Lightweight monadic programming in ML

Abstract

Many useful programming constructions can be expressed as monads. Examples include probabilistic modeling, functional reactive programming, parsing, and information flow tracking, not to mention effectful functionality like state and I/O. In this paper, we present a type-based rewriting algorithm to make programming with arbitrary monads as easy as using ML's built-in support for state and I/O. Developers write programs using monadic values of type m τ as if they were of type τ, and our algorithm inserts the necessary binds, units, and monad-to-monad morphisms so that the program type checks. Our algorithm, based on Jones' qualified types, produces principal types. But principal types are sometimes problematic: the program's semantics could depend on the choice of instantiation when more than one instantiation is valid. In such situations we are able to simplify the types to remove any ambiguity but without adversely affecting typability; thus we can accept strictly more programs. Moreover, we have proved that this simplification is efficient (linear in the number of constraints) and coherent : while our algorithm induces a particular rewriting, all related rewritings will have the same semantics. We have implemented our approach for a core functional language and applied it successfully to simple examples from the domains listed above, which are used as illustrations throughout the paper.

Polymonad programming in Haskell

“…Swamy et al [42] previously worked on automatically inserting bind and return operations into programs as necessary. This allows a programmer to mix pure and monadic computations without having to explicitly lift values or mechanically insert bind operations.…”

Verifying higher-order programs with the dijkstra monad

“…The v : choice of monad M is left as a parameter in the system, except that it must be indexed by both a result type t' and a predicate transformer φ . By restricting monadic types to the co-domain of functions only, we borrow an insight from Swamy et al (2011b), who use a similar restriction to develop a type inference algorithm for monadic ML. We generalize their work to the setting of a dependently typed language.…”

The sequential semantics of producer effect systems

“…For example, information-flow effect systems [29] and contextual effects [21] do not meet the requirements of Theorem 4 and so cannot be formalized using parameterized monads. Interestingly, though, should we allow EFF for E S,≤ to be just a subset of S × S rather than all pairs of states, then we can represent information-flow effect systems and contextual effects.…”

“…Interestingly, though, should we allow EFF for E S,≤ to be just a subset of S × S rather than all pairs of states, then we can represent information-flow effect systems and contextual effects. For example, in [29] the states are levels of secrecy, so EFF contains only those pairs s, s where s is a lower level of secrecy than s , since inputs can be propagated to outputs. Thus, Theorem 4 suggests such effect systems must be formalizable by something very similar to a parameterized monad.…”