Monads are often presented as a tool to describe computations as _sequences_ of steps (instructions, commands, effects, ...). Some even say that monads are the _essence_ of sequencing. On one hand, it's easy to see why monads are often associated with sequencing: In a strictly evaluated language like Scala, an expression must be fully evaluated before it can be mapped and/or flattened. In Haskell, an otherwise lazy language, the special IO monad enforces sequential evaluation of effects. In both Scala and Haskell, there is syntactic support (monad/for comprehensions) for the "sequence of steps" style. On the other hand, the mathematical definition of a monad says nothing about sequencing. Indeed, Haskell's laziness already allows—for the case of pure, deterministic computations—flatMapping without (fully) evaluating the input.

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In this talk, Tomas will go further and show examples of lawful monads in a concurrent, effectful, and non-deterministic setting. Specifically, attendees will see that the monad laws do not necessitate sequential execution, ordering of effects, or even determinism. The examples will come from Libretto, a Scala DSL for declarative concurrency, where causal dependence is the only form of sequencing.