# Tutorial 12: Preventing Confusion with Distinct Kinds

Many engineering domains have quantities that share the same physical dimension but represent
fundamentally different concepts. Hydraulic engineering uses "_head_"—a measure of
**_potential energy per unit weight_** expressed as an equivalent _height_—in two
incompatible ways:

- **_Fluid head_**: _Potential energy_ normalized to the actual fluid's _density_
  (e.g., 2 m of mercury)
- **_Water head_**: _Potential energy_ normalized to water's _density_ (e.g., 27.2 m water
  equivalent)

Both express **_energy_** using _length_ dimensions, but mixing them produces physically
meaningless results—like mixing _gauge_ and _absolute pressure_ without conversion.
Traditional code using raw `double` values allows such mistakes to silently compile.
Remarkably, even units libraries from C++ and also other programming languages cannot
prevent this error—they only check dimensional compatibility, not physical meaning.

This tutorial demonstrates how **mp-units** uses `is_kind` to create distinct quantity
**subkinds within an existing hierarchy**—a capability unique among units libraries worldwide.
The key insight: `is_kind` lets quantities **inherit** properties (dimension, unit) from a
parent while **isolating** them from each other. Just as the library prevents mixing
_plane angles_ and _solid angles_ (both subkinds of _dimensionless_), you can create
custom subkinds like _fluid head_ and _water head_ (both subkinds of _height_) that
cannot be accidentally mixed.


## Problem Statement

Consider a pump system design for a chemical processing plant. Engineers must verify that
the _pump capacity_ is adequate for the fluid being handled. This requires comparing:

- **System requirement**: The fluid column that must be lifted, expressed as _fluid head_
  (_energy_ normalized to the actual fluid's _density_)
- **Pump specifications**: Rated in _water head_ (_energy_ normalized to _water density_)

The relationship between _fluid head_ and _water head_ reflects _energy conservation_
with different _density_ normalizations:

$$H_{water} = H_{fluid} \cdot SG$$

$$H_{fluid} = \frac{H_{water}}{SG}$$

Where _specific gravity_ is the dimensionless ratio of _fluid density_ to _water density_.
The same _potential energy_ is expressed as a larger _height_ for lighter fluids (water)
and a smaller _height_ for denser fluids (mercury).

Here's how different approaches handle (or fail to handle) this scenario:

=== "Raw doubles"

    ```cpp
    // Traditional approach - all heights are just doubles
    double h_mercury_m = 2.0;        // Height of mercury column
    double h_pump_rating_m = 10.0;   // Pump rated for water
    double sg_mercury = 13.6;        // Specific gravity

    // Direct addition - compiles but physically wrong!
    double total_head = h_mercury_m + h_pump_rating_m;  // 12 m - WRONG!
    // This treats 2 m of mercury as if it were 2 m of water

    // Correct calculation requires manual tracking:
    double h_mercury_as_water = h_mercury_m * sg_mercury;  // 27.2 m
    
    // Compare system requirement vs pump capacity
    if (h_mercury_as_water > h_pump_rating_m) {
      std::cout << "Pump is undersized!\n";  // This will trigger!
    }
    ```

=== "Boost.Units (C++)"

    ```cpp
    #include <boost/units/systems/si.hpp>
    
    using namespace boost::units;
    using namespace boost::units::si;
    
    quantity<length> h_mercury = 2.0 * meters;
    quantity<length> h_pump_rating = 10.0 * meters;
    double sg_mercury = 13.6;
    
    // Direct addition - compiles but physically wrong!
    quantity<length> total_head = h_mercury + h_pump_rating;  // WRONG!
    // Both are lengths, so Boost.Units allows this
    
    // Correct calculation still requires manual tracking:
    quantity<length> h_mercury_as_water = h_mercury * sg_mercury;
    
    // Compare system requirement vs pump capacity
    if (h_mercury_as_water > h_pump_rating) {
      std::cout << "Pump is undersized!\n";  // This will trigger!
    }
    ```
    
    **Problem**: Boost.Units checks dimensional compatibility (both are lengths), but cannot
    distinguish between physically incompatible types of length.

