<s>
lambda	B-Language
calculus	I-Language
"	O
.	O
</s>
<s>
closures	B-Language
.	O
</s>
<s>
The	O
presentation	O
here	O
uses	O
sequents	O
(	O
)	O
rather	O
than	O
hypothetical	O
judgments	O
in	O
order	O
to	O
ease	O
comparison	O
with	O
the	O
simply	O
typed	O
lambda	B-Language
calculus	I-Language
.	O
</s>
<s>
In	O
kappa	B-Application
calculus	I-Application
an	O
expression	O
has	O
two	O
types	O
:	O
the	O
type	O
of	O
its	O
source	O
and	O
the	O
type	O
of	O
its	O
target	O
.	O
</s>
<s>
Expressions	O
in	O
kappa	B-Application
calculus	I-Application
are	O
assigned	O
types	O
according	O
to	O
the	O
following	O
rules	O
:	O
</s>
<s>
Kappa	B-Application
calculus	I-Application
obeys	O
the	O
following	O
equalities	O
:	O
</s>
<s>
This	O
is	O
the	O
basic	O
mechanism	O
which	O
ensures	O
that	O
all	O
functions	O
are	O
first-order	B-Language
.	O
</s>
<s>
functions	O
from	O
typed	O
lambda	B-Language
calculi	I-Language
by	O
restricting	O
the	O
grammar	O
of	O
types	O
.	O
</s>
