functions in Python. A lambda function is a small (one line) anonymous function that is defined without a name. It is typically used when you

From playlist Advanced Python - Complete Course

Video thumbnail

Giovanni Peccati: Some applications of variational techniques in stochastic geometry I

Some variance estimates on the Poisson space, Part I I will introduce some basic tools of stochastic analysis on the Poisson space, and describe how they can be used to develop variational inequalities for assessing the magnitude of variances of geometric quantities. Particular attention

From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability

Related pages

Category of sets | Typing rule | Parametric polymorphism | Type constructor | Set theory | Natural deduction | System F | Principal type | Typing environment | Type safety | Alonzo Church | Church encoding | Operational semantics | Typed lambda calculus | Currying | Coproduct | Tautology (logic) | Dialectica interpretation | Lambda calculus | Completeness (logic) | Polynomial | Function type | Untyped lambda calculus | Type inference | Topos | Apply | Product (category theory) | Minimal logic | Dependent type | Backus–Naur form | Decidability (logic) | Normalisation by evaluation | Equivalence class | Closed monoidal category | Grzegorczyk hierarchy | Natural number | Type system | Set (mathematics) | Function space | Cartesian product | Morphism | Type inhabitation | Functor | Joachim Lambek | Type erasure | Type theory | Fixed-point combinator | Intuitionistic logic | Simply typed lambda calculus | Recursion | Combinatory logic