<s>
In	O
mathematical	O
logic	O
and	O
computer	B-General_Concept
science	I-General_Concept
,	O
the	O
lambda-mu	B-Application
calculus	I-Application
is	O
an	O
extension	O
of	O
the	O
lambda	B-Language
calculus	I-Language
introduced	O
by	O
M	O
.	O
Parigot	O
.	O
</s>
<s>
It	O
introduces	O
two	O
new	O
operators	O
:	O
the	O
μ	O
operator	O
(	O
which	O
is	O
completely	O
different	O
both	O
from	O
the	O
μ	O
operator	O
found	O
in	O
computability	O
theory	O
and	O
from	O
the	O
μ	O
operator	O
of	O
modal	B-Application
μ-calculus	I-Application
)	O
and	O
the	O
bracket	O
operator	O
.	O
</s>
<s>
According	O
to	O
the	O
Curry	O
–	O
Howard	O
isomorphism	O
,	O
lambda	B-Language
calculus	I-Language
on	O
its	O
own	O
can	O
express	O
theorems	O
in	O
intuitionistic	O
logic	O
only	O
,	O
and	O
several	O
classical	O
logical	O
theorems	O
ca	O
n't	O
be	O
written	O
at	O
all	O
.	O
</s>
<s>
Semantically	O
these	O
operators	O
correspond	O
to	O
continuations	O
,	O
found	O
in	O
some	O
functional	B-Language
programming	I-Language
languages	I-Language
.	O
</s>
<s>
We	O
can	O
augment	O
the	O
definition	O
of	O
a	O
lambda	O
expression	O
to	O
gain	O
one	O
in	O
the	O
context	O
of	O
lambda-mu	B-Application
calculus	I-Application
.	O
</s>
<s>
The	O
three	O
main	O
expressions	O
found	O
in	O
lambda	B-Language
calculus	I-Language
are	O
as	O
follows	O
:	O
</s>
<s>
In	O
addition	O
to	O
the	O
traditional	O
λ-variables	O
,	O
the	O
lambda-mu	B-Application
calculus	I-Application
includes	O
a	O
distinct	O
set	O
of	O
μ-variables	O
.	O
</s>
<s>
The	O
terms	O
that	O
are	O
added	O
by	O
the	O
lambda-mu	B-Application
calculus	I-Application
are	O
of	O
the	O
form	O
:	O
</s>
<s>
The	O
basic	O
reduction	O
rules	O
used	O
in	O
the	O
lambda-mu	B-Application
calculus	I-Application
are	O
the	O
following	O
:	O
</s>
