Q
0 is
Peter Andrews' formulation of the
simply-typed lambda calculus
The simply typed lambda calculus (\lambda^\to), a form
of type theory, is a typed interpretation of the lambda calculus with only one type constructor (\to) that builds function types. It is the canonical and simplest example of a typed lambda ca ...
,
and provides a foundation for mathematics comparable to first-order logic plus set theory.
It is a form of
higher-order logic
mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more express ...
and closely related to the logics of the
HOL theorem prover
HOL (Higher Order Logic) denotes a family of interactive theorem proving systems using similar (higher-order) logics and implementation strategies. Systems in this family follow the LCF approach as they are implemented as a library which defin ...
family.
The theorem proving system
TPS and ETPSare based on Q
0. In August 2009, TPS won the first-ever competition
among higher-order theorem proving systems.
The CADE-22 ATP System Competition (CASC-22)
/ref>
Axioms of Q0
The system has just five axioms, which can be stated as: