Functional logic programming and probabilistic programming have demonstrated the broad benefits of combining laziness (non-strict evaluation with sharing of the results) with non-determinism. Yet these benefits are seldom enjoyed in functional programming, because the existing features for non-strictness, sharing, and nondeterminism in functional languages are tricky to combine. We present a practical way to write purely functional lazy non-deterministic programs that are efficient and perspicuous. We achieve this goal by embedding the programs into existing languages (such as Haskell, SML, and OCaml) with high-quality implementations, by making choices lazily and representing data with non-deterministic components, by working with custom monadic data types and search strategies, and by providing equational laws for the programmer to reason about their code.

The call-by-need lambda calculus provides an equational framework for reasoning syntactically about lazy evaluation. This paper examines its operational characteristics. By a series of reasoning steps, we systematically unpack the standard-order reduction relation of the calculus and discover a novel abstract machine definition which, like the calculus, goes “under lambdas. ” We prove that machine evaluation is equivalent to standard-order evaluation. Unlike traditional abstract machines, delimited control plays a significant role in the machine’s behavior. In particular, the machine replaces the manipulation of a heap using store-based effects with disciplined management of the evaluation stack using control-based effects. In short, state is replaced with control. To further articulate this observation, we present a simulation of call-by-need in a call-by-value language using delimited control operations.

Abstract. We propose type systems that abstractly interpret small-step rather than big-step operational semantics. We treat an expression or evaluation context as a structure in a linear logic with hypothetical reasoning. Evaluation order is not only regulated by familiar focusing rules in the operational semantics, but also expressed by structural rules in the type system, so the types track control flow more closely. Binding and evaluation contexts are related, but the latter are linear. We use these ideas to build a type system for delimited continuations. It lets control operators change the answer type or act beyond the nearest dynamically-enclosing delimiter, yet needs no extra fields in judgments and arrow types to record answer types. The typing derivation of a directstyle program desugars it into continuation-passing style. 1

Abstract. A constraint programming system combines two essential components: a constraint solver and a search engine. The constraint solver reasons about satisfiability of conjunctions of constraints, and the search engine controls the search for solutions by iteratively exploring a disjunctive search tree defined by the constraint program. The Monadic Constraint Programming framework gives a monadic definition of constraint programming where the solver is defined as a monad threaded through the monadic search tree. Search and search strategies can then be defined as firstclass objects that can themselves be built or extended by composable search transformers. Search transformers give a powerful and unifying approach to viewing search in constraint programming, and the resulting constraint programming system is first class and extremely flexible. 1