Draft: prelude with dimensionful angles

examples/consistency_others.nbt

@@ -64,7 +64,8 @@ assert_eq(1 calorie, 4.184 J)
 assert_eq(1 BTU, 1055.05585262 J)
 assert_eq(1 lbf, 4.448222 N)
 assert_eq(1 ozf, (4.448222 / 16.0) N, 1e-5 N)
-assert_eq(60 RPM, 1 Hz)
+assert_eq(60 RPM, 1 rev / s)
+assert_eq(60 RPM, 360° / s)
 assert_eq(1 fortnight, 2 week)
 assert_eq(1 mmHg, 133.322387415 Pa, 1e-5 Pa)
 assert_eq(1 PSI, 6.894757 kPa)

examples/dimensionful_angles.nbt

@@ -0,0 +1,34 @@
+# This file uses the dimensionful_angles prelude
+
+print("h = {planck_constant}")
+print("ℏ = {ℏ}")
+print("ȟ = {ȟ}")
+
+# harmonic oscillation
+let ω = 2π rad / s
+let t = 0.4 s
+let amplitude = Sin(ω·t)
+print("Amplitude: {amplitude}")
+
+# Tangential velocity
+let r = 20 cm
+let v: Velocity = r ω / θC  # This is one of the "text book formulas" that needs adaptation
+print("Linear velocity: {v}")
+
+# Rotational motion
+assert_eq(60 rpm, 360° / s)
+
+# Arc length
+fn arc_length(radius: Length, θ: Angle) -> Length = radius × θ / θC
+print(arc_length(1 m, 45°))
+
+# Rotational energy
+let mass = 1 kg
+let radius = 1 m
+let I: MomentOfInertia = mass × radius^2 / θC^2
+let ω_rot: AngularFrequency = 180° / 5 s
+let E_rot: Energy = 1/2 * I * ω_rot^2
+print("E_rot = {E_rot -> J}")
+
+# Cyclotron frequency
+let ω_cyc: AngularFrequency = electron_charge/electron_mass × 50 µT × θC

examples/projectile_motion.nbt

@@ -1,8 +1,8 @@
 # https://en.wikipedia.org/wiki/Projectile_motion
 
-fn max_height(v: Velocity, θ: Angle) -> Length = v² · sin(θ)^2 / (2 · g0)
-fn max_distance(v: Velocity, θ: Angle) -> Length = v² · sin(2 θ) / g0
-fn time_of_flight(v: Velocity, θ: Angle) -> Time = 2 v · sin(θ) / g0
+fn max_height(v: Velocity, θ: Angle) -> Length = v² · Sin(θ)^2 / (2 · g0)
+fn max_distance(v: Velocity, θ: Angle) -> Length = v² · Sin(2 θ) / g0
+fn time_of_flight(v: Velocity, θ: Angle) -> Time = 2 v · Sin(θ) / g0
 
 assert_eq(max_height(10 m/s, 45 deg),      2.55 m,  1 cm)
 assert_eq(max_distance(10 m/s, 45 deg),   10.20 m,  1 cm)

examples/readme-demo.nbt

@@ -2,6 +2,6 @@ use units::currencies
 
 8 km / (1 h + 25 min)
 140 € -> GBP
-atan2(30 cm, 1 m) -> deg
-let ω = 2π c / 660 nm
+ATan2(30 cm, 1 m) -> deg
+let ω = 2π θC c / 660 nm
 print("Energy of red photon: {ℏ ω -> eV}")

examples/unicode.nbt

@@ -3,7 +3,7 @@ let ν = c / λ
 
 assert_eq(ν, 499.7 GHz, 0.1 GHz)
 
-let ω = 2 π ν
+let ω = 2 π θC ν
 let E = ℏ ω
 
 assert_eq(E, 2 meV, 0.1 meV)

numbat-wasm/deploy.sh

@@ -4,11 +4,6 @@ set -euo pipefail
 
 current_branch=$(git rev-parse --abbrev-ref HEAD)
 
-if [[ "$current_branch" != "master" ]]; then
-    echo "You are currently on the '$current_branch' branch, not 'master'."
-    exit 1
-fi
-
 bash build.sh
 
