Abstraction - ib tug txheej txheem kawm

Cov tswvyim no twb qhia los ntawm Boethius raws li lwm cov neeg txhais lus ntawm cov Greek lo lus siv los ntawm Aristotle. Abstract (txhais txhais tau tias "rauj") - yog tus puas siab puas ntsws sib cais ntawm ib co ob tog, ties los yog thaj chaw ntawm cov txheej xwm thiab cov khoom nyob rau hauv kev txiav txim mus rau ntsiab ib co ntawm cov tseem ceeb nta thiab cov yam ntxwv. Zoo li cov designs yuav tsis muaj analogues nyob rau hauv lub ntiaj teb no. Qhov no yog raug ntawm ib co zauv disciplines. Abstraction - ib tug ncaj qha txim ntawm lub saum toj no cov lus. Txawm li cas los, nws twb sawv cev rau ib yam ntawm cov vib this los ntawm kev txawj ntse.

Abstraction - yuav yog lub tswvyim ntawm kev xaav

Nyob rau hauv ntawv thov no txoj kev tshuaj xyuas qhov transformation qauv hauv ib co systems (e.g., IP). Nyob rau hauv cov ntaub ntawv no, tag nrho cov system yog muab faib mus rau hauv cov ntsiab, uas yog subsystems. Hais tias yog, tus abstraction - ib lub lag luam uas tau nyob rau hauv lub complex qauv yog hloov los ntawm ib tug yooj yim zog, tsawg differential muaj ntsiab uas, yog li, yog ntau. Raws li ib qho piv txwv, cov txheej txheem ntawm kev hloov high-txhais video on ib tug tsawg zoo rau ceev cov ntaub ntawv ua thiab zaub mov xa tuaj.

Nta thiab hierarchy nyob rau hauv cov saw hlau ntawm abstractions

Tellingly, kev xws differential lag luam tau raws infinite. Abstraction - ib txoj kev, uas tom qab daim ntawv thov mus rau lub kev them nyiaj yug tej khoom, koj yuav tau txais ib co zoo ntawm cov qauv. Txawm li cas los, qhov no xyov yuav dua khiav lag luam nyob rau hauv tib txoj kev. Tej mus yuav myriad. Piv txwv li, nws yog ua tau rau paub daws teeb tej ib feem ntawm ib tug predetermined txawv, tawm hauv lwm tus unchanged, ces txav mus rau tom ntej no xaiv piece. Raws li ib tug tshwm sim, qhia lub ntsiab ntawm cov ntaub ntawv nyob rau hauv ib "tsob ntoo". Rau txhua qauv, koj yuav tau txais ib tug thiaj li hu ua qhov chaw abstractions, uas yog ib phau ntawm poob lawm kom nyob rau hauv kev cai tswjhwm kev cai. Nyob rau hauv kev muaj tiag, ntawm chav kawm, infinite faib tag nrho mus rau hauv qhov chaw yuav tsis muaj. Yog li ntawd, sib tham txog ib tug tsawg tus naj npawb ntawm cov qauv, muab los ntawm tus thawj tsab, hu ua "paub daws teeb hierarchical saw."

typing tswv yim

Abstraction - yog kev txawj ntse yuav tsum tau, thaum koj yuav tau mus nrhiav qhov sib txawv ntawm cov kev kwv thiab qhov xwm ntawm tus teeb meem txuam nrog rau nws. Piv txwv li, ib tug neeg pom lub roob raws li ib tug txheej ntawm geometric ntaub ntawv.

Txawm li cas los, nws yuav tsum tau ntaus abstraction los ntawm hom:

• generalizing uas muab ib tug paub daws teeb duab phenomenon; raws li ib tug tshwm sim, koj yuav tau qhia hais tias ntau thaj chaw ntawm lub kawm ua qauv;
• idealizing - kev hloov ntawm qhov cov empirical tiag tiag tshwm sim paub daws teeb zoo tagnrho tswvyim;
• ua tau infinite abstraction - kho txhua infinite caij ntawm lub teeb (kev xav raws li xaus);
• Insulating - xaiv ntawm qhov kev kuaj yam khoom los yog qhov yuav tsum tau tej yam kev mob ntawm kev ncaj ncees, rau piv txwv, Occam lub rab chais ;
• constructive - "coarsening" rau ib thaj tsam ntawm lub tiag tiag kwv, ib tug cuam tshuam los ntawm lawv cov tsis paub tseeb.

Cov kev xav ntawm "abstraction" kuj yuav ntaus thiab cov hom phiaj:

• formal - rho tawm ntawm qhov tseem ceeb thaj chaw rau ntxiv tsom xam;
• muaj nuj nqis - cov kev xaiv ntawm cov tswv yim zoo.

sib xyaw cov tswv yim

Concretization thiab abstraction - cov nqe lus, sib tham txog uas yog yuav luag tsis yooj yim sua cais. Cov ntsiab lus yog rov qab mus rau txhua lwm yam. Yuav kom hloov rau hauv Circuit Court mus rau lub tom ntej no theem ntawm abstraction yog tsim nyog yuav tau mus thov kev rau specifying validation xaiv cov kev ntawm cov thawj txheej. Qhov no ua rau nws tau tsis txhob poob lub kev twb kev txuas nrog lub tsab.