Wed 10 Jan 2018 16:40 - 17:05 at Watercourt - Types Chair(s): Thorsten Altenkirch

Definitions are traditionally considered to be a safe mechanism for introducing concepts on top of a logic known to be consistent. In contrast to arbitrary axioms, definitions should in principle be treatable as a form of abbreviation, and thus compiled away from the theory without losing provability. In particular, definitions should form a conservative extension of the pure logic. These properties are crucial for modern interactive theorem provers, as they ensure the consistency of the logic and a suitable environment for total/certified functional programming.

We prove these properties, namely, safety and conservativity, for Higher-Order Logic (HOL), a logic implemented in several mainstream theorem provers and relied upon by thousands of users. Some unique features of HOL, such as the requirement to give non-emptiness proofs when defining new types and the impossibility to unfold type definitions, make the proof of these properties, and also the very formulation of safety, nontrivial.

Our study also factors in the essential variation of HOL definitions featured by Isabelle/HOL, a popular member of the HOL-based provers family. The current work improves on recent results which showed a weaker property, consistency of Isabelle/HOL’s definitions.

Wed 10 Jan (GMT-07:00) Tijuana, Baja California change

15:50 - 17:30: Research Papers - Types at Watercourt
Chair(s): Thorsten AltenkirchUniversity of Nottingham
POPL-2018-papers15:50 - 16:15
POPL-2018-papers16:15 - 16:40
William J. BowmanNortheastern University, USA, Youyou CongOchanomizu University, Japan, Nick RiouxNortheastern University, USA, Amal AhmedNortheastern University, USA
Link to publication DOI Pre-print
POPL-2018-papers16:40 - 17:05
Ondřej KunčarTechnische Universität München, Germany, Andrei PopescuMiddlesex University, London
POPL-2018-papers17:05 - 17:30
Paolo CapriottiUniversity of Nottingham, Nicolai KrausUniversity of Nottingham