Monadsat

Monadsat is a theoretical construct in functional programming and formal methods that fuses the monad abstraction with embedded satisfiability checking. The term appears in discussions of constraint-aware computation to describe a monad that threads logical constraints through a computation and seeks a model that satisfies them. It is not a standard, widely implemented formalism but a conceptual bridge between monadic sequencing and constraint solving.

In a Monadsat design, a computation of type M a represents a value of type a together with a set of constraints that must hold. The interface extends typical monad operations with constraint management, including a way to add constraints and an operation to attempt a satisfiability check, often called runSAT or solve, which yields either a satisfying model or indicates infeasibility.

Semantics are defined so that bind propagates the current constraint set, and the embedded SAT solver is invoked to prune branches and search for assignments compatible with subsequent computations. This approach allows expressing choices and dependencies among variables while ensuring that only satisfiable paths are explored.

Implementation can be realized as a monad transformer that layers a constraint-solving component on top of an underlying monad such as Maybe, List, or IO. It draws on ideas from constraint monads and logic programming, and can be oriented toward pure functional or effectful settings.

Applications include program synthesis, planning under constraints, symbolic execution, and formal verification. Criticisms focus on practicality, solver integration complexity, and the lack of a standardized semantics or library support.

See also monad, constraint monad, SAT solver, monad transformer, constraint programming.