-rsync --archive --stats --progress --human-readable -r www/ shark.fish:numbat.dev/
+rsync --archive --stats --progress --human-readable -r www/ shark.fish:numbat.dev/angles/

numbat/modules/core/dimensions.nbt

@@ -1,6 +1,6 @@
 ### Physical dimensions
 
-dimension Angle = 1  # SI: plane angle
+dimension Angle  # SI: plane angle
 dimension SolidAngle = Angle^2
 
 dimension Length
@@ -14,6 +14,8 @@ dimension Velocity = Length / Time
 dimension Acceleration = Length / Time^2
 dimension Jerk = Length / Time^3
 dimension FlowRate = Volume / Time
+dimension AngularFrequency = Angle / Time
+dimension AngularAcceleration = Angle / Time^2
 
 dimension Mass
 dimension Momentum = Mass × Velocity
@@ -24,7 +26,7 @@ dimension Pressure = Force / Area = Energy / Volume  # also: stress
 dimension Action = Energy × Time
 dimension MassDensity = Mass / Length^3
 dimension MomentOfInertia = Mass × Length^2 / Angle^2
-dimension AngularMomentum = MomentOfInertia × Angle / Time = Mass × Length^2 / Time / Angle
+dimension AngularMomentum = MomentOfInertia × AngularFrequency = Mass × Length^2 / Time / Angle
 dimension Torque = Length × Force / Angle  # also: moment of force
 dimension EnergyDensity = Energy / Volume
 dimension MassFlow = Mass / Time
@@ -45,7 +47,7 @@ dimension ElectricChargeDensity = ElectricCharge / Volume
 dimension CurrentDensity = Current / Area
 dimension ElectricDipoleMoment = ElectricCharge × Length
 dimension ElectricQuadrupoleMoment = ElectricCharge × Length^2
-dimension MagneticDipoleMoment = Current × Area = Torque / MagneticFluxDensity
+dimension MagneticDipoleMoment = Current × Area = Torque / MagneticFluxDensity * Angle
 dimension ElectricFieldStrength = Voltage / Length
 dimension ElectricDisplacementFieldStrength = ElectricCharge / Area
 dimension ElectricPermittivity = Time^4 × Current^2 / Mass / Length^3 × Angle = ElectricDisplacementFieldStrength / ElectricFieldStrength × Angle

numbat/modules/physics/constants.nbt

@@ -24,7 +24,9 @@ let planck_constant: Action = 6.626_070_15e-34 J / Hz
 @name("Reduced Planck constant")
 @url("https://en.wikipedia.org/wiki/Planck_constant#Reduced_Planck_constant_%E2%84%8F")
 @aliases(h_bar)
-let ℏ: AngularMomentum = planck_constant / 2π
+let ℏ: AngularMomentum = planck_constant / 2π θC
+let h_bar = ℏ
+let ȟ: Action = planck_constant / 2π
 
 @name("Electron mass")
 @url("https://en.wikipedia.org/wiki/Electron_mass")
@@ -38,22 +40,22 @@ let elementary_charge: ElectricCharge =  1.602_176_634e-19 C
 @name("Vacuum permeability / magnetic constant")
 @url("https://en.wikipedia.org/wiki/Vacuum_permeability")
 @aliases(µ0,μ0,mu0)
-let magnetic_constant: MagneticPermeability =  1.256_637_062_12e-6 N / A²
+let magnetic_constant: MagneticPermeability =  1.256_637_062_12e-6 N / A² / rad
 
 @name("Vacuum electric permittivity / electric constant")
 @url("https://en.wikipedia.org/wiki/Vacuum_permittivity")
 @aliases(ε0,eps0)
-let electric_constant: ElectricPermittivity = 1 / (µ0 c²) -> F/m
+let electric_constant: ElectricPermittivity = 1 / (µ0 c²) -> F/m × rad
 
-@name("Bohr magneton")
-@aliases(µ_B,μ_B)
-@url("https://en.wikipedia.org/wiki/Bohr_magneton")
-let bohr_magneton: Energy / MagneticFluxDensity = electron_charge ℏ / 2 electron_mass -> J/T
+#@name("Bohr magneton")
+#@aliases(µ_B,μ_B)
+#@url("https://en.wikipedia.org/wiki/Bohr_magneton")
+#let bohr_magneton: Energy / MagneticFluxDensity = electron_charge ℏ / 2 electron_mass -> J/T
 
-@name("Fine structure constant")
-@url("https://en.wikipedia.org/wiki/Fine-structure_constant")
-@aliases(α, alpha)
-let fine_structure_constant: Scalar = electron_charge^2 / (2 eps0 ℎ c)
+#@name("Fine structure constant")
+#@url("https://en.wikipedia.org/wiki/Fine-structure_constant")
+#@aliases(α, alpha)
+#let fine_structure_constant: Scalar = electron_charge^2 / (2 eps0 ȟ c)
 
 @name("Proton mass")
 @url("https://en.wikipedia.org/wiki/Proton")
@@ -85,15 +87,15 @@ let gas_constant: Energy / (AmountOfSubstance × Temperature) = k_B × N_A
 @name("Bohr radius")
 @url("https://en.wikipedia.org/wiki/Bohr_radius")
 @aliases(a0)
-let bohr_radius: Length = 4 pi ε0 ℏ^2 / (electron_charge^2 electron_mass)
+let bohr_radius: Length / Angle = 4 pi ε0 ℏ^2 / (electron_charge^2 electron_mass) -> m/rad
 
