An algebra of HTTP

A description of HTTP in an integral algebra serves as yet another tool for reasoning about principles.

The response is a point in the domain that is HTTP. A GET request is an identity relation on that point. A function from the domain of the request into the domain of the response exists, whether explicit or implied. The function is implied when a resource is created but not returned in the response.

Therefore the expression

  GET /index.html

identifies a point in the domain of HTTP. And likewise the expressions

  PUT /index.html
  DELETE /index.html

are operations on the same point.

Compare this to arithmetic. The identity expression is

  1 = 1

and operational expressions include

  1 + 1
  1 - 1

.

The equivalent algebraic identity expression would read as

  "GET /index.html" = "response entity body data"

.

When we can see this algebra, then we have new eyes.