Step 6: Indexed Values¶

In this step, you'll work with indexed collections to handle multiple related values, like a delta-v budget with several maneuvers.

Defining an Index¶

An index declaration defines a finite set of labels:

index Maneuver = { Departure, Correction, Insertion };

Indexed Values¶

Use [IndexName] to declare an indexed value:

dim Velocity = Length / Time;

node delta_v: Velocity[Maneuver] = {
    Maneuver.Departure: 2.46 km/s,
    Maneuver.Correction: 0.12 km/s,
    Maneuver.Insertion: 1.83 km/s,
};

Each label in the index gets its own value.

Direct Element Access¶

Access a specific element with [Index.Label]:

node departure_dv: Velocity = @delta_v[Maneuver.Departure];

`for` Comprehensions¶

Transform each element of an indexed value with for:

node double_dv: Velocity[Maneuver] = for m: Maneuver {
    @delta_v[m] * 2.0
};

This produces a new indexed value with each element doubled.

Aggregations¶

Reduce an indexed value to a single scalar:

node total_dv: Velocity = sum(for m: Maneuver { @delta_v[m] });
node max_dv: Velocity = max(for m: Maneuver { @delta_v[m] });
node min_dv: Velocity = min(for m: Maneuver { @delta_v[m] });
node mean_dv: Velocity = mean(for m: Maneuver { @delta_v[m] });
node n_maneuvers: Dimensionless = count(for m: Maneuver { @delta_v[m] });

Available aggregation functions: sum, max, min, mean, count.

Scan (Cumulative Fold)¶

scan computes a running accumulation across the index:

node cumulative_dv: Velocity[Maneuver] = scan(@delta_v, 0.0 m/s, |acc, val| acc + val);

This produces:

Departure: 2.46 km/s
Correction: 2.58 km/s (2.46 + 0.12)
Insertion: 4.41 km/s (2.58 + 1.83)

Complete Example¶

dim Velocity = Length / Time;

index Maneuver = { Departure, Correction, Insertion };

node delta_v: Velocity[Maneuver] = {
    Maneuver.Departure: 2.46 km/s,
    Maneuver.Correction: 0.12 km/s,
    Maneuver.Insertion: 1.83 km/s,
};

node double_dv: Velocity[Maneuver] = for m: Maneuver {
    @delta_v[m] * 2.0
};

node total_dv: Velocity = sum(for m: Maneuver { @delta_v[m] });
node max_dv: Velocity = max(for m: Maneuver { @delta_v[m] });
node cumulative_dv: Velocity[Maneuver] = scan(@delta_v, 0.0 m/s, |acc, val| acc + val);
node departure_dv: Velocity = @delta_v[Maneuver.Departure];

What You Learned¶

index declarations for finite label sets
Indexed values with Type[Index] syntax
for comprehensions to transform each element
Aggregations: sum, max, min, mean, count
scan for cumulative folds
Aggregation functions that work with any index

What's Next?¶

Congratulations! You've completed the tutorial. You now know the core features of Graphcal.

For deeper understanding, explore the Language Reference for formal documentation of all features, or check the CLI Reference for all command-line options.