Algebra of programming
Types and programming languages
Types and programming languages
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Advanced Functional Programming, First International Spring School on Advanced Functional Programming Techniques-Tutorial Text
HOL2P - a system of classical higher order logic with second order polymorphism
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
The open theory standard theory library
NFM'11 Proceedings of the Third international conference on NASA Formal methods
A mechanized translation from higher-order logic to set theory
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Stateless higher-order logic with quantified types
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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A new logic is posited for the widely used HOL theorem prover, as an extension of the existing higher order logic of the HOL4 system. The logic is extended to three levels, adding kinds to the existing levels of types and terms. New types include type operator variables and universal types as in System F . Impredicativity is avoided through the stratification of types by ranks according to the depth of universal types. The new system, called HOL-Omega or HOL *** , is a merging of HOL4, HOL2P[11], and major aspects of System F *** from chapter 30 of [10]. This document presents the abstract syntax and semantics for the kinds, types, and terms of the logic, as well as the new fundamental axioms and rules of inference. As the new logic is constructed according to the design principles of the LCF approach, the soundness of the entire system depends critically and solely on the soundness of this core.