Question

Show how the meaning of the following curried function definition can be formalised in terms of lambda expressions: $$\begin{aligned} & \text { mult : : Int } \rightarrow \text { Int } \rightarrow \text { Int } \rightarrow \text { Int } \\ & \text { mult } x \text { y } z=x^{\star} y^{\star} z \end{aligned}$$

Name: Problem 7, Chapter 4: Programming in Haskell
Uploaded: 2020-05-06T18:11:51-08:00
Duration: 59 s
Channel: Vikash Ranjan
Description: Show how the meaning of the following curried function definition can be formalised in terms of lambda expressions: mult : : Int → Int → Int → Int mult x y z=x^⋆ y^⋆ z

   Show how the meaning of the following curried function definition can be formalised in terms of lambda expressions:
$$\begin{aligned}
& \text { mult : : Int } \rightarrow \text { Int } \rightarrow \text { Int } \rightarrow \text { Int } \\
& \text { mult } x \text { y } z=x^{\star} y^{\star} z
\end{aligned}$$

Programming in Haskell

Graham Hutton 2nd Edition

Chapter 4, Problem 7

Instant Answer

Solved by Expert Vikash Ranjan

05/06/2020

Step 1

First, let's define the curried function `mult` in terms of lambda expressions: ``` mult = \x -> (\y -> (\z -> x * y * z)) ``` Here, `\x` represents the first argument of `mult`, `\y` represents the second argument, and `\z` represents the third argument. Show more…

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Show how the meaning of the following curried function definition can be formalised in terms of lambda expressions: $$\begin{aligned} & \text { mult : : Int } \rightarrow \text { Int } \rightarrow \text { Int } \rightarrow \text { Int } \\ & \text { mult } x \text { y } z=x^{\star} y^{\star} z \end{aligned}$$

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Key Concepts

Currying

Currying is the process of transforming a function that takes multiple arguments into a sequence of functions, each with a single argument. It allows a function defined for several parameters to be broken down into a chain of functions that are applied one argument at a time. This is a key concept in functional programming and lambda calculus, enabling partial application and the creation of higher-order functions.

Lambda Calculus

Lambda calculus is a formal system used to express computation based on function abstraction and application. In this context, it is utilized to formally represent curried functions by using lambda expressions. Each lambda abstraction corresponds to one function argument, and successive applications of these lambda functions model the original multi-argument function in a rigorous and mathematical way.

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