Algebraic Data Type¶
An algebraic data type is a composite type built by combining simpler types through two fundamental operations: product and sum.
A product type holds values of several types simultaneously, connected by AND. Every field is always present. A struct, record, or tuple is a product type: { name: string, age: int } means a name AND an age, always both.
A sum type holds a value of exactly one of several alternatives, connected by OR. Only one case is active at a time, and each case may carry different data. Circle(Float) | Rectangle(Float, Float) means either a circle, with a radius, or a rectangle, with two sides, never both at once.
Full ADT systems pair sum types with exhaustive pattern matching: the compiler enforces that every case is handled, turning incomplete switches into compile-time errors.
PHP supports product types natively through classes and arrays. Sum types are approximated by union types int|string and by enums, but neither carries associated data per variant, and match does not perform exhaustive structural decomposition over union type values.
PHP does not support true ADT.
See also Algebraic data types in Wikipedia and ADTs in PHP: an approximation guide.
Related : Sum Type, Generalized Algebraic Data Type (GADT), Union Type, Enumeration (enum), Intersection Type, Pattern Matching, Type System, Generics
