Lamda Expression Learning (2)--LAMDA transformation

Source: Internet
Author: User

Review Λ-calculus Syntax:

T:: = terms:

X variable

ΛX.T Abstraction

T T application

λ- transform: Maintains the meaning of the λ-item while transforming it.

1.α- Transform: Change the name of the bound variable, the meaning is still the same.

ΛX.T→ΛY.T (x:=y)

( replaces the free appearance of all x in the body T of an expression with the name y)

Two lamda Expressions If they can be transformed from one to the other by means of an α-transform (which may be applied to a child), they are said to be congruent .

2.β- statute: The transformation of application , which represents the concept of functional function.

Replace all free x in t1 with T2 as the result.

Lambda expressions that do not allow any beta normalization are called beta paradigms . Not all expressions can be normalized to a normal form.

3.η- Transform :

Eta-conversion expresses the idea of extensionality, which in the "This" is "that" and "functions is" the same if and only If they give the same result for all arguments. Eta-conversion converts betweenλx. (f x) and F whenever X does not appear free in F.

Lamda Expression Learning (2)--LAMDA transformation

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