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A type whose values are described by named data constructors with specified fields. For example, data Tree a = One a | Two (Tree a) (Tree a) describes a leaf-labelled binary tree. Its two alternatives are distinguished by pattern matching; the recursive fields give a recursive type.

The occurs check tests whether a type variable occurs inside the expression proposed as its replacement during type unification. After discarding a trivial equation such as $\alpha =\alpha$, solving $\alpha =\tau$ by a type substitution requires that $\alpha$ not occur in $\tau$. Thus $\alpha =\mathrm{int}\to \beta$ is permitted when $\alpha$ and $\beta$ are distinct, but $\alpha =\alpha \to \beta$ is rejected in our finite simple type grammar.

There is a short reason for the rejection. If a finite replacement $T$ for $\alpha$ existed, with replacement $B$ for $\beta$, the equation would become $T=T\to B$. The right side's abstract syntax tree has one new arrow node plus the nodes of $T$ and $B$, so it has strictly more nodes than $T$. Equal finite type expressions cannot have different sizes. Recursive types are a different design: they explicitly describe self-reference and specify how it interacts with typing judgments.

A recursive type explicitly names a type in terms of itself. Notation $\mu \alpha .\tau$ binds $\alpha$ within $\tau$. A programming language must specify whether unfolding gives type equality or requires explicit operations; this is outside the finite simple type grammar used here. See Benjamin C. Pierce's treatment of recursive types in chapters 20–21. ^[ref]