dimensions as types

7.29:

. how to mix dimensions with (data)typing?

dimensions are like vector operators:

. they give type to a literal;

you could type a variable to be a dimension,

and then any literal assignment imlicitely has that dimension;

[12.16: eg,

num * inch /sec .

. length and time are a dimension of type number`real;

{inch, sec} are subtypes

of {length, time}, respectively .

. the subtyping allows conversions between

measuring systems within the same dimension .

]

10.17: sci.adda/unifying dimensions and map`keys:

. I've been confused in my use of "(dimension):

. in the expression (x cup rice),

rice is the dimension

-- like the unit vector when giving imaginary as (x i),

. this has a meaning equivalent to named param'association;

eg, complex could be either (y+ x i) or (y, i: x) .

. how does adda have types declare dimensions?

eg, how should num declare i to be

an imaginary dimension of complex?

. by the currently designed syntax rules,

i is a postfix operator: (real)i.imaginary .

. another view is vector notation:

C.type`= <> = x + y i

. that is, R is already defined as the reals,

and any postfixed symbols in that

are taken as declaring dim's .

[10.18: = .(real.R, i.R) ? ]

10.12: adda/syntax/conversion:

. if a function call doesn't need to use parentheticals as arg,

how is the parser knowing when a function is being defined?

. the first use of the symbol

does need to use a parenthetical

along with the dot-extension

indicating the return`type or obj`type;

eg,

id(...).type .

. if it wasn't dotted to a datatype,

and the symbol wasn't defined yet,

then there would be the ambiguity of

{ function(arg), biop(right.side`arg)} .

. notice that there could be another ambiguity

unless you're careful with your spaces:

. if the syntax for type conversion

is (expression).[new type]

then ( f(x).t ) means I'm defining f now;

whereas ( f (x).t ) means f( (x).t )

ie,

f is already declared as a uniop,

and it's being applied to an arg whose type

is being either coerced or converted to t.type .

. it helps to remember that during a function decl',

the parenthetical expression is part of the name,

so a function's name must be immediately followed by

the parenthetical expression;

whereas, during use of a name declared to be function,

the arg is already expected,

so you don't need paren's to shovel one in .

. this helps both to minimize syntax

and to use args that are

variables rather than list`literals .

10.15:

. when considering how conversions should be expressed,

keep in mind not only the syntax for applying it,

but also how the type.mgt will be defining [it].

. the type.mgt of the object being converted

may not even have the conversion routine,

so then the syntax should not be object-oriented .

. it's also important to

express them the way english-math already does

unless there is some higher reason not to:

that way is applying a dimension name

as a postfixed operator .

. a similar syntax for operator definition would be:

(x)f.y;

eg,

phys`dimension.type`= number;

length.type`= phys`dimension;

ft.type`= length;

inch.type`= length;

(x)inch.ft`= x/12;

(x)ft.inch`= x*12 .

11.9: adda/oop/dimensions:

. unifying the subtype polymorphism syntax choice

with that of dimensions and measuring systems .

. how are dimensions being obj's of classes?

. obj's of dimension have numeric state

[11.14: eg, in the view of that language,

length is a dimension,

and a measurement of that is an object .

]

. one dimension can have several measuring std's

eg, length has sublcass {metric, english, ...} .

[11.14:

. numeric models of a dynamic object system

include a number of dimensions that can be multiplied or divided

in order to express numeric relations .

. each dimension can have a number of measuring systems

and more can be added later by describing them in terms of

currently recognized measures .

eg, physics.system is

foot.length: 0.3048 meters .

]

bk.chem:

mass, length, time, vol.type = length**3

liter.vol = meter **3/10

density = mass/vol

. temperature, like density, is an intensive property

(doesn't depend on qty or mass)

whereas, vol and mass are externsive properties

. signif digits refer to measurements actually being uncertain +- some error factor

so shorthand is to give all signif digits with one digit of uncertainty;

signif digits include exactly one uncertain digit .

. sci notation standardizes placement of decimal

in order to make zero idicate significance:

eg, 100 has an ambigous range of uncertainty:

significant digits ?

( 3: 99..101

, 2: 90.. 110

) but 1.00 * 10**2 means 3 signif digits unambiguously .

. one reason the metric system has a name for every factor of the base

is so that choosing the right one can have the same effect as sci'notation .

eg, 1000 m rephrased as 1.0000 km

will have unambiguous significance .

(however, many order names have fallen out of use .)

[11.14: . to refer to exact amounts, don't use decimal points,

refer to floats with fractions ]

. so by being able to shift magnitude

the decimal point is always free to indicate the precision

(otherwise for large numbers with uncertain numbers of units,

there's ambiguity)

. rounding is defined in terms of significant {digit, figures};

mult and div result has the minimum of the 2 arg's signif'digits;

also, rounding {up, down} for 5 depends on {even, odd};

eg,

.25 -> .2

.35 -> .4

todo:

(see numana`text for alt's and caveates) .

. for determining signif'digits of an {add, subtract},

convert args to have same order

eg, 1 km + 1m

-> 1 km + 0.001 km

then km has zero decimal places,

so result must also have zero places:

= 1 km .

adda/oop/dimensions/automatic dimensional analysis:

. must make dimensional analysis automatic

. I can type x.ft assign it mm

and have the sublcass system will find the conversion auto'ly .

. this system is user {definable extendable} too;

eg, for adding new currencies .

. a dimension type has atleast one subtype

then other subtypes define a conversion from the original sub

eg the original in pkg physics is metric,

then english `physics is subclassing metric .

11.11: adda/oop/theory of dimensions:

[11.11: needs to handle dimensions from the supertype,

but also exensible later ]

ratio (n.qua, d.qua).type

density.ratio(mass, vol),

subtype(supertype.type).type

qua.type.

-- quaality has been synon with dimension, as in dimensional analysis .

rct vs polar coord's

bk.adda/physics:

velocity.ratio(distance, time),

acceleration.ratio(velocity, time),

force = mass * acceleration

density.type = mass /vol

vol = length**3

area = length**2

mass is resistance to acceleration

. unlike types, a symbol can have multiple concrrent dim's

that are not subtypes of each other .

. dim's are part of the number class

since numeric operations may encounter them as factors;

ie,

a number value consists of a qty

times zero or more dim's or their inverses .

. part of root physics system is the dim'set:

{time length mass money charge} .

charge is coulomb (C) = joule /volt .

Joule = length**2 / time**2 * mass

capacitance = C/volt

amp= C/sec

volt = joule/C

but an electron volt is a fraction of a joule

. electric field = force /charge (newton/col) or (volt/meter),