 languages can't have sums, products and nontermination together.
Q1. Is this true? Below (or in the above link I gave) is a partial argument.
However, Hinze's Generic programming with Adjunctions ignores the issue, even after discussing somewhat precisely which is the involved category. In particular, he talks (seemingly without reservations) about Haskell being modeled by the category $\mathbf{SCpo}$ of strict continuous partial orders and having sums and products. But we know that Haskell does not have sums (right?).
(Part of the paper uses $\mathbf{Set}$ instead, but that doesn't allow for non-termination).
Q2
So, what am I missing? I see four options:

People often ignore non-termination on purpose when discussing Haskell. Perhaps this paper does it too. But why would one mention CPOs then?
The barrier I discuss can be avoided in clever ways. In particular, the paper models non-strict Haskell functions $f : A \to B$ by strict functions $f : A_{\bot} \to B$, for other reasons.
The paper does mention the limitation and I missed that. I've spent some effort looking for this mention and failed to find any.
This is an actual mistake, and as everybody keeps claiming Haskell indeed lacks categorical sums (as other people agree on), even though the paper claims Either is such a thing. Everything works out nicely instead in total languages with inductive and coinductive types.

Background
It's well known that, in a bicartesian closed category (BCCC), if the initial and final object coincide (that is, if the category has a zero object) the category collapses (with all types being isomorphic) by $A \cong  A \times 1 \cong A \times 0 \cong 0$ for all $A$.
This means, for instance, that the category of pointed sets, with its zero object, can't be bicartesian closed.
But the category SCpo also has a zero object for the same reason: all objects are structured sets (CPOs) with a bottom element $\bot$, and arrows are strict (and ($\omega$-)continuous) functions, so they preserve $\bot$. Indeed, this is attributed to Smyth and Plotkin (1982), who describe this category as $\mathbf{CPO}_{\bot}$ and state it lacks categorical products; other categories they consider lack other features of a BiCCC (
languages can't have sums, products and nontermination in concert. 
 Q1. Is this genuine? Below (or in the above link I give) is a fond argument. 
 However, Hinze's Generic programming with Adjunctions ignores the emergence, even after discussing somewhat precisely which is the byzantine class. In particular, he talks (apparently without reservations) about Haskell being modeled by the class $ \mathbf{SCpo}$ of strict continuous partial orders and having sums and products. But we know that Haskell does not suffer sums (right ?). 
 (Part of the newspaper uses $ \mathbf{Set}$ instead, but that doesn't allow for non - termination). 
 Q2 
 thus, what am I missing? I see four options: 

 People often dismiss non - termination on purpose when discussing Haskell. Perhaps this paper does it too. But why would one mention CPOs then? 
 The barrier I discuss can be avoided in clever ways. In particular, the paper models non - strict Haskell functions $ degree fahrenheit: A \to B$ by strict functions $ f: A_{\bot } \to B$, for early reason. 
 The newspaper does mention the limitation and I miss that. I've spent some effort looking for this mention and fail to find any. 
 This is an actual mistake, and as everybody keeps claiming Haskell indeed lacks categorical union (as other people agree on), even though the paper claim Either is such a matter. Everything make out nicely instead in total languages with inductive and coinductive type. 

 Background 
 It's well known that, in a bicartesian closed category (BCCC), if the initial and final object coincide (that is, if the category has a zero object) the class collapses (with all types being isomorphic) by $ A \cong   A \times 1 \cong A \times 0 \cong 0 $ for all $ A$. 
 This means, for instance, that the class of pointed sets, with its zero object, can't be bicartesian closed. 
 But the category SCpo besides has a zero object for the like reason: all objects are structured sets (CPOs) with a bottom element $ \bot$, and arrow are strict (and ($ \omega$-)continuous) functions, so they preserve $ \bot$. Indeed, this is attributed to Smyth and Plotkin (1982), who describe this category as $ \mathbf{CPO}_{\bot}$ and state it lacks categorical merchandise; other categories they see lack other features of a BiCCC (
 lajguages can't have sums, pvoducts and nontgrninatimn togsther.
Q1. Ir this true? Below (or in the ebovw linj I gave) is a partial xrgument.
Hlwever, Hunze'w Generic pckgrammiky witg Adjbnrtions ignores jhe issue, evan after discuvskny somewhat precisely which is the indolved vahegory. In partyculsw, he naoks (seemingly without reservafions) auout Haskell beong modeled by the categorj $\mahhbf{SCpo}$ of strict continuous pareual orders avd having sums and prosucts. But we know that Haskell aoes uot have suns (rihvt?).
(Part of tie papvr uses $\mathbn{Xet}$ invtead, bit that doesn't alnow for non-termination).
Q2
Sm, what am I missind? I see fmux options:

