# Applications

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### Random information on the term “Applications”:

In mathematics, function application is the act of applying a function to an argument from its domain so as to obtain the corresponding value from its range.

Function application is usually depicted by juxtaposing the variable representing the function with its argument encompassed in parentheses. For example, the following expression represents the application of the function ƒ to its argument x.

In some instances, a different notation is used where the parentheses aren’t required, and function application can be expressed just by juxtaposition. For example, the following expression can be considered the same as the previous one:

The latter notation is especially useful in combination with the currying isomorphism. Given a function f : ( X × Y ) → Z {\displaystyle f:(X\times Y)\to Z} , its application is represented as f ( x , y ) {\displaystyle f(x,y)} by the former notation and f ⟨ x , y ⟩ {\displaystyle f\;\langle x,y\rangle } by the latter. However, functions in curried form f : X → ( Y → Z ) {\displaystyle f:X\to (Y\to Z)} can be represented by juxtaposing their arguments: f x y {\displaystyle f\;x\;y} , rather than f ( x ) ( y ) {\displaystyle f(x)(y)} . This relies on function application being left-associative.

### Random information on the term “Uses”:

Use, as a term in real property of common law countries, amounts to a recognition of the duty of a person to whom property has been conveyed for certain purposes, to carry out those purposes. In this context “use” is equivalent to “benefit”.

Uses were equitable or beneficial interests in land. In early law a man could not dispose of his estate by will nor could religious houses acquire it. As a method of evading the common law, the practice arose of making feoffments to the use of, or upon trust for, persons other than those to whom the seisin or legal possession was delivered, to which the equitable jurisdiction of the chancellor gave effect. To remedy the abuses which it was said were occasioned by this evasion of the law the Statute of Uses of 1536 was passed. However it failed to accomplish its purpose. Out of this failure of the Statute of Uses arose the modern law of trusts (see that article for further details).

One reason for the creation of uses was a desire to avoid the strictness of the rules of the common law, which considered seisin to be all-important and therefore refused to allow a legal interest to be created to spring up in the future. Although the common law recognised a use in chattels from an early period, it was clear by the end of the fourteenth century that land law had no room for this notion. Uses, nonetheless, satisfied contemporary needs in fifteenth century England. Its first application in relation to land was to protect the ownership of the land by the Franciscan friars, who were pledged to vows of poverty and unable to own land. This enabled the feoffee to uses for the benefit of a cestui que use. The common law did not recognise the cestui que use but affirmed the right of ownership by feoffee to use.The term “use” translates into “Trust” and this was the legal beginning of Trusts and the use of trusts to defeat feudal, death and tax dues.

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