=== "Pint (Python)"

    ```python
    import pint
    ureg = pint.UnitRegistry()
    
    h_mercury = 2.0 * ureg.meter
    h_pump_rating = 10.0 * ureg.meter
    sg_mercury = 13.6
    
    # Direct addition - works but physically wrong!
    total_head = h_mercury + h_pump_rating  # WRONG!
    # Both have dimension [length], so Pint allows this
    
    # Correct calculation still requires manual tracking:
    h_mercury_as_water = h_mercury * sg_mercury
    
    # Compare system requirement vs pump capacity
    if h_mercury_as_water > h_pump_rating:
        print("Pump is undersized!")  # This will trigger!
    ```
    
    **Problem**: Pint prevents dimensional errors but cannot distinguish between different
    physical meanings of the same dimension.

The fundamental limitation: **Units libraries check dimensional compatibility
(_length_ + _length_ = OK), but cannot enforce that quantities with the same dimension
may represent incompatible physical concepts.** This is where **mp-units** breaks new
ground with its `is_kind` feature.

**Problems common to all these approaches:**

1. **No distinction**: Both _fluid head_ and _water head_ have the same dimensional type
   (_length_), making them indistinguishable to the type system
2. **Silent errors**: Adding incompatible _head_ types compiles successfully but produces
   physically nonsense results
3. **Manual tracking**: Programmers must remember which variables represent which type
   of _head_—the type system provides no help
4. **Comparison confusion**: `2 m < 10 m` numerically, but `2 m` of mercury represents
   far more _energy_ (and _pressure_) than `10 m` of water
5. **Easy to forget**: Forgetting the SG conversion factor leads to severely undersized
   equipment—a potentially catastrophic error in chemical plants

**Real-world scenario:**

A chemical plant pump system must:

- Handle mercury (SG = 13.6) from a 2 m column in a reactor vessel
- Verify a pump rated for 10 m _water head_ can handle this load
- Convert the mercury _fluid head_ to equivalent _water head_ for comparison
- Prevent accidentally mixing _fluid head_ and _water head_ values
- Require explicit conversion through _specific gravity_

**The challenge:** Both are _heights_ (dimension: _length_), but they're physically
incompatible without conversion through _specific gravity_.


## Your task

Implement a type-safe hydraulic head calculation system using **mp-units** that prevents
mixing fluid head and water head without explicit conversion.

Create:

1. **Distinct kinds**: Define `fluid_head` and `water_head` as separate kinds derived from
  `isq::height`
2. **Specific gravity type**: Define `specific_gravity` as a dimensionless `quantity_spec`
3. **Conversion functions**: Implement type-safe conversions between the two head types:
   - `to_water_head(h_fluid, sg)` — converts _fluid head_ to _water head_ using SG
   - `to_fluid_head(h_water, sg)` — converts _water head_ to _fluid head_ using SG

The solution should:

