Final answer:
In functional programming, 'let' expressions can be represented using lambda abstraction. The 'let x = E1 in E2' is equivalent to a lambda function (λx.E2) applied to E1, showing the expression's underlying structure and semantics.
Step-by-step explanation:
In functional languages like Haskell, let expressions such as let x = E1 in E2 can be translated into an equivalent lambda abstraction. This transformation is a key aspect of understanding the language's semantics. The let expression is syntactic sugar, meaning it's a shorthand for a more complex underlying structure that can be represented in other ways.
To define let x = E1 in E2 using lambda abstraction, we would create a lambda function that takes one argument, x, and returns E2; we then immediately apply this lambda function to E1. The definition would look like this: (λx.E2) E1. Here, the lambda abstraction λx.E2 represents a function where x is bound to the value E1 when the function is applied.
Complete question is:
Lambda notations and functional languages such as Haskell provide let expressions of the form: let x = E1 in E2. For example, let x = 10 in X + 1 evaluates to 11. It is a syntactic sugar in that it is a shorthand notation and its meaning can be defined in terms of other language constructs. Define the meaning of the let expression, let x = E1 in E2, by writing an equivalent expression using lambda abstraction. This way of defining the meaning of a language is related to the semantics.