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HOL is an acronym commonly used in logic and computer science to denote Higher-Order Logic, a formal system that allows quantification over functions and predicates and supports expressive mathematical formalization. In HOL, types organize terms and a functional calculus enables higher-order constructs. Higher-Order Logic serves as the foundation for several interactive theorem-proving environments and formalization projects.

Notable HOL implementations include HOL Light and HOL4, both descendants of the original HOL system developed

Outside of formal logic, the term HOL can appear as an acronym for various organizations or concepts

in
the
1980s
as
part
of
the
LCF
family.
HOL
Light,
designed
to
be
small
and
trusted,
was
developed
by
John
Harrison
and
has
been
used
to
formalize
substantial
parts
of
mathematics.
HOL4
is
a
later,
more
scalable
successor.
The
Isabelle/HOL
session
provides
a
higher-order
logic
framework
within
the
Isabelle
proof
assistant,
combining
HOL
with
Isabelle’s
generic
infrastructure.
These
systems
are
widely
used
in
formal
verification
of
software
and
hardware,
as
well
as
in
formalized
mathematics
and
in
academic
research
on
proof
systems.
in
different
fields.
In
the
context
of
this
article,
HOL
refers
to
Higher-Order
Logic
and
related
theorem-proving
environments.