Programming paper: The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new constructors, such as by adding a new object implementin...

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Researchers present an algorithmic type system and unification algorithm for Polarity, a dependently typed language that treats inductive (data) and coinductive (codata) types symmetrically. The work addresses the expression problem by enabling both pattern matching extensibility and interface-based extensibility while adding support for implicit arguments. The paper provides comprehensive algorithms for reduction semantics, conversion checking, and pattern-matching unification that maintain the language's core symmetry between data and codata types.

Filling the Gaps of Polarity: Implementing Dependent Data and Codata Types with Implicit Arguments