Language Primer

At its heart, turo is really a small calculator language, written in javascript.

The parser is implemented using pegjs.

The language itself is relatively stable, in that the documented parts are unlikely to change. However, it is by no means complete.

Built in functionality

When using any turo apps, the .turo files in the base-lib directory have already been included. These give you a bunch of units and constants to use.

Units

We rarely calculate with pure abstract numbers. Most of things we are calculating are things with dimensions that we measure with units.

However, units are a complicated mix of history and convention, and even doing the simplest of arithmetic with them is tricky with conventional languages and calculators.

 >> width = 6ft + 1 inch
... width = 6 ft + 1 inch = 6.0833333333333 ft

Once you're calculating with multiples, most people give in to estimating conversions, where extra error comes in. Turo keeps track of this for you.

 >> length = 120m
... length = 120 m = 120 m
 >> area = width * length
... area = width * length = 222.504 m^2
 >> area in acre
... area in acre = 0.05498193579797 acre

More exotic operators also work with units:

 >> sqrt(area) in m
... sqrt(area) in m = 14.916567969878 m

Error detection is brilliant, but error reporting is best effort at best. You can only add and subtract units of the same dimension.

 >> 1 m + 1 kg
... Eval problem, DIMENSION_MISMATCH: 1 m + 1 kg
                                      ^^^^^^^^^^
 >> 2 / (3 - 9 * 1/3)
... Eval problem, DIVIDE_BY_ZERO: 2 / (3 - 9 * 1/3)
                                      ^^^^^^^^^^^^^                                      

Variables

You can define and use variables, just naming your expression with an equals.

 >> width = 6ft + 1 inch
... width = 6 ft + 1 inch = 6.0833333333333 ft

Now width is available as a variable to subsequent calculations. If you change the value of width, those calculations that used width will also update.

Constants are defined in the same way as variables, but with the const keyword.

>> const c = 299792458 m/s

Operators

Operator support is fleshed out for the usual infix and prefix operators for number scalar values:

• simple arithmetic operators, +, -, *, / and parentheses.
• trigonometric and hyperbolic variants functions: sin, cos, tan, asin, acos, atan. You can specify deg or radian as units. There's also an nth_root but it's really ugly to type.
• logarithms (log and ln), powers (^, e.g. e^pi, 10^3)

Glaring omissions: % and !.

Making new units

Units give expressions context to help us write and understand them.

unit GBP : Currency
unit person : People

workingYear = 40 h/wk * 1 year
salary = 50000 GBP per person / workingYear
attendees = 5 person
duration = 2h
cost_of_meeting = attendees * salary * duration

You can also make new units, relative to an existing unit.

 >> unit parsec : 1e31 m

This definition tells turo that parsec is something that has the same dimensionality as m i.e. Length, and how to convert between parsec and m. By doing this, now turo knows how to convert between parsec and any other unit of dimension Length.

 >> 1 parsec in km
... 1 parsec in km = 1e+28 km

To be clear, George, parsecs are a unit of distance.

 >> kessel_run = 12 parsec
... kessel_run = 12 parsec = 12 parsec
 >> kessel_run in mile
... kessel_run in mile = 7.456454306848e+28 mile
 >> kessel_run in year
... Eval problem, DIMENSION_MISMATCH: kessel_run in year
                                      ^^^^^^^^^^^^^^^^^^

More unit definition language

You can name compound dimensions when you define the corresponding unit, after the colon, but before the units it being defined as:

unit kph : Speed, 1 km/h

Once this has been defined, anything that is defined in terms of Length/Time is identified as Speed.

Where synonyms of the same unit exist, turo will parse this, but not do anything with it. This is an unimplemented future feature.

unit 3 ft foot feet : yd;

Finally, to make managing vast number of units easier, for example making a keyboard from the units we've defined, you can define unit schemes: these are names of units systems.

unit yard (Imperial) : 1 m;

Units can belong to more than one unit scheme, and can be defined all at once, or by adding more unit schemes later on.

unit m (SI Metric) : Length

or:

unit m (SI) : Length
unit m (Metric)

Unless you're adding a unit scheme, the unit scheme will propogate to the new units:

unit Pa pascal (Science) : Pressure, 1 N/m^2
unit kPa kilopascal : 1000 Pa

Now, kPa will have the same dimension and unit scheme as Pa.

Units without unit schemes will appear in all unit schemes. e.g.

unit s seconds : Time

Possible next steps for language

• Boolean types and operators to generate them from numbers e.g. p >= q; and use them e.g. a AND b, pattern matching (switch statements)
• Sequence types. Matlab has some interesting syntax here for defining ranges.
• String types. Principally for generating messages with switch statements and booleans.
• More flexible unit conversion:
  • 1 m in imperial -> 3 ft 3 in
  • 1 N in ft lb wk -> 1 lb ft/wk^2. This is principally to help builders of non-keyboard based UIs.
• functions. Bonus marks: definition language for functions. There are great reasons to do this, but UI would be difficult to implement, and don't want to get too bogged down in implementation, and/or theory. Scala has some nice syntax to chew on, especially around anonymous variables.
• 'prompt' tokens. In all likelihood, this would be a lightweight token which decorates an existing value, which becomes the default.