The scalar product of two lists of integers x s and y s of...

The scalar product of two lists of integers $x s$ and $y s$ of length $n$ is given by the sum of the products of corresponding integers: $$ \sum_{i=0}^{n-1}\left(x s_i * y s_i\right) $$ In a similar manner to chisqr, show how a list comprehension can be used to define a function scalarproduct $::$ [Int] $\rightarrow$ [Int] $\rightarrow$ Int that returns the scalar product of two lists. For example: $>$ scalarproduct $[1,2,3] \quad[4,5,6]$ 32

The scalar product of two lists of integers $x s$ and $y s$ of length $n$ is given by the sum of the products of corresponding integers:
$$
\sum_{i=0}^{n-1}\left(x s_i * y s_i\right)
$$
In a similar manner to chisqr, show how a list comprehension can be used to define a function scalarproduct $::$ [Int] $\rightarrow$ [Int] $\rightarrow$ Int that returns the scalar product of two lists. For example:
$>$ scalarproduct $[1,2,3] \quad[4,5,6]$
32

Key Concepts

Functional Programming

Functional programming is a paradigm that treats computation as the evaluation of mathematical functions and avoids changing state or mutable data. This approach emphasizes the use of pure functions, higher-order functions, and declarative constructs like list comprehensions. In Haskell, these principles allow the development of concise, readable, and maintainable code, as exemplified by the implementation of the scalar product using a list comprehension.

Type Signatures

Type signatures in Haskell are declarations that explicitly state the types of inputs and outputs of a function. They provide clarity and safety by ensuring the function is applied to the correct types of data. For the scalar product function, the type signature is [Int] -> [Int] -> Int, indicating that the function takes two lists of integers and returns an integer.

Scalar Product

The scalar product, also known as the dot product, is a function that takes two equal-length sequences of numbers and returns a single number. This is done by multiplying corresponding elements of the two lists and then summing all of those products. It plays a key role in vector mathematics and is used to measure the similarity in direction between vectors.

List Comprehension

List comprehension is a syntactic construct used in functional programming languages like Haskell to create lists based on existing lists in a concise and readable way. It involves an expression followed by one or more generators and optional predicates, allowing the transformation and filtering of elements. In the context of computing the scalar product, list comprehension can be used to generate the list of products of corresponding elements.

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