Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
A framework for defining logics
Journal of the ACM (JACM)
The TH ∃ OREM ∀ project: a progress report
Symbolic computation and automated reasoning
Theory of Judgments and Derivations
Progress in Discovery Science, Final Report of the Japanese Discovery Science Project
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
On equivalence and canonical forms in the LF type theory
ACM Transactions on Computational Logic (TOCL)
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
A simple theory of expressions, judgments and derivations
ASIAN'04 Proceedings of the 9th Asian Computing Science conference on Advances in Computer Science: dedicated to Jean-Louis Lassez on the Occasion of His 5th Cycle Birthday
External and internal syntax of the λ-calculus
Journal of Symbolic Computation
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We propose a logical framework, called Natural Framework (NF), which supports formal reasoning about computation and logic (CAL) on a computer. NF is based on a theory of Judgments and Derivations. NF is designed by observing how working mathematical theories are created and developed. Our observation is that the notions of judgments and derivations are the two fundamental notions used in any mathematical activity. We have therefore developed a theory of judgments and derivations and designed a framework in which the theory provides a uniform and common play ground on which various mathematical theories can be defined as derivation games and can be played, namely, can write and check proofs. NF is equipped with a higher-order intuitionistic logic and derivations (proofs) are described following Gentzen's natural deduction style. NF is part of an interactive computer environment CAL and it is also referred to as NF/CAL. CAL is written in Emacs Lisp and it is run within a special buffer of the Emacs editor. CAL consists of user interface, a general purpose parser and a checker for checking proofs of NF derivation games. NF/CAL system has been successfully used as an education system for teaching CAL for undergraduate students for about 8 years. We will give an overview of the NF/CAL system both from theoretical and practical sides.