Top new questions this week:
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This is somewhat conceptual beginner’s question about proof assistants. I’ve been re-reading the famous Seven Trees in One / Objects of categories as complex numbers. The gist: The type $T$ of binary …
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This is a 3rd in a series of questions, spurred by my attempts to encode an argument by Danielsson [1] [2] regarding existence of syntactically non-strictly positive datatype. The idea (rephrased): …
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So, obviously for a term $t$ of type $T$, I would represent it as: T +———–+ | | | t | | | +———–+ That is a node …
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By HOL I mean something like inference rules of HOL Light with the 3 axioms of infinity, extensionality and choice ($\varepsilon$ operator). By predicative dependent types, I am thinking of MLTT + W-…
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I’m wondering how much overlap (read: code-reusage) there is between a PA and an ATP system. Are they based upon the same type system at least? I’m wondering, because right now I’m working on …
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Greatest hits from previous weeks:
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I keep seeing these phrasing in some proof assistants/elaborators and their issues/internal discussions (e.g. Github search results in cooltt), that seems not that related to the actual proofs/…
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I’ve started to play with mechanizing some set theory stuff. I’m not sure if I want a constructive flavor or not yet. Anyhow you can do stuff like axiomize the empty set $$ \top \vdash \exists P. \…
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Coq’s built-in termination checker accepts some rather intricate recursion patterns with functional values in data types, as shown by this example …
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For a project I’m planning on doing with some students this summer, I’m looking for an implementation of normalization-by-evaluation whose code the students can read, understand, and extend. So I’d …
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What is a good starting point to learn about proof assistants? The answer will invariably depend on the area of interest: mathematics (and its areas, e.g. algebra,combinatorics, analysis, logic), CS – …
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Type systems, and the proof assistants based on them, are frequently divided into predicative and impredicative. What exactly does this mean? I’ve heard the slogan “impredicativity means you can’…
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A type that is a member of a universe can be coerced into a higher universe. Is that coercion injective? That is, if two elements of U1 are equal after being coerced to U2, does that imply they are …
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