In this rewritten article we explore algebraic data types and codata types in the Fun and Core languages, translating and adapting the content for Spanish-speaking audiences. Algebraic data types, or ADTs, are inductive structures built from constructors that combine values, while codata represent potentially infinite structures described through destructors or observers. This duality is fundamental for reasoning about programs that produce data and programs that consume it.
A key distinction is made between pattern matching and copattern matching. Pattern matching is the classic mechanism for inspecting and decomposing values built by constructors, useful for finite, inductively defined types. In contrast, copattern matching proposes a dual view: a value is defined by the operations that allow observing it, that is, by its destructors. This approach is natural for codata such as infinite streams or lazy structures that are defined by how they can be queried.
In the design of Core, a complete symmetry is achieved between constructors and destructors, and between producers and consumers. This symmetry unifies the treatment of data and codata, allowing both the construction of values and their observation to be expressed uniformly. Thanks to this approach, concepts such as lazy evaluation or infinite flow are elegantly integrated into the same theoretical framework as classical algebraic types.
Illustrative examples help understand the practical advantage. An infinite stream can be defined as a codatum whose destructors return the head and the tail; the tail in turn is another stream. The construction of streams uses copatterns to specify exactly how their components are observed, and the Core engine guarantees consistency with lazy semantics. Lazy evaluation is another manifestation: values can be exposed through destructors that evaluate components only when observed, avoiding unnecessary computations and allowing infinite flows to be modeled safely.
Another simple example is the swap function that exchanges components in a pair or tuple. From the perspective of producers and consumers, swap can be seen both as a producer that generates a new pair with the order changed, and as a transformer that redefines the destructors to present the pair in reverse order. This dual reading shows the power of symmetry in Core and facilitates optimizations and formal reasoning about code.
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