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- Garrin Kimmell, Aaron Stump, +7 authors Ki Yung Ahn
- PLPV
- 2012

Dependently typed programming languages provide a mechanism for integrating verification and programming by encoding invariants as types. Traditionally, dependently typed languages have been based on constructive type theories, where the connection between proofs and programs is based on the Curry-Howard correspondence. This connection comes at a price,… (More)

- Vilhelm Sjöberg, Chris Casinghino, +7 authors Stephanie Weirich
- MSFP
- 2012

We present a full-spectrum dependently typed core language which includes both nontermination and computational irrelevance (a.k.a. erasure), a combination which has not been studied before. The two features interact: to protect type safety we must be careful to only erase terminating expressions. Our language design is strongly influenced by the choice of… (More)

This paper proves normalization for Stratified System F, a type theory of predicative polymorphism studied by D. Leivant, by an extension of the method of hereditary substitution due to F. Pfenning. The advantage of normalization by hereditary substitution over normalization by reducibility is that the proof method is substantially less intricate, which… (More)

- Harley D. Eades, Aaron Stump, Ryan McCleeary
- Logical Methods in Computer Science
- 2016

We propose a new bi-intuitionistic type theory called Dualized Type The-<lb>ory (DTT). It is a simple type theory with perfect intuitionistic duality, and corresponds<lb>to a single-sided polarized sequent calculus. We prove DTT strongly normalizing, and<lb>prove type preservation. DTT is based on a new propositional bi-intuitionistic logic… (More)

- Aaron Stump, Andrew Reynolds, +4 authors Ruoyu Zhang
- 2012

This paper presents work in progress on a new version, for public release, of the Logical Framework with Side Conditions (LFSC), previously proposed as a proof meta-format for SMT solvers and other proof-producing systems. The paper reviews the type-theoretic approach of LFSC, presents a new input syntax which hides the type-theoretic details for better… (More)

- Harley D. Eades, Aaron Stump
- COS
- 2013

Hereditary substitution is a form of type-bounded iterated substitution, first made explicit by Watkins et al. and Adams in order to show normalization of proof terms for various constructive logics. This paper is the first to apply hereditary substitution to show normalization of a type theory corresponding to a non-constructive logic, namely the… (More)

We propose a new bi-intuitionistic type theory called Dualized Type Theory (DTT). It is a type theory with perfect intuitionistic duality, and corresponds to a single-sided polarized sequent calculus. We prove DTT strongly normalizing, and prove type preservation. DTT is based on a new propositional bi-intuitionistic logic called Dualized Intuitionistic… (More)

This paper proposes a new syntax and proof system called Dualized Intuitionistic Logic (DIL), for intuitionistic propositional logic with the subtraction operator. Our goal is a conservative extension of standard propositional intuitionistic logic with perfect duality (symmetry) between positive and negative connectives. The proof system should satisfy the… (More)

We introduce the use of formal languages in place of zerodivisor graphs used to study theoretic properties of commutative rings. We show that a regular language called a graph language can be constructed from the set of zero-divisors of a commutative ring. We then prove that graph languages are equivalent to their associated graphs. We go on to define… (More)

- Harley Eades, Aaron Stump
- 2013

Hereditary substitution is a form of type-bounded iterated substitution, first made explicit by Watkins et al. and Adams in order to show normalization of proof terms for various constructive logics. This paper is the first to apply hereditary substitution to show normalization of a type theory corresponding to a non-constructive logic, namely the λ… (More)

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