[reaanb2]

"Object-relational mapper" is a misnomer, they should be called network data model to SQL mappers. They're not primarily for mapping between different arrangements of the same data, but about recreating a network data model perspective. How many ORMs support composite primary keys and non-binary relationships?

As you said, the challenge of understanding math is why the relational vision failed, but also why the industry keeps reviving the network data model.

[9rx]

> How many ORMs support composite primary keys and non-binary relationships?

Theoretically all. However, often ORM and query building are combined into a unified framework that links them together into a higher order abstraction. You may know this type of thing by names like the active record pattern or the data mapper pattern, with concrete implementations like ActiveRecord and Entity Framework. Such frameworks often make it difficult to use the ORM component in isolation (and even where that isn't the case, doing so largely defeats the purpose of using the framework anyway), and as such you become constrained by the limits of the query builder. I suspect that is what you are really thinking of.

[reaanb2]

EF is limited to binary relationships: https://learn.microsoft.com/en-us/ef/core/modeling/relations.... When entities are mapped to rows and relationships to foreign key constraints, it results in a network data model interpretation of SQL databases. The relational model is better conceptualized from a fact-oriented modeling perspective, in which entities map to values, domains to FK constraints, relationships to the association of two or more entity sets in a table, and rows represent propositions about entities rather than entities themselves. However, non-binary relationships don't easily translate into navigational data access (cf. Bachman's paper "The programmer as navigator" about the network data model) and a logical view is difficult for the non-mathematical programmer, while structs and pointers are naïvely easy to understand, that's why ORMs remain popular. The impedance mismatch is less about mapping flat to rich data structures than about the network data model vs fact-oriented perspectives and row-at-a-time vs batch data access.