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Math & linear algebra

Units & conversions

tracked physical units for temperature (degC/ degF), an affine (not linear) scale.

catalog/qu_temperature_units.qu

A temperature literal (`10 degC`) stays a distinct unit-tagged value, not a bare number: it compares correctly across scales (through Kelvin internally), a plain-number shift keeps it a temperature ("5 degrees warmer"), but scaling one (`2 * (10 degC)`) is rejected outright, since doubling a Celsius reading isn't physically meaningful the way doubling a Kelvin one is -- the offset doesn't scale. Subtracting two temperatures IS meaningful (the affine offset cancels) and yields a plain number, a delta in Kelvin/Celsius-sized degrees, not a temperature itself.

What it exercises

• 10 degC / 98.6 degF -- unit literals
• (a degC) - (b degC) -- a plain Num delta
• (a degC) + 5 -- stays a temperature
• (a degC) == (b degF) -- cross-scale comparison via Kelvin
• try/catch on an affine-scale violation (2 * temperature)

How it works

room = 21 degC
body = 98.6 degF
print("room = {room}")
print("body = {body}")
print("body warmer than room: {body > room}")

freezing_c = 0 degC
freezing_f = 32 degF
print("0 degC == 32 degF: {freezing_c == freezing_f}")

morning = 15 degC
afternoon = 23 degC
warmup = afternoon - morning
print("warmup = {warmup} degrees (a plain number, not itself a temperature)")

forecast = morning + 5
print("forecast = {forecast}")

try
    doubled = 2 * room
catch err
    print("rejected as expected: {err.message}")
end

Results

room = 21 degC
body = 98.6 degF
body warmer than room: true
0 degC == 32 degF: true
warmup = 8 degrees (a plain number, not itself a temperature)
forecast = 20 degC
rejected as expected: operator `*` is not defined on a temperature — Celsius/Fahrenheit are affine scales, so scaling one is not physically meaningful (see docs/design/physical-units.md §2).

The whole program

Runnable as it stands: qu run catalog/qu_temperature_units.qu

# qu_temperature_units.qu -- tracked physical units for temperature (degC/

# degF), an affine (not linear) scale.

#

# A temperature literal (`10 degC`) stays a distinct unit-tagged value, not

# a bare number: it compares correctly across scales (through Kelvin

# internally), a plain-number shift keeps it a temperature ("5 degrees

# warmer"), but scaling one (`2 * (10 degC)`) is rejected outright, since

# doubling a Celsius reading isn't physically meaningful the way doubling a

# Kelvin one is -- the offset doesn't scale. Subtracting two temperatures

# IS meaningful (the affine offset cancels) and yields a plain number, a

# delta in Kelvin/Celsius-sized degrees, not a temperature itself.

#

# Constructs exercised (all real, verified-working syntax):

#   10 degC / 98.6 degF        -- unit literals

#   (a degC) - (b degC)        -- a plain Num delta

#   (a degC) + 5               -- stays a temperature

#   (a degC) == (b degF)       -- cross-scale comparison via Kelvin

#   try/catch on an affine-scale violation (2 * temperature)


backend auto

#%% Unit literals and cross-scale comparison (converted through Kelvin)

room = 21 degC
body = 98.6 degF
print("room = {room}")
print("body = {body}")
print("body warmer than room: {body > room}")

freezing_c = 0 degC
freezing_f = 32 degF
print("0 degC == 32 degF: {freezing_c == freezing_f}")

#%% Deltas: subtracting two temperatures cancels the offset -> a plain number

morning = 15 degC
afternoon = 23 degC
warmup = afternoon - morning
print("warmup = {warmup} degrees (a plain number, not itself a temperature)")

#%% A temperature shifted by a plain number stays a temperature

forecast = morning + 5
print("forecast = {forecast}")

#%% Scaling a temperature is physically meaningless and rejected

try
    doubled = 2 * room
catch err
    print("rejected as expected: {err.message}")
end