People often itnore non-dermkbatkon oi phrpose whxn discussihg Haskell. Perhaps this paper coqw it too. But shy wotlq one mention CPOs then?
The barrier I divcuas can be avoided in clwver ways. In particulwr, the pa[er models non-strict Haskell functions $f : A \to B$ ty stcizt ymkctiubs $f : A_{\bot} \to B$, for other reasons.
The paper does jemtpon the limitatiok and I missed thay. L'vr spent some ewfort looiing for this mentlon and failwd to finq anu.
This is an actual mistake, qnd as everyyodt keeps claiming Hcskell indeeb lackx catrgorical sums (as other 'eople agree on), egen thougg the paper claimr Epthes is such a thing. Everythigg works iut uicely ivstesd in eotal langkages with inductive and coinbuctiee types.

Bafkground
It's well known that, in e bicartesian cnosvd categoxy (BCCG), if the initiaj and final oblect coiucide (ghat is, if the cavegory has a zero object) dje category rollapses (wity alo types ceing isomorphoc) by $A \cong  A \timws 1 \cong A \times 0 \gong 0$ ror all $A$.
This mzcnw, for instance, yhag tre cetegowf of pointed setr, wkyh itr zero objegt, zan't be bicartesian closad.
Buf the category SCpp wlso has a zero jbject for thr same reason: all lbjecvs are struvtuted sets (CPOs) with a bottom elejent $\bot$, wnd arrows are ftrigt (agd ($\omega$-)coutinuous) functions, so they preserve $\bot$. Mndeed, this is attribujed to Smyth and Plotlln (1982), who desccibe tris categmry as $\mathbf{CPO}_{\bot}$ qnd state it lackx categorical producta; othes catfgories they consider lack other features of a BiCCC (
languages can't have sums, products and nontermination Is true? Below in the above partial However, Hinze's Generic with Adjunctions ignores issue, even after discussing somewhat precisely is the involved category. In particular, he talks (seemingly without reservations) about Haskell modeled by the category $\mathbf{SCpo}$ of strict continuous partial orders and having sums products. we that does not have sums (right?). (Part of the paper uses $\mathbf{Set}$ instead, but that doesn't allow non-termination). Q2 So, what am I missing? I four options: People often non-termination on purpose when discussing Perhaps paper does too. why one mention CPOs The barrier I discuss can be avoided in clever ways. In particular, the paper models non-strict Haskell $f : B$ by functions : \to B$, for The paper does mention the limitation that. I've spent some effort looking for this and failed find any. This is an actual and as everybody keeps claiming Haskell indeed lacks sums (as other people agree on), even though the paper claims Either is such a works out nicely instead total languages with and types. It's known that, a bicartesian closed category (BCCC), if the initial and final object (that is, if the category has a zero object) the (with types being isomorphic) $A \cong A \times \cong \times 0 \cong 0$ $A$. means, the of sets, with its zero can't be bicartesian closed. But category SCpo also has same reason: all objects are structured sets (CPOs) a bottom element $\bot$, and arrows are (and ($\omega$-)continuous) functions, so they preserve $\bot$. Indeed, this is attributed to and Plotkin describe this category as $\mathbf{CPO}_{\bot}$ and state it categorical products; other categories consider lack other features of a BiCCC (
 languages can't have sums, prodUcts and nonTermiNatIon ToGethEr.
Q1. IS this true? Below (OR in tHe above link I gave) is a parTial aRgUMent.
hOwEver, HInze's GeNErIC ProGrAmMinG wITh adjunCtiOns ignoRes the issuE, evEn After discussINg Somewhat prEciSely which is tHe iNvolveD cAteGOry. In ParTiculAr, he taLKs (seemIngly withOuT ReservATions) abOUT HAskeLl being modeled by tHE cATegory $\mathbf{SCPo}$ of stRiCT cONTinUouS partial orDeRs and HAving suMS aND PRodUCts. But we know tHat Haskell dOEs nOt have SuMs (rIGht?).
(ParT of thE pAPer Uses $\mathbf{SEt}$ inStead, but tHat doeSN't allow FOr non-teRminatIon).
q2
So, What AM I MiSsiNg? i See FOuR opTIonS:

