<s>
λProlog	B-Language
,	O
also	O
written	O
lambda	B-Language
Prolog	I-Language
,	O
is	O
a	O
logic	B-Language
programming	I-Language
language	I-Language
featuring	O
polymorphic	B-Application
typing	I-Application
,	O
modular	B-Architecture
programming	I-Architecture
,	O
and	O
higher-order	B-Application
programming	I-Application
.	O
</s>
<s>
These	O
extensions	O
to	O
Prolog	B-Language
are	O
derived	O
from	O
the	O
higher-order	O
hereditary	O
Harrop	O
formulas	O
used	O
to	O
justify	O
the	O
foundations	O
of	O
λProlog	B-Language
.	O
</s>
<s>
Higher-order	B-Algorithm
quantification	I-Algorithm
,	O
simply	O
typed	O
λ-terms	O
,	O
and	O
higher-order	O
unification	O
gives	O
λProlog	B-Language
the	O
basic	O
supports	O
needed	O
to	O
capture	O
the	O
λ-tree	O
syntax	O
approach	O
to	O
higher-order	B-Application
abstract	I-Application
syntax	I-Application
,	O
an	O
approach	O
to	O
representing	O
syntax	O
that	O
maps	O
object-level	O
bindings	O
to	O
programming	O
language	O
bindings	O
.	O
</s>
<s>
Programmers	O
in	O
λProlog	B-Language
need	O
not	O
deal	O
with	O
bound	O
variable	O
names	O
:	O
instead	O
various	O
declarative	O
devices	O
are	O
available	O
to	O
deal	O
with	O
binder	O
scopes	O
and	O
their	O
instantiations	O
.	O
</s>
<s>
Since	O
1986	O
,	O
λProlog	B-Language
has	O
received	O
numerous	O
implementations	O
.	O
</s>
<s>
The	O
Abella	O
theorem	O
prover	O
has	O
been	O
designed	O
to	O
provide	O
an	O
interactive	O
environment	O
for	O
proving	O
theorems	O
about	O
the	O
declarative	O
core	O
of	O
λProlog	B-Language
.	O
</s>
