definefunrec

definefunrec is a construct used in some formal languages and tooling to declare recursive functions or predicates in a single declaration block. It is designed to express self-referential definitions, allowing a function or relation to be defined in terms of itself, often together with one or more non-recursive base cases.

In practice, definefunrec appears most prominently in the fixed-point or recursive definition facilities of certain theorem provers and SMT (satisfiability modulo theories) solvers. The idea is to specify a symbol, its argument types, and one or more defining equations that may reference the symbol itself. When multiple definitions are allowed, mutual recursion can be expressed, enabling the encoding of complex properties such as reachability, transitive closure, or recursive numerical relations. The solver then treats the collection of equations as defining a least-fixpoint or similar fixpoint semantics, solving by unfolding the recursion as needed during reasoning.

A typical usage pattern involves providing a base case and one or more recursive cases. For example, a recursive function such as factorial can be informally defined with fact(n) equal to 1 when n is at most 1, and equal to n times fact(n minus 1) otherwise. More complex cases can define mutually recursive predicates, such as a pair of relations that reference each other, to model graph reachability or inductive properties.

Compatibility and limitations vary by tool. Not all languages or solvers support definefunrec, and those that do may impose termination or well-foundedness requirements, or require fixed-point interpretation. When supported, definefunrec offers a compact, declarative way to encode recursive reasoning within a formal proof or verification workflow. See also fixed-point logic, define-fun, and mutual recursion.