From : "1337777.OOO" <1337777.ooo AT gmail.com>

: "1337777.OOO" <1337777.ooo AT gmail.com> To : nipkow AT in.tum.de, fom AT cs.nyu.edu, cl-isabelle-users AT lists.cam.ac.uk, coq-club AT inria.fr, SF-LIT AT listserv.loc.gov, categories AT mta.ca

: nipkow AT in.tum.de, fom AT cs.nyu.edu, cl-isabelle-users AT lists.cam.ac.uk, coq-club AT inria.fr, SF-LIT AT listserv.loc.gov, categories AT mta.ca Subject : Re: [Coq-Club] [isabelle] New AFP entry: Monoidal Categories

: Re: [Coq-Club] [isabelle] New AFP entry: Monoidal Categories Date : Fri, 9 Mar 2018 20:37:28 +0800

: Fri, 9 Mar 2018 20:37:28 +0800 Authentication-results : mail2-smtp-roc.national.inria.fr; spf=None smtp.pra=1337777.ooo AT gmail.com; spf=Pass smtp.mailfrom=1337777.ooo AT gmail.com; spf=None smtp.helo=postmaster AT mail-ot0-f195.google.com

: mail2-smtp-roc.national.inria.fr; spf=None smtp.pra=1337777.ooo AT gmail.com; spf=Pass smtp.mailfrom=1337777.ooo AT gmail.com; spf=None smtp.helo=postmaster AT mail-ot0-f195.google.com Ironport-phdr: 9a23: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

Re: [Coq-Club] [isabelle] New AFP entry: Monoidal Categories, 1337777.OOO, 03/09/2018

