Laws for Folds and Theorems for Free by David Laing
The laws associated with typeclasses are often expressing information that the type system cannot. There are also many laws that come directly from the types of various functions.
We'll look at the fold fusion law, which we'll derive, and the laws that arise from it. This talk will cover those laws and an example of using them to transform a small program to improve the performance of a program while preserving the semantics.
We'll also look at natural transformations, which describe relationships between functors, and "free theorems", which can be derived solely from the types of polymorphic functions.
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