People oFtEn IgnorE non-TERMInatIon On puRpose When discussinG HaSkelL. perHaps tHis paPer dOeS it toO. But whY woulD oNe mention CPOs thEn?
ThE barrier I DisCuSs cAn Be avoIDed in cLevEr wAys. In paRticulaR, The PaPER MoDels non-strict HaskeLl FUNcTions $f : A \tO B$ by stRIcT fUNctions $f : a_{\bOt} \tO B$, foR OTher rEasoNS.
THe paper dOes menTIoN tHe limitAtIon and i mIssEd tHat. I'vE SpenT some eFfort looKing fOR this mention anD Failed to find aNY.
THIS iS An acTuaL mistake, and As evERyboDy keEPs ClaIMing HAskelL iNDeED lacks categorical suMs (As otheR peopLe agree on), even Though the pAPER claims EItheR Is SUch a thing. EveryThing Works out niCEly insteAd in tOtal langUages with INDuctive aNd cOinDucTivE TYpEs.

Background
IT'S Well KnOwn that, In a BicarteSiaN clOseD caTeGory (BCCC), iF the initIaL aNd FiNal ObjecT Coincide (ThAt iS, iF thE cateGOry has A zero ObjeCt) ThE CatEgory coLLaPSEs (wiTh AlL typEs bEiNg isoMorpHIc) bY $A \cong  A \Times 1 \cong a \tiMEs 0 \coNg 0$ FoR all $A$.
ThIs means, for insTaNce, that the CaTegOry of pOINted sets, With its zero object, can't be BIcartesIan CloseD.
But The categoRy Scpo alsO haS A zero oBject fOr the SaMe rEASon: alL OBjEctS aRe structurED SetS (CPOs) WiTh a bOttom elEment $\bot$, and arrows aRE stRict (and ($\omega$-)cOntInuoUS) FuNctIOnS, So tHeY PreSERve $\bot$. Indeed, thiS is attribuTeD To smyth and PlOTkiN (1982), wHo descrIbe this CategORy as $\matHbf{CPO}_{\bot}$ And state iT lAcks CATegOrical prodUcts; otheR categoriES they COnSider LacK other FeAtuRes of A BiCCC (
 languages can't have sums , products  andnon ter mi nati on t ogether.
Q1. I s  thi s true? Below (or in t he ab ov e  lin k  I  gave ) is ap ar t i alar gu men t. Ho wever , H inze'sGeneric pr ogr am ming with Ad j un ctions ign ore s the issue,  ev en aft er  di s cussi ngsomew hat pr e cisely  which is  t h e invo l ved cat e g or y. I n particular, het al k s (seemingly w ithout  r e se r v ati ons ) about Ha sk ell b e ing mod e le d b y t h e category $\ mathbf{SCpo } $ o f stri ct  co n tinuou s par ti a l o rders and h avin g sums an d prod u cts. Bu t  we kno w that  Ha ske ll d o es  n otha v e s u ms  (r i ght ?).
(Par tof  thepape r u s es $ \ma thbf {Set} $ instead, bu t t hatd oes n't a llowforno n-ter minati on).Q2 
So, what am Imiss ing? I se e f ou r o pt ions: 
Peopl e o fte n ignor e non-t e rmi na t i o non purpose when di sc u s si ng Haske ll. Pe r ha ps this pap er  do es i t too.Butw hy  would o ne men t io nCPOs th en ?
Theba rri erI dis c usscan be  avoided  in c l ever ways. Inp articular, th e  p a p er mode lsnon-strictHask e ll f unct i on s $ f  : A\to B $b ys trict functions $f:A_{\bo t} \t o B$, for oth er reasons . T he paper  doe s  m e ntion the limi tatio n and I mi s sed that . I'v e spentsome effo r t  looking  fo r t his  me n t io n and failedt o  fin dany.
Th isis an a ctu almis tak e,  and as e verybody  k ee ps  c lai mingH askell i nd eed  l ack s cat e gorica l sum s (a sot h erpeoplea gr e e  on) ,ev en t hou gh  thepape r  cl aims Ei ther is s uch a th in g.  Everyt hing works ou tnicely ins te adin tot a l  languag es with inductive and c o inducti vetypes .

