sarahzrf

@sarah_zrf

computational trinitarian, but only read Church on easter and christmas. in my edgy commie college student phase. she. neuroatypical/white/trans

maine
Vrijeme pridruživanja: studeni 2010.

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  1. Prikvačeni tweet
    25. srp 2017.

    stuff next to my bed: - pill bottles - fidget spinner - copy of Capital vol 1 - copy of Topoi: The Categorial Analysis of Logic - duct tape

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  2. 1. velj

    oh whoops actually just john baez's account but a post written by and

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  3. 1. velj
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  4. 1. velj

    here's what ▷ does

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  5. 1. velj

    i really didn't think anything ray sipe did could surprise me at this point but

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  6. 1. velj

    wait fuck i think it's actually like this

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  7. 1. velj

    one stray thought: if we only use the address ranges as the underlying p.c.m. instead of heaps w/ contents included, then maybe we get a semantics for a pure language which captures part of the notion that the runtime can update in place if the program is linear 🤔

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  8. 1. velj

    which sounds like a pretty good notion of "separating product" to me! just not sure how to handle mutation yet :)

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  9. 1. velj

    the action of the functor on morphisms is just inclusions. then an element of (A ⊗ B)(h) works out to be a pair of a contiguous region in h storing ints and a tree in h, such that none of the locations involved in the tree are the same as the contiguous region!

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  10. 1. velj

    so for example, maybe R is a p.c.m. of heaps w/ the extension/divisibility ordering, A could be integer arrays, B could be trees. given a heap h, A(h) is the set of contiguous regions in h storing integers, B(h) is similar in spirit but more complicated.

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  11. 1. velj

    the quotient is that if y_1 ≤ y_1' and y_2 ≤ y_2', with y_1, y_2 and y_1', y_2' both pairs as above, then an A(y_1) × B(y_2) pair is identified with its A(y_1') × B(y_2') weakening as an element of (A ⊗ B)(y).

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  12. 1. velj

    so, up to a quotient, a y-owning value of A ⊗ B is a pair of a y_1-owning A and a y_2-owning B, such that y_1 ⊗ y_2 is defined and ≤ y.

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  13. 1. velj

    now say A, B in PSh(R^op). we can take a "separating product" of A and B, the day convolution. writing ⊗_R for the promonoidal product, (A ⊗ B)(y) = ∫^{y_1, y_2} (y_1 ⊗_R y_2)(y) × A(y_1) × B(y_2)

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  14. 1. velj

    if we have x ≤ y, then we can go F(x) → F(y)—we can weaken our bound on what a given value owns. this lines up well with the fact that having nontrivial inequalities in an ordered p.c.m. can cause the resulting separation logic to be affine, whereas discrete order = linear

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  15. 1. velj

    say F is an object of PSh(R^op). let's think of it as semantics for a type. given x in R, we'll think of F(x) as the set of values of type F which own x, or at least for which x is an upper bound (in R's ordering) on their resource footprint.

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  16. 1. velj

    yes, I think it might be! say R is a preordered p.c.m. of "resources". the p.c.m. structure furnishes a promonoidal structure. take PSh(R^op); we can set ⊗ and ⊸ to be day convolution and its adjoint.

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  17. 1. velj
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  18. 31. sij

    fun 2 work out why they call PSh(N) the "topos of trees" (with N a thin category under its usual ordering)

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  19. 31. sij

    john baez posts to the ncatlab about optics, its a sign that my time is about to come 😈

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  20. proslijedio/la je Tweet

    Like I always say, regret narratives are popular because they're emotionally resonant with cis people - because they think *they* would regret it - because they would - because they are cis.

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  21. proslijedio/la je Tweet
    31. sij

    12 oz Gum (episode: varmints)

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