Lists – Lists can be encoded in the lambda calculus. A way to do this, is by defining a lambda term that, like a "cons", inserts an element at the head of a list, initially empty. Rather than showing the full lambda term, we introduce the defined term cons. For example, the result of reducing the encoding of the expression cons 3 [7, 8] will be the encoding for the list [3, 7, 8] . Assume that you have available the fixed-point operator Y and the terms cons, sqr and succ , respectively for list construction, square and successor functions. Which expressions will these terms define? Show your argument before the final answer. 1. Y λl.(cons x l) 2. Y (λf.λn.(cons (sqr n)(f(succ n)))) 0
Concepts in Designing Database
A database design is the process of data organization based on a database model. The process deals with identifying what data should be stored in a database and how data elements relate to each other.
Entity Relationship Diagram
Complex real-world applications call for large volumes of data. Therefore, it is necessary to build a great database to store data safely and coherently. The ER data model aids in the process of database design. It helps outline the structure of an organization’s database by understanding the real-world interactions of objects related to the data. For example, if a school is tasked to store student information, then analyzing the correlation between the students, subjects, and teachers would help identify how the data needs to be stored.
Lists – Lists can be encoded in the lambda calculus. A way to do this, is by defining a
lambda term that, like a "cons", inserts an element at the head of a list, initially empty. Rather
than showing the full lambda term, we introduce the defined term cons. For example, the
result of reducing the encoding of the expression cons 3 [7, 8] will be the encoding for the
list [3, 7, 8] .
Assume that you have available the fixed-point operator Y and the terms
cons, sqr and succ , respectively for list construction, square and successor functions.
Which expressions will these terms define? Show your argument before the final answer.
1. Y λl.(cons x l)
2. Y (λf.λn.(cons (sqr n)(f(succ n)))) 0
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