  This paper proposes new mathematical models of the untyped Lambda-mu
calculus. One is called the stream model, which is an extension of the lambda
model, in which each term is interpreted as a function from streams to
individual data. The other is called the stream combinatory algebra, which is
an extension of the combinatory algebra, and it is proved that the extensional
equality of the Lambda-mu calculus is equivalent to equality in stream
combinatory algebras. In order to define the stream combinatory algebra, we
introduce a combinatory calculus SCL, which is an abstraction-free system
corresponding to the Lambda-mu calculus. Moreover, it is shown that stream
models are algebraically characterized as a particular class of stream
combinatory algebras.
