Bisimulation through probabilistic testing
Information and Computation
Algebra of programming
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
FUNCTIONAL PEARLS: Probabilistic functional programming in Haskell
Journal of Functional Programming
Bisimulation relations for weighted automata
Theoretical Computer Science
Matrices as arrows!: a biproduct approach to typed linear algebra
MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
Relational Mathematics
Formal Aspects of Computing
Just do it: simple monadic equational reasoning
Proceedings of the 16th ACM SIGPLAN international conference on Functional programming
A coalgebraic perspective on linear weighted automata
Information and Computation
Exercises in quantifier manipulation
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Towards linear algebras of components
FACS'10 Proceedings of the 7th international conference on Formal Aspects of Component Software
Towards a linear algebra of programming
Formal Aspects of Computing - Celebrating the 60th Birthday of Carroll Morgan
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There is a need for a language able to reconcile the recent upsurge of interest in quantitative methods in the software sciences with logic and set theory that have been used for so many years in capturing the qualitative aspects of the same body of knowledge. Such a lingua franca should be typed, polymorphic, diagrammatic, calculational and easy to blend with traditional notation. This paper puts forward typed linear algebra (LA) as a candidate notation for such a role. Typed LA emerges from regarding matrices as morphisms of suitable categories whereby traditional linear algebra is equipped with a type system. In this paper we show typed LA at work in describing weighted (probabilistic) automata. Some attention is paid to the interface between the index-free language of matrix combinators and the corresponding index-wise notation, so as to blend with traditional set theoretic notation.