Fix to the definitions of min and max#1270
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Why not just define min and max by recursion without any |
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So having |
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They made it like this in #1262 for efficiency, because the |
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Also, I think this is precisely the advantage of using |
anshwad10
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Nov 12, 2025
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Ah right, I had forgotten about that. I wonder how much one should worry about efficiency for functions on unary nat though... If we want things to be fast we should at least have a binary representation? |
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I don't know if that would help; It wouldn't be better in terms of storage at least, because Agda compiles Nat to built in arbitrary-precision binary integers, and idt it would speed up arithmetic because the builtin operations are O(1) while binary arithmetic is O(logN) |
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@mortberg this is part of work to enable fast operations on Integers -> Rationals -> and finaly beeing able to quickly calculatate things like Nth digit of |
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@mortberg I realized that I haven't actively participated in the discussion so far, which may have unintentionally given the impression that this PR is not yet ready to be merged. Anyway, those changes have already been merged previously. In this PR, I am only adding an additional In my view, the one remaining aspect that might need review is the new comment above the definition of |
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* Resolve naming inconsistency between Iso and Category.isIso (agda#1274) s/leftInv/ret; s/rightInv/sec --------- Co-authored-by: Madeleine Sydney Ślaga <msyds@deertopia.net> * isIso name change fix (agda#1281) * Update fin (agda#1279) * Exchange Fin in Cubical.Data.Fin for the deifinition from Cubical.Data.Fin.Inductive. WIP * Fixed finj, predFin, inject<, flast, ¬Fin0 to work with new definition of Fin. * Minor changes * Fix sumFinGen * fix any? * Everything type checks now. Important changes: - Implicit argument added to toN - Implicit arguments in toN-injective slightly changed - Argument changed from implicit to explicit in elim * some formatting * change ¬Fin0 * remove comments * Add <ᵗ-asym * make properties type check * Remove dependencies on Cubical.Data.Fin.Inductive.Base * Things that work * Properties type check * more working files * factorEquiv * comment fix * LehmerCode type checks * SumFin.Base type checks * some cleanup and Axiom.Choice type checks not reliant on old Fin * Remove dependence on Fin.Inductive * Remove dependence on Fin.Inductive * Remove dependency on Fin.Infuctive * Remove dependency on Fin.Inductive * Remove dependencies on Fin.Inductive * type check * fix FinSet * _<ᵗ_ is well founded * type checks with new Fin * Everything builds * Move everything from Fin.Inductive.Properties to Fin.Properties and remove Fin.Inductive, Fin.Inductive.Base, Fin.Inductive.Properties * some cleanup * more cleanup * fix trailing whitespaces * files end with newline --------- Co-authored-by: croos <76143n@gmail.com> * fix defintions of `min` and `max`, add comment on limitations of `UsingEq` (agda#1270) * Change implementation of Inductive Order on Nat (agda#1283) * use boolean comparison in `Nat.Order.Inductive`, add non-strict and flipped inductive order, make faster instance search in `Fin.Literals` * fix typo * Place holder for paper (agda#1286) * placeholder * whitespae * Cellpaper2 (agda#1287) * placeholder * whitespae * form * fix imports: `Fin.Inductive.Base/Properties` → `Fin.Base/Properties` --------- Co-authored-by: Madeleine Sydney Ślaga <65362461+msyds@users.noreply.github.com> Co-authored-by: Madeleine Sydney Ślaga <msyds@deertopia.net> Co-authored-by: Max S. New <maxsnew@gmail.com> Co-authored-by: Caroline Roos <croos.math@gmail.com> Co-authored-by: croos <76143n@gmail.com> Co-authored-by: Axel Ljungström <49276137+aljungstrom@users.noreply.github.com>
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* Fast int properties with pl and ocr instances (#23) * add fast implementation of integers and their properties * move properties of min and max over `ℕ` to the appropriate file * reorganize and format code * remove `--safe` flag * remove `--safe` flag * Fast int (#2) * direct solver application * direct solver application --------- Co-authored-by: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> * add fast implementation of integers and their properties * move properties of min and max over `ℕ` to the appropriate file * reorganize and format code * remove `--safe` flag * remove `--safe` flag * remove `--safe` flag * Fast int (#2) * direct solver application * direct solver application --------- Co-authored-by: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> * fix compatibility with the library * fix compatibility after rebase, start proving properties of fast integer min and max * add instances of `Nat` and `Int` as `Pseudolattice`, and of `Int` as `OrderedCommRing` * fix typo, add better make from Posets to Pseudolattices * update `makePseudolatticeFromPoset` and instances built using it * move `maxLUB` and `minGLB` to `Data.Nat.Order`, remove unnecessary imports * rewrite properties from `minAssoc` to `-max`, add temporary lemmas in `Nat`, add `UsingEq` into `min` and `max` over the Naturals * fix naming clash on import * rewrite properties from `pos+posLposMin` to `·DistNegsucLMax` * start work on Order: adapt properties from `isProp≤` to `≤SumLeftPos`, add boolean