- Prevent direct addition or comparison of _fluid head_ and _water head_ (compile-time error)
- Require explicit conversion through _specific gravity_
- Use `QuantityOf` constraints for type safety
- Work with any units of _length_ (meters, feet, etc.)

```cpp
// ce-embed height=800 compiler=clang2110 flags="-std=c++23 -stdlib=libc++ -O3" mp-units=trunk
#include <mp-units/systems/si.h>
#include <iostream>

using namespace mp_units;

// TODO: Define fluid_head as a distinct kind derived from isq::height
// TODO: Define water_head as a distinct kind derived from isq::height
// TODO: Define specific_gravity as a dimensionless quantity_spec

// TODO: Implement to_water_head conversion function
// Formula: H_water = H_fluid * SG
// Hint: Return type should be QuantityOf<water_head> auto

// TODO: Implement to_fluid_head conversion function
// Formula: H_fluid = H_water / SG

int main()
{
  using namespace si::unit_symbols;

  // Scenario: Chemical reactor with 2m mercury column (SG = 13.6)
  quantity h_mercury = fluid_head(2 * m);
  quantity sg_mercury = specific_gravity(13.6 * one);

  // Pump rated for 10m water head
  quantity h_pump_rating = water_head(10 * m);

  std::cout << "Pump System Design Analysis\n";
  std::cout << "============================\n\n";

  std::cout << "Mercury column height: " << h_mercury << "\n";
  std::cout << "Mercury specific gravity: " << sg_mercury << "\n";
  std::cout << "Pump rating (water head): " << h_pump_rating << "\n\n";

  // Safety check: This should NOT compile!
  // quantity wrong = h_mercury + h_pump_rating;  // Error: cannot mix kinds

  // Convert mercury fluid head to equivalent water head
  quantity h_mercury_as_water = to_water_head(h_mercury, sg_mercury);
  
  std::cout << "Mercury equivalent (water head): " << h_mercury_as_water << "\n\n";

  // Verify pump capacity against system requirement
  if (h_mercury_as_water > h_pump_rating) {
    std::cout << "WARNING: System requirement (" << h_mercury_as_water 
              << ") exceeds pump rating (" << h_pump_rating << ")!\n";
    std::cout << "Pump is UNDERSIZED for this application.\n";
  }
  else {
    quantity excess_capacity = h_pump_rating - h_mercury_as_water;
    std::cout << "Pump capacity is adequate.\n";
    std::cout << "Excess capacity: " << excess_capacity << "\n";
  }

  // Demonstrate reverse conversion
  quantity h_back_to_fluid = to_fluid_head(h_mercury_as_water, sg_mercury);
  std::cout << "\nVerification - converted back: " << h_back_to_fluid << "\n";
}
```

??? "Solution"

    ```cpp
    #include <mp-units/systems/si.h>
    #include <iostream>

    using namespace mp_units;

    // 1. Define the distinct kinds (The Safety Layer)
    inline constexpr struct fluid_head final : quantity_spec<isq::height, is_kind> {} fluid_head;
    inline constexpr struct water_head final : quantity_spec<isq::height, is_kind> {} water_head;

    // 2. Define a type for Specific Gravity (Dimensionless)
    inline constexpr struct specific_gravity final : quantity_spec<dimensionless> {} specific_gravity;

    // 3. Define Conversion Helpers
    // Formula: H_water = H_fluid * SG
    constexpr QuantityOf<water_head> auto to_water_head(QuantityOf<fluid_head> auto h_fluid, 
                                                        QuantityOf<specific_gravity> auto sg)
    {
      // We explicitly cast the result to water_head because we know the physics is correct
      return water_head(isq::height(h_fluid) * sg);
    }

    // Formula: H_fluid = H_water / SG
    constexpr QuantityOf<fluid_head> auto to_fluid_head(QuantityOf<water_head> auto h_water, 
                                                        QuantityOf<specific_gravity> auto sg)
    {
      return fluid_head(isq::height(h_water) / sg);
    }

    int main()
    {
      using namespace si::unit_symbols;

      // Scenario: Chemical reactor with 2m mercury column (SG = 13.6)
      quantity h_mercury = fluid_head(2 * m);
      quantity sg_mercury = specific_gravity(13.6 * one);

      // Pump rated for 10m water head
      quantity h_pump_rating = water_head(10 * m);

      std::cout << "Pump System Design Analysis\n";
      std::cout << "============================\n\n";

      std::cout << "Mercury column height: " << h_mercury << "\n";
      std::cout << "Mercury specific gravity: " << sg_mercury << "\n";
      std::cout << "Pump rating (water head): " << h_pump_rating << "\n\n";

