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bartoszmilewski.com | ||
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sitr.us
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| | | | | Dependent types provide an unprecedented level of type safety. A quick example is a type-safe printf implementation. They are also useful for theorem proving. According to the Curry-Howard correspondence, mathematical propositions can be represented in a program as types. An implementation that satisfies a given type serves as a proof of the corresponding proposition. In other words, inhabited types represent true propositions. | |
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www.jeremykun.com
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| | | | | Last time we worked through some basic examples of universal properties, specifically singling out quotients, products, and coproducts. There are many many more universal properties that we will mention as we encounter them, but there is one crucial topic in category theory that we have only hinted at: functoriality. As we've repeatedly stressed, the meat of category theory is in the morphisms. One natural question one might ask is, what notion of morphism is there between categories themselves? | |
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ncatlab.org
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blog.bencope.land
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| | | There are a number of ways one might approach designing the logic of a domain problem. Most enterprise software engineers may be accustomed to modeling the problem using object-oriented programming, where classes encapsulate behavior and data. In this approach, the design often reflects the use of various design patterns, such | ||
