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tomasp.net | ||
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ncatlab.org
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| | | | | [AI summary] The nLab entry explores philosophical aspects of mathematics, including metaphysics, foundational issues, and historical paradigms, with references to key thinkers and texts. | |
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existentialtype.wordpress.com
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| | | | | The Christian doctrine of trinitarianism states that there is one God that is manifest in three persons, the Father, the Son, and the Holy Spirit, who together form the Holy Trinity. The doctrine of computational trinitarianism holds that computation manifests itself in three forms: proofs of propositions, programs of a type, and mappings between... | |
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www.jeremykun.com
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| | | | | Perhaps primarily due to the prominence of monads in the Haskell programming language, programmers are often curious about category theory. Proponents of Haskell and other functional languages can put category-theoretic concepts on a pedestal or in a mexican restaurant, and their benefits can seem as mysterious as they are magical. For instance, the most common use of a monad in Haskell is to simulate the mutation of immutable data. Others include suspending and backtracking computations, and even untying tangled rope. | |
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www.jeremykun.com
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| | | Decidability Versus Efficiency In the early days of computing theory, the important questions were primarily about decidability. What sorts of problems are beyond the power of a Turing machine to solve? As we saw in our last primer on Turing machines, the halting problem is such an example: it can never be solved a finite amount of time by a Turing machine. However, more recently (in the past half-century) the focus of computing theory has shifted away from possibility in favor of determining feasibility. | ||