-@name("Rydberg constant")
-@url("https://en.wikipedia.org/wiki/Rydberg_constant")
-let rydberg_constant: Wavenumber = (electron_mass electron_charge^4) / (8 ε0^2 ℎ^3 c)
+#@name("Rydberg constant")
+#@url("https://en.wikipedia.org/wiki/Rydberg_constant")
+#let rydberg_constant: Wavenumber = (electron_mass electron_charge^4) / (8 ε0^2 ℎ^3 c)
 
-@name("Rydberg unit of energy")
-@url("https://en.wikipedia.org/wiki/Rydberg_constant")
-unit Ry: Energy = ℎ c × rydberg_constant
+#@name("Rydberg unit of energy")
+#@url("https://en.wikipedia.org/wiki/Rydberg_constant")
+#unit Ry: Energy = ℎ c × rydberg_constant
 
 @name("Atomic Mass constant")
 @url("https://en.wikipedia.org/wiki/Atomic_mass_constant")

numbat/modules/prelude.nbt

@@ -1,3 +1,26 @@
+# The following prelude is based on a proposal to treat angles
+# as dimensionful quantities [1].
+#
+#
+# Literature
+# ----------
+#
+# Pro:
+#   - [1] Angles in the SI: a detailed proposal for solving the problem, https://arxiv.org/abs/2108.05704
+#   - [2] Angles are inherently neither length ratios nor dimensionless, https://arxiv.org/abs/1909.08389
+#   - [3] Brownstein K R, Angles—let’s treat them squarely, Am. J. Phys. 65 605–14 (1997).
+#   - [4] Dimensionless units in the SI, https://arxiv.org/abs/1409.2794
+#
+# Contra:
+#   - [4] Dimensional angles and universal constants, https://doi.org/10.1119/1.18964
+#   - [5] M. Grötschel, H. Hanche-Olsen, H. Holden, Comment on ‘Angles are inherently neither length ratios nor dimensionless’.
+#     (and companion paper https://arxiv.org/abs/2011.05779v4)
+#   - [6] Comment on 'Angles in the SI: a detailed proposal for solving the problem', B P Leonard, https://iopscience.iop.org/article/10.1088/1681-7575/ac5433/meta
+#     (and reply to comment: https://iopscience.iop.org/article/10.1088/1681-7575/ac5434)
+#
+# Review:
+#   - [7] Implications of adopting plane angle as a base quantity in the SI, https://arxiv.org/pdf/1604.02373.pdf
+
 use core::scalar
 use core::quantities
 use core::dimensions
@@ -36,3 +59,11 @@ use chemistry::elements
 
 use datetime::functions
 use datetime::human
+
+fn Sin(θ: Angle) -> Scalar = sin(θ / θC)
+fn Cos(θ: Angle) -> Scalar = cos(θ / θC)
+fn Tan(θ: Angle) -> Scalar = tan(θ / θC)
+fn ASin(x: Scalar) -> Angle = asin(x) × θC
+fn ACos(x: Scalar) -> Angle = acos(x) × θC
+fn ATan(x: Scalar) -> Angle = atan(x) × θC
+fn ATan2<Q: Dim>(y: Q, x: Q) -> Angle = atan2(y, x) × θC

numbat/modules/units/hartree.nbt

@@ -7,4 +7,4 @@ unit hartree: Energy = ℏ^2 / (electron_mass a0^2)
 
 @name("Bohr")
 @url("https://en.wikipedia.org/wiki/Hartree_atomic_units")
-unit bohr: Length = a0
+unit bohr: Length = a0 × θC

numbat/modules/units/misc.nbt

@@ -58,7 +58,7 @@ unit revolution: Angle = 360°
 @name("Revolutions per minute")
 @url("https://en.wikipedia.org/wiki/Revolutions_per_minute")
 @aliases(RPM: short)
-unit rpm: Frequency = 1 / minute
+unit rpm: AngularFrequency = revolutions per minute
 
 @name("Millimeter of mercury")
 @url("https://en.wikipedia.org/wiki/Millimeter_of_mercury")

numbat/modules/units/planck.nbt

@@ -4,20 +4,20 @@ use physics::constants
 
 @name("Planck length")
 @url("https://en.wikipedia.org/wiki/Planck_length")
-unit planck_length: Length = sqrt(ℏ G / c^3) -> m
+unit planck_length: Length = sqrt(ȟ G / c^3) -> m
 
 @name("Planck mass")
 @url("https://en.wikipedia.org/wiki/Planck_mass")
-unit planck_mass: Mass = sqrt(ℏ c / G) -> kg
+unit planck_mass: Mass = sqrt(ȟ c / G) -> kg
 
 @name("Planck time")
 @url("https://en.wikipedia.org/wiki/Planck_time")
-unit planck_time: Time = sqrt(ℏ G / c^5) -> s
+unit planck_time: Time = sqrt(ȟ G / c^5) -> s
 