Prophsolves how 1337777 mom associativity pentagon is some recursive square(reflective-functorial associativity-bracket-eliminationcut-elimination resolution)The only thing to remember : this grammaticalassociativity-bracket-elimination cut-elimination resolution andconfluence technique is the foundation of polymorph mathematics ...What is the metalogic for polymorphism ? ( "HOL vs COQ" )HOL has its own metalogic which is parallel-search ( "sequent/natural", using unlimited-outer-nesting-of-metaconsequences as questioned byKubota ) deduction with unification of metavariables . Therefore HOLmay erase logical-properties from progamming and instead deleguate ,to some ad-hoc particular "object-logic" , the task of automaticinferences involved during programming-under-logical-context . Forexample , definite/indefinite descriptions or how to simulate implicitparameters in the polymorphism object-logic :( wellIndexed f A B ==> wellIndexed g B C ==> ( CompositionImplicit f g= ( Composition A B f C g :: morphismsDatatype ) ) )COQ unites programs carrying logical-properties via indexed/dependentdatatypes ; the consequence is the semi-automaticinference/unification of implicit/hidden parameters viaexistential/meta-variables . Does this say that dependent-types (beyond its semi-automatic inference/unification algorithms ) is betterfor polymorphism ( "category theory" ) ? NO ... The pretty search intothe ``categorical semantics of (higher-)dependent-types as internallogic'' is for the museum mostly ; the angle of view of polymorphismmathematics is that itself is ( by-definition ... ) some computationallogic .-----Prophsolves half of some question of Cartier which is how to programgrammatical polymorph internal ( "typed" , "small" )pairing-projections ( "product" ) ...The ends is to do polymorph mathematics which is internal/small/typedref some indexer/types (metacategory/topos/modos) ; this infers thatthe objects and morphisms can no longer be touched individually butmany objects shall be touched at the same time via someindexing/dimension/type and many morphisms shall be touched at thesame time via some indexing/dimension/type . And for internalpolymorph mathematics , the common operations on the morphisms arecoordinatewise/dimensional/pointwise ; this contrast fromenriched/multifolded polymorph mathematics where each object istouched individually and many morphisms are touched at the same timeand the common operations on the morphisms are multiplicative .How to describe the two indexes which encode those pair objects andthose pairing-projections morphisms ? Oneself could decode ( "Yoneda") these two index-for-objects and index-for-morphisms as twometafunctors on this indexer/metacategory ; then these twometafunctors may be commonly programmed by twoinductive-families-presentations where the constructors of these twoinductive-families-presentations are the decoding ( "Yoneda" ) asmetatransformations of the whatever-is-interesting arrows betweenthese two index-for-objects and index-for-morphisms .The conversion-relation shall convert across two morphisms whosedomain/codomain-computation arguments are notsyntactically/grammatically-the-same. But oneself does show that, bylogical-deduction, these two domain/codomain-computations are indeedpropositionally equal ( "soundness lemma" ) .Finally, some linear total/asymptotic grade is defined on themorphisms and the tactics-automated degradation lemma shows that eachof the conversion indeed degrades the redex morphism .For instant first impression , the conversion-relation constructorwhich says that the first projection morphism is natural/polyarrowing(commutativity along the arrow-action cut-constructor) , is written as#+BEGIN_EXAMPLE| Project1_arrow : forall (A : obIndexer) (F1 F2 : obCoMod A),forall (Z1 : obCoMod A) (zz1 : 'CoMod(0 F1 ~> Z1 )0),forall (A' : obIndexer) (a : 'Indexer(0 A' ~> A )0),( ~_1 @ (ObCoMod_Poly a F2) o>CoMod (a o>* zz1) )* ( ~_1 @ F2 o>CoMod zz1 ) )#+END_EXAMPLEKEYWORDS : 1337777.OOO ; COQ ; cut-elimination ; internal functors ;internal product ; polymorph metafunctors-grammar ; modosOUTLINE :* Generating data internal some indexer , by decoding the indexes asmetafunctors and the arrows as metatransformations* Grammatical presentation of objects and morphisms internal someindexer , by decoding the indexes as metafunctors and the arrows asmetatransformations** Grammatical presentation of objects** Grammatical presentation of morphisms* Grammatical conversions of morphisms , which infer the samedomain/codomain-computation** Grammatical conversions of morphisms** Same domain/codomain-computation for convertible morphisms** Linear total/asymptotic grade and the degradation lemma* Solution** Solution morphisms without polyarrowing/polymorphism** Destruction of morphisms with inner-instantiation of object-indexes* Polyarrowing/polymorphism/cut-elimination bycomputational/total/asymptotic/reduction/(multi-step) resolution-----Prophsolves half of some question of Cartier which is how to programgrammatical polymorph contextual ( "weighted" ) multifold ( "enriched") pairing-projections ( "product" ) ...The ends is to do polymorph mathematics which is multifolded/enrichedref some indexer (symmetric-associative-monoidalmetalogic/metacategory) ; this infers that the morphisms can no longerbe touched individually but many morphisms shall be touched at thesame time via some indexing/multiplier . And for multifold-enrichedpolymorph mathematics , the common operations on the morphisms aremultifold/multiplicative ; this contrast from internal polymorphmathematics where many objects are touched