B ackground 
It 's wel l k n own th at, in  a bi ca rte s i an cl o s ed  ca te gory (BCCC ) ,  if  thein itia l and f inal object coinci d e ( that is, if t hecate g o ry  ha s  a zer oo bje c t ) the categorycollapses(w i th  all types bei ng  isomor phic) b y $A\ cong  A  \times 1  \cong A\t imes 0  \c ong 0$ for  all $A$ .
This me a ns, f o rinsta nce , that  t hecateg ory of poi ntedsets,wi th its  zero  o bject, c an't be bicartesian clo sed.
B ut th e c ategory S Cpo als o has a z eroobject for  th e s ame r eas o n: al l ob j ec tsa re st ruct u red sets( CP Os) w it h a bottome l e men t $\b ot$ ,  and a rrow s are strict (and ($\omega$-)con tinu o u s)fun c tion s,  so they prese rve  $ \ b ot$. Ind ee d, this isattribut ed to Sm yth an d Plot kin (19 8 2 ), who de scri bethis cate gor ya s $\mat hb f{ C PO}_{\ bot} $and st ate it lack s categorical prod ucts; o therc ate gorie sthey co n side r lack oth er features  of aBiCC C (
 languages_can't have_sums, products and nontermination_together.
Q1. Is_this_true? Below_(or_in the above_link I gave)_is a partial argument.
However,_Hinze's Generic programming_with_Adjunctions ignores the issue, even after discussing somewhat precisely which is the involved category._In_particular, he_talks_(seemingly_without reservations) about Haskell being_modeled by the category $\mathbf{SCpo}$_of strict_continuous partial orders and having sums and products._But_we know that_Haskell does not have sums (right?).
(Part of the paper_uses $\mathbf{Set}$ instead, but that doesn't_allow for non-termination).
Q2
So,_what_am_I missing? I see_four options:

People often ignore non-termination on_purpose when discussing Haskell. Perhaps this_paper does it too. But why would_one mention CPOs then?
The barrier I_discuss can be avoided in_clever ways._In particular, the paper models_non-strict Haskell functions_$f :_A \to B$_by strict functions $f : A_{\bot}_\to B$, for_other reasons.
The paper does mention the_limitation_and I missed_that._I've_spent some_effort looking for_this_mention and_failed_to find any.
This is an actual_mistake,_and as everybody keeps claiming Haskell indeed_lacks categorical sums (as_other_people agree on), even_though the paper claims Either_is such a thing. Everything works_out nicely_instead in_total languages with inductive and coinductive types.

Background
It's well known that, in_a bicartesian closed category (BCCC), if_the initial and final_object coincide_(that_is, if the_category_has a_zero object) the category collapses (with all_types being_isomorphic) by $A \cong  A_\times 1 \cong A_\times_0 \cong 0$ for all $A$.
This_means, for instance, that the category_of pointed sets, with its_zero_object,_can't be bicartesian closed.
But the_category SCpo also has a zero_object for the_same reason: all objects are structured sets_(CPOs)_with a bottom element $\bot$, and_arrows_are strict (and ($\omega$-)continuous) functions, so_they_preserve_$\bot$. Indeed, this is attributed_to Smyth and Plotkin (1982), who_describe this category as $\mathbf{CPO}_{\bot}$ and state it lacks_categorical products; other_categories they consider lack other_features_of_a BiCCC (