Daniel Licata | Carnegie Mellon University (original) (raw)

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Papers by Daniel Licata

Research paper thumbnail of AGRAWAL, Mukesh CMU-CS-11-101 AKELLA, Aditya CMU-CS-11-100, CMU-CS-11-117

Research paper thumbnail of Calculating the Fundamental Group of the Circle in Homotopy Type Theory

Abstract: Recent work on homotopy type theory exploits an exciting new correspondence between Mar... more Abstract: Recent work on homotopy type theory exploits an exciting new correspondence between Martin-Lof's dependent type theory and the mathematical disciplines of category theory and homotopy theory. The category theory and homotopy theory suggest new principles to add to type theory, and type theory can be used in novel ways to formalize these areas of mathematics. In this paper, we formalize a basic result in algebraic topology, that the fundamental group of the circle is the integers.

Research paper thumbnail of Proving Meta-theorems with Twelf

Research paper thumbnail of Mechanizing Language Definitions (Draft of April 17, 2006)

Research paper thumbnail of Mechanizing a Decision Procedure for Coproduct Equality

Research paper thumbnail of Focusing on Computation with Binding

Research paper thumbnail of 2-Dimensional Directed Dependent Type Theory

Research paper thumbnail of The Impact of Background Network Traffic on Foreground Network Traffic

Research paper thumbnail of A Pronominal Approach to Binding and Computation

Typed Lambda Calculi and …, Jan 1, 2009

There has been a great deal of research on programming languages for computing with binding and s... more There has been a great deal of research on programming languages for computing with binding and scope (bound variables, ��-equivalence, capture-avoiding substitution). These languages are useful for a variety of tasks, such as implementing domain-specific languages and formalizing the metatheory of programming languages. Functional programming with binding and scope involves two different notions of function: functions-as-data and functions-as-computation. Functions-as-data, used to represent abstract syntax with variable ...

Research paper thumbnail of Foundations and Applications of Higher-Dimensional Directed Type Theory

Research paper thumbnail of Canonicity for 2-dimensional type theory

Research paper thumbnail of 2-Dimensional Directed Type Theory

Research paper thumbnail of A simple module system for Twelf

Research paper thumbnail of The Cult of the Bound Variable: The 9th Annual ICFP Programming Contest

… of Computer Science, …, Jan 1, 2006

Research paper thumbnail of Mechanizing metatheory in a logical framework. Submitted for publication

Research paper thumbnail of Positively dependent types

Proceedings of the 3rd workshop on …, Jan 1, 2009

Research paper thumbnail of A monadic formalization of ML5

Arxiv preprint arXiv:1009.2793, Jan 1, 2010

Research paper thumbnail of Mechanizing language definitions

Submitted for publication, Jan 1, 2006

Research paper thumbnail of Dependently typed programming with domain-specific logics

Draft available from http://www. cs. cmu. edu/drl, Jan 1, 2008

Research paper thumbnail of An extensible theory of indexed types

Submitted to POPL, Jan 1, 2008

Research paper thumbnail of AGRAWAL, Mukesh CMU-CS-11-101 AKELLA, Aditya CMU-CS-11-100, CMU-CS-11-117

Research paper thumbnail of Calculating the Fundamental Group of the Circle in Homotopy Type Theory

Abstract: Recent work on homotopy type theory exploits an exciting new correspondence between Mar... more Abstract: Recent work on homotopy type theory exploits an exciting new correspondence between Martin-Lof's dependent type theory and the mathematical disciplines of category theory and homotopy theory. The category theory and homotopy theory suggest new principles to add to type theory, and type theory can be used in novel ways to formalize these areas of mathematics. In this paper, we formalize a basic result in algebraic topology, that the fundamental group of the circle is the integers.

Research paper thumbnail of Proving Meta-theorems with Twelf

Research paper thumbnail of Mechanizing Language Definitions (Draft of April 17, 2006)

Research paper thumbnail of Mechanizing a Decision Procedure for Coproduct Equality

Research paper thumbnail of Focusing on Computation with Binding

Research paper thumbnail of 2-Dimensional Directed Dependent Type Theory

Research paper thumbnail of The Impact of Background Network Traffic on Foreground Network Traffic

Research paper thumbnail of A Pronominal Approach to Binding and Computation

Typed Lambda Calculi and …, Jan 1, 2009

There has been a great deal of research on programming languages for computing with binding and s... more There has been a great deal of research on programming languages for computing with binding and scope (bound variables, ��-equivalence, capture-avoiding substitution). These languages are useful for a variety of tasks, such as implementing domain-specific languages and formalizing the metatheory of programming languages. Functional programming with binding and scope involves two different notions of function: functions-as-data and functions-as-computation. Functions-as-data, used to represent abstract syntax with variable ...

Research paper thumbnail of Foundations and Applications of Higher-Dimensional Directed Type Theory

Research paper thumbnail of Canonicity for 2-dimensional type theory

Research paper thumbnail of 2-Dimensional Directed Type Theory

Research paper thumbnail of A simple module system for Twelf

Research paper thumbnail of The Cult of the Bound Variable: The 9th Annual ICFP Programming Contest

… of Computer Science, …, Jan 1, 2006

Research paper thumbnail of Mechanizing metatheory in a logical framework. Submitted for publication

Research paper thumbnail of Positively dependent types

Proceedings of the 3rd workshop on …, Jan 1, 2009

Research paper thumbnail of A monadic formalization of ML5

Arxiv preprint arXiv:1009.2793, Jan 1, 2010

Research paper thumbnail of Mechanizing language definitions

Submitted for publication, Jan 1, 2006

Research paper thumbnail of Dependently typed programming with domain-specific logics

Draft available from http://www. cs. cmu. edu/drl, Jan 1, 2008

Research paper thumbnail of An extensible theory of indexed types

Submitted to POPL, Jan 1, 2008

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