Introduction to higher order categorical logic
Introduction to higher order categorical logic
Computational lambda-calculus and monads
Proceedings of the Fourth Annual Symposium on Logic in computer science
The semantics of second-order lambda calculus
Information and Computation
Notions of computation and monads
Information and Computation
The essence of functional programming
POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Imperative functional programming
POPL '93 Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Handbook of logic in computer science (vol. 2)
Monad transformers and modular interpreters
POPL '95 Proceedings of the 22nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Category theory for computing science, 2nd ed.
Category theory for computing science, 2nd ed.
Science of Computer Programming - Special issue on mathematics of program construction
Composing monads using coproducts
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
Modular Denotational Semantics for Compiler Construction
ESOP '96 Proceedings of the 6th European Symposium on Programming Languages and Systems
Notions of Computation Determine Monads
FoSSaCS '02 Proceedings of the 5th International Conference on Foundations of Software Science and Computation Structures
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
Natural Deduction for Intuitionistic Non-communicative Linear Logic
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Mathematical Structures in Computer Science
Implementing collection classes with monads
Mathematical Structures in Computer Science
Premonoidal categories and notions of computation
Mathematical Structures in Computer Science
Combining effects: sum and tensor
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
On the construction of free algebras for equational systems
Theoretical Computer Science
ESOP '09 Proceedings of the 18th European Symposium on Programming Languages and Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
ESOP '09 Proceedings of the 18th European Symposium on Programming Languages and Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
Arrows, like Monads, are Monoids
Electronic Notes in Theoretical Computer Science (ENTCS)
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
What is a Categorical Model of Arrows?
Electronic Notes in Theoretical Computer Science (ENTCS)
Monatron: an extensible monad transformer library
IFL'08 Proceedings of the 20th international conference on Implementation and application of functional languages
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
Extensible effects: an alternative to monad transformers
Proceedings of the 2013 ACM SIGPLAN symposium on Haskell
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The incremental approach to modular monadic semantics constructs complex monads by using monad transformers to add computational features to a pre-existing monad. A complication of this approach is that the operations associated to the pre-existing monad need to be lifted to the new monad. In a companion paper by Jaskelioff, the lifting problem has been addressed in the setting of system F@w. Here, we recast and extend those results in a category-theoretic setting. We abstract and generalize from monads to monoids (in a monoidal category), and from monad transformers to monoid transformers. The generalization brings more simplicity and clarity, and opens the way for lifting of operations with applicability beyond monads.