Proceedings of a tutorial and workshop on Category theory and computer programming
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
A Complete Axiom System for Isomorphism of Types in Closed Categories
LPAR '93 Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning
A Higher-Order Calculus for Categories
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Categorical Fixed Point Calculus
CTCS '95 Proceedings of the 6th International Conference on Category Theory and Computer Science
Isomorphisms of generic recursive polynomial types
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A short survey of isomorphisms of types
Mathematical Structures in Computer Science
Parametric datatype-genericity
Proceedings of the 2009 ACM SIGPLAN workshop on Generic programming
Sorting with bialgebras and distributive laws
Proceedings of the 8th ACM SIGPLAN workshop on Generic programming
Kan extensions for program optimisation or: art and dan explain an old trick
MPC'12 Proceedings of the 11th international conference on Mathematics of Program Construction
Generic programming with adjunctions
SSGIP'10 Proceedings of the 2010 international spring school conference on Generic and Indexed Programming
Adjoint folds and unfolds-An extended study
Science of Computer Programming
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When are two types the same? In this paper we argue that isomorphism is a more useful notion than equality. We explain a succinct and elegant approach to establishing isomorphisms, with our focus on showing their existence over deriving the witnesses. We use category theory as a framework, but rather than chasing diagrams or arguing with arrows, we present our proofs in a calculational style. In particular, we hope to showcase to the reader why the Yoneda lemma and adjunctions should be in their reasoning toolbox.