at the same time andmoreover many morphisms are touched at the same time and the commonoperations on the morphisms are coordinatewise/dimensional/pointwise .Each decoding ( "Yoneda" ) of some index-for-morphisms which encodesall the morphisms-at-some-domain-codomain is some metafunctor , whichis programmed by some inductive-family-presentation whoseadditional/embedded 2 constructors signify the functoriality ("parameter-arrow-action" and "structure-arrow-action" ) . Eachdecoding ( "Yoneda" ) of the whatever-is-interesting arrows betweenthe indexes-for-morphisms are metatransformations which are programmedas some grammatical-constructors of this inductive-family-presentationof the morphisms .The conversion-relation would convert across two morphisms whosemultiplicities-indexes are not syntactically/grammatically-the-same.But oneself does show that , by structure-arrow-action (metalogic-deduction ) , these two multiplicities are indeed (symmetric-associative-monoidal-metalogic ) propositionally equal ("soundness lemma" ) .Finally, some linear total/asymptotic grade is defined on themorphisms and the tactics-automated degradation lemma shows that eachof the conversion indeed degrades the redex morphism .For instant first impression , the conversion-relation constructorwhich says that the first projection morphism is natural/polyarrowing(commutativity along the parameter-arrow-action cut-constructor) , iswritten as :#+BEGIN_EXAMPLE| Project1_MorCoMod_Poly_Param : forall (F1 F2 : obCoMod) (Z1 : obCoMod)(A : obIndexer) (zz1 : 'CoMod(0 A |- F1 ~> Z1 )0), forall (A' : obIndexer)(a : 'Indexer(0 A' ~> A @ Cong.MorIndexer_Param.morIndexer )0 %cong),( ~_1 @ F2 o>CoMod (a o>* zz1) )* ( ~_1 @ F2 o>CoMod zz1 ) )#+END_EXAMPLEKEYWORDS : 1337777.OOO ; COQ ; cut-elimination ; multifold-enrichedfunctors ; contextual-weighted multifold-enriched product ; polymorphmetafunctors-grammar ; modosOUTLINE :* Indexer metalogic for multifold-enrichment , lemma for commutationof parameter-polyarrowing along structure-arrow-action** Indexer metalogic is half-grammatical half-sense and issymmetric-associative-monoidal with some context ( "product-weight" )constructor , and is presented in the congruent-rewrite style** Lemma for commutation of parameter-polyarrowing alongstructure-arrow-action* Generating data multifolded-enriched ref some indexer* Grammatical presentation of objects and morphismsmultifolded/enriched ref some indexer , by distinguishingparameter-polyarrowing from structure-arrow-action* Grammatical conversions of morphisms , which infer the samemultiplicity-computation** Grammatical conversions of morphisms** Same multiplicity-computation for convertible morphisms** Linear total/asymptotic grade and the degradation lemma* Solution** Solution morphisms without (parameter-polyarrowing)/polymorphism** Destruction of morphisms with inner-instantiation of object-indexes* (parameter-polyarrowing)/polymorphism/cut-elimination bycomputational/total/asymptotic/reduction/(multi-step) resolution-----{YinYang> fiction } so are you going to also ... pay/review/cite 1337777 mom recursive square ? hint : github.com/1337777/maclane/issues but but I don't want to "endorse" her recursive square you mean that you would insteadforce-fool-and-theft/lie/falsification and misappropriate public funds viainterdependent-detour ... detournement de fonds publics anybody needs to steal these stuff ? these trivial stuffdon't solve world hunger did YOUR heir steal MY autonomous stuff , as medium forcoward malice ? hint : it is not absence of knowledge ... primo your lies-that-your-are-not-thief causes thewrong question , secondo your answer to this wrong question isperverted ! here is some analogy/parallel along the "aircraftparadox" en.wikipedia.org/wiki/Survivorship_bias at the end , two questions are possible : (A) did tribalistic-interdependence (cockpit area)steal the money-funding (SAM projectile hit) of the failedwork-projects (downed lost aircraft) ? or (B) from the visible surviving work-projects(returning surviving aircraft) which are only half of the totalwork-projects (aircraft missions) , how to make the money-funding"more uniform" across the public (wing area) andtribalistic-interdependence (cockpit area) ? primo, tribalistic-interdependencelies-that-it-did-not-steal will cause the distraction from question(A) to question (B) secondo, aesthetic-perversion will cause to make themoney-funding "more uniform" by shielding the public (wing area)against receiving money-funding !1? I meant ...{yang> you are not Gauss or something } anyway the public audience is seeking to hire some newpublisher-in-chief your new tooling is simple : ` wget https://github.com/1337777/maclane/ -erobots=off -np -r -l 1 -p --warc-file=maclaneCache ; ipwb indexmaclaneCache.warc.gz >> maclaneCache.cdxj ; ipwb replay10101010IPFS0101SWARM0101 ` but but the "reviewer" must have his tribalistic-interdependencehidden such to "feel" "freedom of speech" of mathematics this is for another "aircraft paradox"-style or "linuxvs micro$oft"-style question , but let's skip to the punchline you forgot ITP2015 quickly eh ? so you want to hide that youare the same "reviewer" who did deny to pay the 1337777 momrecursive square and forced her son out of your noiseaous classroom ...{yin> mandatory bidet-washlet is not enough , LOL } by calling the PLA army ?!1! INAPPROPRIATE ! WOOF ! WOOF ! INAPPROPRIATE !-----BUY MOM RECURSIVE T-SQUARE paypal.me/13377771337777.OOO AT gmail.com微信支付2796386464 AT qq.com; eth0x54810dcb93b37DBE874694407f78959Fa222D920 ; amazonamazon.com/hz/wishlist/ls/28SN02HR4EB8W ; irc #OOO1337777