In computer science and mathematical logic, a function type (or arrow type or exponential) is the type of a variable or parameter to which a function has or can be assigned, or an argument or result type of a higher-order function taking or returning a function. A function type depends on the type of the parameters and the result type of the function (it, or more accurately the unapplied type constructor ยท โ ยท, is a higher-kinded type). In theoretical settings and programming languages where functions are defined in curried form, such as the simply typed lambda calculus, a function type depends on exactly two types, the domain A and the range B. Here a function type is often denoted A โ B, following mathematical convention, or BA, based on there existing exactly BA (exponentially many) set-theoretic functions mappings A to B in the category of sets. The class of such maps or functions is called the exponential object. The act of currying makes the function type adjoint to the product type; this is explored in detail in the article on currying. The function type can be considered to be a special case of the dependent product type, which among other properties, encompasses the idea of a polymorphic function. (Wikipedia).
Working with Functions (1 of 2: Notation & Terminology)
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From playlist Working with Functions
Functions of equations - IS IT A FUNCTION
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
๐ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi
From playlist Characteristics of Functions
In this video, I talk about the definition of a function and properties of functions. I also go over some examples of how to determine whether a relation is a function or not and how to evaluate functions. Enjoy! Facebook: https://www.facebook.com/braingainzofficial Instagram: https://
From playlist College Algebra
Determine if a Relation is a Function
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From playlist Intro to Functions
How to determine if an ordered pair is a function or not
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function
C9 Lectures: Dr. Erik Meijer - Functional Programming Fundamentals Chapter 3 of 13
We've kicked off C9 Lectures with a journey into the world of Functional Programming with functional language purist and high priest of the lambda calculus, Dr. Erik Meijer (you can thank Erik for many of the functional constructs that have shown up in languages like C# and VB.NET. When yo
From playlist Haskell - Functional Programming Fundamentals (Dr. Erik Meijer )
Advanced Features - The Rust Book chapter 19 (part 66)
I'm streaming every weekday morning on Twitch at https://www.twitch.tv/brookzerker. Please feel free to stop by and say hi! Links Rust book: https://doc.rust-lang.org/book/second-edition/ My code: https://github.com/BrooksPatton/learning-rust The Learning Wiki: https://github.com/BrooksP
From playlist Rust Book
Why Algebraic Data Types Are Important
Strong static typing detects a lot of bugs at compile time, so why would anyone prefer to program in JavaScript or Python? The main reason is that type systems can be extremely complex, often with byzantine typing rules (C++ comes to mind). This makes generic programming a truly dark art.
From playlist Functional Programming
DjangoCon 2019 - Static Typing in Python by Dustin Ingram
DjangoCon 2019 - Static Typing in Python by Dustin Ingram In this talk, we'll discuss the advantages and disadvantages to a static type system, as well as recent efforts to introduce static typing to Python via optional "type hints" and various tools to aid in adding types to Python code.
From playlist DjangoCon US 2019
Brian Beckman: Don't fear the Monad
Cross posted from msdn's channel 9. Functional programming is increasing in popularity these days given the inherent problems with shared mutable state that is rife in the imperative world. As we march on to a world of multi and many-core chipsets, software engineering must evolve to bett
From playlist Software Development Lectures
Programming with Math (Exploring Type Theory)
As programs are getting more complex, it's time to go back to basics, to the old well tested approach to complexity called mathematics. Let compilers deal with the intricacies of Turing machines. Our strength is abstract thinking. Let's use it! EVENT: รredev 2018 SPEAKER: Bartosz Milew
From playlist Software Development
Toward A Better Front End Architecture: ELM
Amidst the overwhelming cacophony of competing JavaScript frameworks, Elm is a promising voice. Elm is a relatively new language that compiles to JavaScript. Elm is a functional language that encourages describing UI, state, and events in a declarative manner, while performing as good as o
From playlist Elm
Dustin Ingram: Static Typing in Python
In this talk, weโll discuss the advantages and disadvantages to a static type system, as well as recent efforts to introduce static typing to Python via optional โtype hintsโ and various tools to aid in adding types to Python code.
From playlist PyColorado 2019
ElixirConf 2016 - Dialyzer: Optimistic Type Checking for Erlang and Elixir by Jason Voegele
Optimistic Type Checking for Erlang and Elixir by Jason Voegele Static typing versus dynamic typing is an age-old debate amongst computer scientists and programmers, and the fact that we still argue about it suggests that there is no single right answer for all circumstances. But what if
From playlist ElixirConf 2016
Determine if the equation represents a function
๐ Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r
From playlist What is the Domain and Range of the Function