Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Institutions: abstract model theory for specification and programming
Journal of the ACM (JACM)
Proof, language, and interaction
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
Higher-Order Superposition for Dependent Types
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
On the Interpretation of Type Theory in Locally Cartesian Closed Categories
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Automated Theorem Proving in a Simple Meta-Logic for LF
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Handbook of automated reasoning
The design and implementation of VAMPIRE
AI Communications - CASC
Institution-independent Model Theory
Institution-independent Model Theory
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
TYPES'07 Proceedings of the 2007 international conference on Types for proofs and programs
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We present DFOL, an extension of classical first-order logic with dependent types, i.e., as in Martin-Löf type theory, signatures may contain type-valued function symbols. A model theory for the logic is given that stays close to the established first-order model theory. The logic is presented as an institution, and the logical framework LF is used to define signatures, terms and formulas. We show that free models over Horn theories exist, which facilitates its use as an algebraic specification language, and show that the classical first-order axiomatization is complete for DFOL, too, which implies that existing first-order theorem provers can be extended. In particular, the axiomatization can be encoded in LF.