Inheritance

didactic supports both single and multiple inheritance. The Theory derivation handles each in a different way:

• Single inheritance flattens the field set. The metaclass walks the MRO when collecting field specs, so class B(A) simply has every field from A plus its own.
• Multi inheritance triggers a panproto colimit (pushout) of the parent Theories over their lowest common ancestor.

Single inheritance

import didactic.api as dx


class A(dx.Model):
    x: int


class B(A):
    y: int


b = B(x=1, y=2)
b.x      # 1
b.y      # 2

B.__field_specs__ contains both x and y. B.__theory__ is the flat Theory built from the merged spec; no colimit is involved.

Inherited axioms (__axioms__) are also collected: B is checked against both its own and A's.

Multi inheritance

class Shared(dx.Model):
    id: str


class Reads(Shared):
    read_count: int = 0


class Writes(Shared):
    write_count: int = 0


class Both(Reads, Writes):
    note: str = ""

When Both's Theory is built, didactic walks Both's immediate parents (Reads and Writes), finds their lowest common ancestor in the Model lineage (Shared), and computes the colimit:

panproto.colimit_theories(Reads.__theory__, Writes.__theory__, Shared.__theory__)

The result is the categorical pushout. panproto validates that the join is consistent (the shared sub-theory's sorts and operations appear with the same shape in both parents).

For three or more parents, the colimit is computed left-to-right. The end result is the same panproto Theory you would get by listing all the fields on Both directly, but going through colimit_theories asserts that the parents' Theories are compatible at the categorical level.

What goes wrong, and how

A multi-inheritance setup that produces an inconsistent join surfaces as a panproto.GatError at first __theory__ access (which is typically your first interesting use of the class). Common causes:

• Two parents declaring fields with the same name but different types. didactic catches this earlier as a Python-side metaclass error, but a panproto-side variant can still surface for richer shapes.
• Two parents with conflicting axioms. The colimit refuses to merge contradictory equations.

If you see a GatError, the message names the offending sort or equation; the fix is usually to factor the conflict into a common ancestor or to drop one branch.