      // Safety check: This would NOT compile!
      // quantity wrong = h_mercury + h_pump_rating;  // Error: cannot mix kinds

      // Convert mercury fluid head to equivalent water head
      quantity h_mercury_as_water = to_water_head(h_mercury, sg_mercury);
      
      std::cout << "Mercury equivalent (water head): " << h_mercury_as_water << "\n\n";

      // Verify pump capacity against system requirement
      if (h_mercury_as_water > h_pump_rating) {
        std::cout << "WARNING: System requirement (" << h_mercury_as_water 
                  << ") exceeds pump rating (" << h_pump_rating << ")!\n";
        std::cout << "Pump is UNDERSIZED for this application.\n";
      }
      else {
        quantity excess_capacity = h_pump_rating - h_mercury_as_water;
        std::cout << "Pump capacity is adequate.\n";
        std::cout << "Excess capacity: " << excess_capacity << "\n";
      }

      // Demonstrate reverse conversion
      quantity h_back_to_fluid = to_fluid_head(h_mercury_as_water, sg_mercury);
      std::cout << "\nVerification - converted back: " << h_back_to_fluid << "\n";
    }
    ```

    **How the solution works:**

    By marking `fluid_head` and `water_head` with `is_kind`, we create distinct quantity types
    that cannot be mixed despite sharing the `length` dimension:

    - **Compile-time prevention**: Direct addition, comparison, or assignment between fluid head
      and water head results in a compile error
    
    - **Explicit conversion required**: The `to_water_head` and `to_fluid_head` functions
      perform the physics-based conversion through specific gravity, making the conversion
      visible and intentional in the code
    
    - **Type safety at boundaries**: Functions accepting `QuantityOf<fluid_head>` or
      `QuantityOf<water_head>` cannot accidentally receive the wrong type
    
    - **Base quantity access**: When needed, both can be converted to `isq::height` using
      `isq::height(h)`, allowing generic height operations while preserving type safety
      at domain boundaries

    This pattern is similar to how mp-units prevents mixing plane angles and solid angles—
    both dimensionless quantities that share the same dimension but represent fundamentally
    different physical concepts that cannot be meaningfully combined.


## References

- [User's Guide: Systems of Quantities](../users_guide/framework_basics/systems_of_quantities.md)
- [GitHub Discussion #757: Hydraulic Head](https://github.com/mpusz/mp-units/discussions/757)


## Takeaways

- **`is_kind` creates incompatible types**: Even when quantities share the same dimension,
  `is_kind` prevents mixing them without explicit conversion
- **Domain-specific safety**: Hydraulic engineering's distinction between _energy_ measurements
  in different reference frames (_fluid head_ vs _water head_) becomes a compile-time guarantee
- **Explicit conversions**: Physics-based conversions (through _specific gravity_) are visible
  and required in the code
- **Prevents subtle bugs**: The classic mistake of treating 2 m of mercury as 2 m of water
  becomes a compile error
- **Type system as documentation**: The code itself documents that these are different
  physical concepts requiring conversion
- **Similar to built-in protections**: Just as **mp-units** prevents mixing radians and
  steradians (_angular measure_ vs _solid angular measure_), your domain can have custom
  protections
- **Explicit base conversion when needed**: Both can convert to generic `isq::height` using
  `isq::height(h)` for algorithms that work on any _length_—but this requires an explicit
  conversion call; implicit conversion will fail to compile, preserving type safety at
  domain boundaries
- **Real-world safety**: Equipment undersizing due to _head_ calculation errors can be
  catastrophic in chemical plants—type safety prevents this
- **Pattern for other domains**: This technique applies anywhere quantities share dimensions
  but represent incompatible concepts—particularly _energy_ or _power_ measurements in
  different reference frames (e.g., _gauge_ vs _absolute pressure_, _RMS_ vs _peak voltage_,
  _true_ vs _apparent power_)