Using a list comprehension, define an expression fibs ::...

Using a list comprehension, define an expression fibs $::$ [Integer] that generates the infinite sequence of Fibonacci numbers $$0,1,1,2,3,5,8,13,21,34, \ldots$$ using the following simple procedure: - the first two numbers are 0 and 1 ; - the next is the sum of the previous two; - return to the second step. Hint: make use of the library functions zip and tail. Note that numbers in the Fibonacci sequence quickly become large, hence the use of the type Integer of arbitrary-precision integers above.

Using a list comprehension, define an expression fibs $::$ [Integer] that generates the infinite sequence of Fibonacci numbers
$$0,1,1,2,3,5,8,13,21,34, \ldots$$
using the following simple procedure:
- the first two numbers are 0 and 1 ;
- the next is the sum of the previous two;
- return to the second step.
Hint: make use of the library functions zip and tail. Note that numbers in the Fibonacci sequence quickly become large, hence the use of the type Integer of arbitrary-precision integers above.

Key Concepts

Higher-Order Functions (zip and tail)

Higher-order functions are functions that either take other functions as parameters or return them. In the context of list processing, functions like zip and tail are used to manipulate lists by pairing elements or accessing sublists. Zip can combine elements from two lists into pairs, while tail returns all elements of a list except the first, making them indispensable for elegantly defining relationships between sequential elements in a list.

Arbitrary-Precision Integers

Arbitrary-precision integers, like Haskell's Integer type, can represent numbers of any size limited only by system memory. This is essential in computations where numbers can grow rapidly, as in the case of recursive sequences or mathematical series, ensuring that calculations remain accurate without overflow issues.

Infinite Lists

Infinite lists are data structures that have no predefined end and are made possible by lazy evaluation. In functional programming, particularly in Haskell, infinite lists allow for the creation of sequences that can be conceptually unbounded while only computing elements as needed. This technique enables elegant formulations for sequences and series without running into immediate performance or memory issues.

Lazy Evaluation

Lazy evaluation is a strategy that delays the computation of expressions until their values are actually required. In Haskell, this means that even though an infinite list is defined, only the parts of the list that are accessed get computed. This characteristic is crucial for working with potentially infinite data structures and for writing efficient, modular code.

List Comprehensions

List comprehensions provide a concise and expressive way to construct new lists by specifying a set of input ranges, filters, and output expressions. They allow developers to generate lists by applying rules on existing sequences and are a powerful tool in Haskell for creating and transforming data in a readable format.

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