An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
Unification under a mixed prefix
Journal of Symbolic Computation
Higher order unification via explicit substitutions
Information and Computation
On the algebraic models of Lambda calculus
Theoretical Computer Science - Modern algebra and its applications
Birkhoff's HSP-Theorem for Cumulative Logic Programs
ELP '93 Proceedings of the 4th International Workshop on Extensions of Logic Programming
Theoretical Computer Science
The Lattice of Lambda Theories
Journal of Logic and Computation
Information and Computation
Journal of Logic and Computation
Nominal Algebra and the HSP Theorem
Journal of Logic and Computation
A formal calculus for informal equality with binding
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Applying Universal Algebra to Lambda Calculus*
Journal of Logic and Computation
A Nominal Axiomatization of the Lambda Calculus
Journal of Logic and Computation
Curry-Howard for incomplete first-order logic derivations using one-and-a-half level terms
Information and Computation
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Permissive-nominal logic: First-order logic over nominal terms and sets
ACM Transactions on Computational Logic (TOCL)
PNL to HOL: From the logic of nominal sets to the logic of higher-order functions
Theoretical Computer Science
Hi-index | 0.00 |
This paper develops the correspondence between equality reasoning with axioms using λ-terms syntax, and reasoning using nominal terms syntax. Both syntaxes involve name-abstraction: λ-terms represent functional abstraction; nominal terms represent atomsabstraction in nominal sets. It is not evident how to relate the two syntaxes because their intended denotations are so different. We use universal algebra, the logic of equational reasoning, a logical foundation based on an equality judgement form which is spartan but which is sufficiently expressive to encode mathematics in theory and practice. We investigate how syntax, algebraic theories, and derivability relate across λ-theories (algebra over λ-terms) and nominal algebra theories.