This paper proposes an operational semantics for value recursion in the context of monadic metalanguages. Our technique for combining value recursion with computational effects works uniformly for all monads. The operational nature of our approach is related to the implementation of recursion in Scheme and its monadic version proposed by Friedman and Sabry, but it defines a different semantics and does not rely on assignments. When contrasted to the axiomatic approach proposed by Erkök and Launchbury, our semantics for the continuation monad invalidates one of the axioms, adding to the evidence that this axiom is problematic in the presence of continuations. 1

Certain programs making use of monads need to perform recursion over the values of monadic actions. Although the do-notation of Haskell provides a convenient framework for monadic programming, it lacks the generality to support such recursive bindings. In this paper, we describe an enhanced translation schema for the donotation and its integration into Haskell. The new translation allows variables to be bound recursively, provided the underlying monad comes equipped with an appropriate fixed-point operator.

Abstract. Monads have been employed in programming languages for modeling various language features, most importantly those that involve side effects. In particular, Haskell’s IO monad provides access to I/O operations and mutable variables, without compromising referential transparency. Cyclic definitions that involve monadic computations give rise to the concept of value-recursion, where the fixed-point computation takes place only over the values, without repeating or losing effects. In this paper, we describe a semantics for a lazy language based on Haskell, supporting monadic I/O, mutable variables, usual recursive definitions, and value recursion. Our semantics is composed of two layers: A natural semantics for the functional layer, and a labeled transition semantics for the IO layer. Mathematics Subject Classification. 68N18, 68Q55, 18C15.

Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a well-known theorem relating traces and Conway operators in cartesian categories.

Abstract. Stream-based programming has been around for a long time, but it is typically restricted to static data-flow networks. By introducing first-class streams that implement the monad interface, we can describe arbitrary dynamic networks in an elegant and consistent way using only two extra primitives besides the monadic operations. This paper presents an efficient stream implementation and demonstrates the compositionality of the constructs by mapping them to functions over natural numbers. 1

We introduce a monadic metalanguage which combines two previously proposed monadic metalanguages: one for staging and the other for value recursion. The metalanguage includes also extensible records as a basic name management facility. 1

Abstract. With the aim of putting type-based reasoning for functional logic languages, as recently explored by Christiansen et al. (2010), on a formal basis, we develop a denotational semantics for a typed core language of Curry. Dealing with the core language FlatCurry rather than with full Curry suffices, since there exists a type-preserving translation from the latter into the former. In contrast to existing semantics for functional logic languages, we deliberately approach the problem “from the functional side”. That is, rather than adapting approaches previously known from the study of (resolution-like) semantics for logic languages, we aim for a semantics in the spirit of standard denotational semantics for the polymorphic lambda calculus. We claim and set out to prove that the presented semantics is adequate with respect to an existing operational semantics. A particularly interesting aspect, we think, is that we give the first denotational treatment of recursive let-bindings in combination with call-time choice. 1

Forschungsberichte sind erhältlich durch: Technical reports can be requested from:

We investigate evaluation strategies for ML-style modules supporting recursion. More precisely we propose and examine five evaluation strategies: a call-by-value strategy and four call-by-need strategies with different degrees of laziness. We formalize the strategies by translating a source syntax for modules into target languages, which are very much inspired by Felleisen and Hieb’s callby-value lambda calculus with state and Ariola and Felleisen’s call-by-need cyclic lambda calculus. Different strategies are expressed by tweaking the translation as well as the operational semantics of the target languages. We look at the strategies through a series of examples and state inclusion between the strategies. 1