order, suggest alternative definition `_≤'_` * use more efficient implementation of quotient and remainder in `Int.Fast.Divisibility` * adapt properties from `pred-≤-pred` to `0≤o→≤-·o`, move import of `Bool.Base` together with the other imports * adapt properties from `<-·o` to `predℤ-≤-predℤ` * adapt properties from `¬m+posk<m` to `<-+pos-trans` * adapt properties from `<-pos+-trans` to `0<o→≤-·o-cancel` * adapt properties from `≤-o·-cancel` to `≤→min` ; add conversions between the order over the integers and the one over the naturals ; add `maxLUB`, `minGLB` , `≤→max` , `≤→min` to `Data.Nat.Order` * adapt properties from `≤MonotoneMin` to `_≟'_` ; add faster `_≟_` and tests. This finishes (a first but complete version) of `Data.Int.Fast` * edit `_≤'_` using recursive order, add `_≤ᵇ_` and `_≤''_` * update `minIdem` * clean comments, reorganize `Fast` modules, add more properties in `Int.Fast.Order`, add `Trichotomy` and `Ordering` in `BinaryRelation` * add fixity for `_≤_` in `PseudolatticeStr`, add `Properties` file * edit Fast using PL and OCR instances * remove `minIdem`, use PL instance of `Nat` in the `Int.Fast.Order` module * simplify some proofs, with additional converions between the order on Nat and the integer order between negsuc * Add order related instances of `Fast.Int` * revert addition of `Trichotomy` to `BinaryRelation`, add more tests to `Int.Fast.Order` * add missing `'` on commented test code * adapt instances of `Int` and `Int.Fast` as `OCR`, to the branch `ocr+pl-instances'` --------- Co-authored-by: Ettore Forigo <ettore.forigo@gmail.com> Co-authored-by: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> * edit `zero-≤pos`, using an easier proof, add `zero-<possuc` * remove `Int.Fast.Order` and related instances ; merge properties of Pseudolattices and simplify some proofs about min/max in `Int.Fast.Properties` * move `Fast` Integer files to `Fast` folder, and similarly for the algebraic instances * rename the algebraic instances of fast integers * another rename * fix imports, remove unnecessary code in `Pseudolattice.Properties` * remove `Ordering` data type (I'll leave it for the PR with fast integer order) * rebase and fix imports related to `Fin` (#33) * Resolve naming inconsistency between Iso and Category.isIso (#1274) s/leftInv/ret; s/rightInv/sec --------- Co-authored-by: Madeleine Sydney Ślaga <msyds@deertopia.net> * isIso name change fix (#1281) * Update fin (#1279) * Exchange Fin in Cubical.Data.Fin for the deifinition from Cubical.Data.Fin.Inductive. WIP * Fixed finj, predFin, inject<, flast, ¬Fin0 to work with new definition of Fin. * Minor changes * Fix sumFinGen * fix any? * Everything type checks now. Important changes: - Implicit argument added to toN - Implicit arguments in toN-injective slightly changed - Argument changed from implicit to explicit in elim * some formatting * change ¬Fin0 * remove comments * Add <ᵗ-asym * make properties type check * Remove dependencies on Cubical.Data.Fin.Inductive.Base * Things that work * Properties type check * more working files * factorEquiv * comment fix * LehmerCode type checks * SumFin.Base type checks * some cleanup and Axiom.Choice type checks not reliant on old Fin * Remove dependence on Fin.Inductive * Remove dependence on Fin.Inductive * Remove dependency on Fin.Infuctive * Remove dependency on Fin.Inductive * Remove dependencies on Fin.Inductive * type check * fix FinSet * _<ᵗ_ is well founded * type checks with new Fin * Everything builds * Move everything from Fin.Inductive.Properties to Fin.Properties and remove Fin.Inductive, Fin.Inductive.Base, Fin.Inductive.Properties * some cleanup * more cleanup * fix trailing whitespaces * files end with newline --------- Co-authored-by: croos <76143n@gmail.com> * fix defintions of `min` and `max`, add comment on limitations of `UsingEq` (#1270) * Change implementation of Inductive Order on Nat (#1283) * use boolean comparison in `Nat.Order.Inductive`, add non-strict and flipped inductive order, make faster instance search in `Fin.Literals` * fix typo * Place holder for paper (#1286) * placeholder * whitespae * Cellpaper2 (#1287) * placeholder * whitespae * form * fix imports: `Fin.Inductive.Base/Properties` → `Fin.Base/Properties` --------- Co-authored-by: Madeleine Sydney Ślaga <65362461+msyds@users.noreply.github.com> Co-authored-by: Madeleine Sydney Ślaga <msyds@deertopia.net> Co-authored-by: Max S. New <maxsnew@gmail.com> Co-authored-by: Caroline Roos <croos.math@gmail.com> Co-authored-by: croos <76143n@gmail.com> Co-authored-by: Axel Ljungström <49276137+aljungstrom@users.noreply.github.com> * add `Fast` integer order and the related instaces * fix conflicts --------- Co-authored-by: Ettore Forigo <ettore.forigo@gmail.com> Co-authored-by: Marcin Jan Turek-Grzybowski <marcinjangrzybowski@gmail.com> Co-authored-by: Madeleine Sydney Ślaga <65362461+msyds@users.noreply.github.com> Co-authored-by: Madeleine Sydney Ślaga <msyds@deertopia.net> Co-authored-by: Max S. New <maxsnew@gmail.com> Co-authored-by: Caroline Roos <croos.math@gmail.com> Co-authored-by: croos <76143n@gmail.com> Co-authored-by: Axel Ljungström <49276137+aljungstrom@users.noreply.github.com>
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While working on a future PR, I noticed that when performing a "with-abstraction with
UsingEq" onn <ᵇ m, each case was not normalizing to the expected term.This issue is resolved by adding
UsingEqinto the definitions ofminandmax. Interestingly, all proofs that relied on "with-abstraction withotUsingEq" still works unchanged.I added a comment about this limitation above the definition of
UsingEq, but I'm not entirely sure how clear it is, so I also referenced its use inminandmaxover ℕ.Please let me know if there is a clearer way to explain this behavior.