https://en.wikipedia.org/wiki/Type_theory
https://en.wikipedia.org/wiki/Type_theory#Difference_from_set_theory https://en.wikipedia.org/wiki/Type_theory#Relation_to_category_theory https://en.wikipedia.org/wiki/Homotopy_type_theory ("HoTT") https://en.wikipedia.org/wiki/Type_signature ("Type annotation") https://en.wikipedia.org/wiki/Polymorphism_(computer_science)#Subtyping https://en.wikipedia.org/w/index.php?title=Eigenclass_model&oldid=592778140#In_Python https://en.wikipedia.org/wiki/C3_linearization Python and data types https://docs.python.org/3/reference/datamodel.html#objects-values-and-types https://docs.python.org/3/reference/datamodel.html#the-standard-type-hierarchy https://docs.python.org/3/library/stdtypes.html https://docs.python.org/3/library/datatypes.html https://docs.python.org/3/c-api/intro.html#objects-types-and-reference-counts https://docs.python.org/3/c-api/type.html#c.PyTypeObject https://github.com/python/typeshed https://github.com/python/typeshed/blob/master/stdlib/2and3/math.pyi https://github.com/python/typeshed/blob/master/stdlib/3/inspect.pyi ... http://diveintopython3.problemsolving.io/native-datatypes.html http://composingprograms.com/pages/21-introduction.html https://www.scipy-lectures.org/intro/language/basic_types.html https://www.scipy-lectures.org/intro/language/oop.html http://greenteapress.com/thinkpython2/html/ ... https://twitter.com/javierwchavarri/status/1082597155628568577 > One of the most useful ways to categorize type systems is: > > - is it Hindley-Milner based? (Rust, Haskell, OCaml) > - or does it support implicit subtyping (TypeScript, Flow, C#)? > > The first: 1 expression <-> at most 1 type. > The second: 1 expression <-> multiple types. > > A thread 👇 https://en.wikipedia.org/wiki/Hindley–Milner_type_system https://en.wikipedia.org/wiki/Subtyping ... https://en.wikipedia.org/wiki/Python_(programming_language) >From the Python infobox: > Typing discipline <https://en.m.wikipedia.org/wiki/Type_system>: Duck <https://en.m.wikipedia.org/wiki/Duck_typing>, dynamic <https://en.m.wikipedia.org/wiki/Dynamic_typing>, gradual <https://en.m.wikipedia.org/wiki/Gradual_typing> (since 3.5), strong https://en.wikipedia.org/wiki/Duck_typing https://en.wikipedia.org/wiki/Dynamic_typing https://en.wikipedia.org/wiki/Gradual_typing https://en.wikipedia.org/wiki/Strong_typing On Friday, January 25, 2019, kirby urner <kirby.ur...@gmail.com> wrote: > > In my on ramp to Python, for beginners, I find harping on "types" a great > intro (if unoriginal -- a lot of us do it). > > For one thing, we can hold fixed to the "type" idea while changing the > source of the type from built-in, to standard library module, to 3rd party > -- three tiers in my "dimensions of Python". > > These dimensions are (again): > > * keywords and core syntax (punctuation symbols e.g. [ ] ( ) : etc.) > * built-ins > * __ribs__ (special names e.g. __getitem__) > * standard library > * 3rd party (or cloud, or ecosystem, most of what you write yourself) > > What I say about OO and types is: > > this was an attempt to mirror your natural language thinking in terms of > things having type and thereby characteristics. Computer languages were > reaching out to meet us half way, in our native context. "Easy to reason > about" in proportion to one's having a strong sense of metaphor perhaps. > Not self-proving. > > The datetime type is, like the string, great for escaping the vortex of > "number types only" (where high school math teachers seem to wish to > confine themselves for some reason, although this is not a limitation of > maths). > > Many newcomers to programming expect incessant number crunching and > languages that only care about numeric methods. That's a stereotype to > smash early. Some types help us do that. I have a "permutation" type > that's like a number in being very mathy, supports __mul__ and __invert__, > but it's not a "number" type. > > https://repl.it/@kurner/Permutations (repl.it worth checking out if you > haven't) > > datetime also persuades us to appreciate that others have dealt with the > complexity. We get the fruits of their efforts. Calendar stuff is sooo... > tedious? Not forgetting timezones and daylight savings time. It's a lot > of useful machinery that used to stay locked away in temples. > > A good example of a 3rd party type? Actually there's a lot of 3rd party > datetime stuff. > > Lets get back to number crunching why not? gmpy2 - Extended Precision > Decimals. Very like decimals in Standard Library, which is great, for > comparing and contrasting similar types. > > A strong focus on types right from the get go then helps explain the power > of Python's 'class' keyword: Python lets you extend the type system with > types of your own. > > That's the OO model after all (not at all unique to Python), and meant to > mirror reality in some ways, a different goal then being "easy to reason > about" (which is a holy grail as well -- it's not either/or). > > Example using of gmpy2 in a "learning Python" curriculum context: > > https://nbviewer.jupyter.org/github/4dsolutions/Python5/ > blob/master/S_Train.ipynb > (more links from the bottom if wanting more of the same) > > The feature I want to emphasize is the results of decimal calculations > mostly look like this: > > JB Icosa: 18.512295868219161196009899292654531923571426913640152615969 > JB Cubocta: 20.000000000000000000000000000000000000000000000000000000000 > SuperRT: 21.213203435596425732025330863145471178545078130654221097650 > > Not what you'd be seeing with a calculator (too precise). Not floating > point numbers, clearly, in the sense of IEEE 754. > > I find extended precision types useful for inspiring students to > developing that special and useful skill, of going from conventional sigma > notation, to working programs using loops -- what sigmas stand for. > > Ramanujan had some doozies converging to Pi (or 1/Pi) or whatever. We've > looked at those before on edu-sig. > > Example: > https://github.com/4dsolutions/Python5/blob/master/Extended%20Precision. > ipynb > > Kirby > > >
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