 @name("Planck temperature")
 @url("https://en.wikipedia.org/wiki/Planck_temperature")
-unit planck_temperature: Temperature = sqrt(ℏ c^5 / (G k_B^2)) -> K
+unit planck_temperature: Temperature = sqrt(ȟ c^5 / (G k_B^2)) -> K
 
 @name("Planck energy")
 @url("https://en.wikipedia.org/wiki/Planck_energy")
-unit planck_energy: Energy = sqrt(ℏ c^5 / G) -> J
+unit planck_energy: Energy = sqrt(ȟ c^5 / G) -> J

numbat/modules/units/si.nbt

@@ -51,7 +51,11 @@ unit candela: LuminousIntensity
 @url("https://en.wikipedia.org/wiki/Radian")
 @metric_prefixes
 @aliases(radians, rad: short)
-unit radian: Angle = meter / meter
+unit radian: Angle
+
+# The "Cotes angle"
+let theta_C = 1 rad
+let θC = theta_C
 
 @name("Steradian")
 @url("https://en.wikipedia.org/wiki/Steradian")

numbat/modules/units/stoney.nbt

@@ -1,13 +1,13 @@
 use physics::constants
 
-@name("Stoney length")
-@url("https://en.wikipedia.org/wiki/Stoney_units")
-unit stoney_length: Length = sqrt(G × electron_charge^2 / 4 π ε0 c^4)
+#@name("Stoney length")
+#@url("https://en.wikipedia.org/wiki/Stoney_units")
+#unit stoney_length: Length = sqrt(G × electron_charge^2 / 4 π ε0 c^4)
 
-@name("Stoney mass")
-@url("https://en.wikipedia.org/wiki/Stoney_units")
-unit stoney_mass: Mass = sqrt(electron_charge^2 / 4 π ε0 G)
+#@name("Stoney mass")
+#@url("https://en.wikipedia.org/wiki/Stoney_units")
+#unit stoney_mass: Mass = sqrt(electron_charge^2 / 4 π ε0 G)
 
-@name("Stoney time")
-@url("https://en.wikipedia.org/wiki/Stoney_units")
-unit stoney_time: Time = sqrt(G × electron_charge^2 / 4 π ε0 c^6)
+#@name("Stoney time")
+#@url("https://en.wikipedia.org/wiki/Stoney_units")
+#unit stoney_time: Time = sqrt(G × electron_charge^2 / 4 π ε0 c^6)

numbat/tests/interpreter.rs

@@ -258,8 +258,8 @@ fn test_algebra() {
 
 #[test]
 fn test_math() {
-    expect_output("sin(90°)", "1");
-    expect_output("sin(30°)", "0.5");
+    expect_output("Sin(90°)", "1");
+    expect_output("Sin(30°)", "0.5");
     expect_output("sin(pi/2)", "1");
 
     expect_output("atan2(10, 0) / (pi / 2)", "1");
@@ -283,7 +283,7 @@ fn test_incompatible_dimension_errors() {
         get_error_message("kg m / s^2 + kg m^2"),
         @r###"
      left hand side: Length  × Mass × Time⁻²    [= Force]
-    right hand side: Length² × Mass             [= MomentOfInertia]
+    right hand side: Length² × Mass
     "###
     );
 
@@ -420,14 +420,14 @@ fn test_misc_examples() {
     expect_output("2min + 30s -> sec", "150 s");
     expect_output("4/3 * pi * (6000km)³", "9.04779e+11 km³");
     expect_output("40kg * 9.8m/s^2 * 150cm", "588 kg·m²/s²");
-    expect_output("sin(30°)", "0.5");
+    expect_output("Sin(30°)", "0.5");
 
     expect_output("60mph -> m/s", "26.8224 m/s");
     expect_output("240km/day -> km/h", "10 km/h");
     expect_output("1mrad -> °", "0.0572958°");
     expect_output("52weeks -> days", "364 day");
     expect_output("5in + 2ft -> cm", "73.66 cm");
-    expect_output("atan(30cm / 2m) -> deg", "8.53077°");
+    expect_output("ATan(30cm / 2m) -> deg", "8.53077°");
     expect_output("6Mbit/s * 1.5h -> GB", "4.05 GB");
     expect_output("6Mbit/s * 1.5h -> GiB", "3.77186 GiB");
 
@@ -439,7 +439,7 @@ fn test_misc_examples() {
 #[test]
 fn test_bohr_radius_regression() {
     // Make sure that the unit is 'm', and not 'F·J²/(C²·kg·m·Hz²)', like we had before
-    expect_output("bohr_radius", "5.29177e-11 m");
+    expect_output("bohr_radius", "5.29177e-11 m/rad");
 }
 
 #[test]