In a programming language with procedures and assignments, it is often important to isolate uses of state to particular program fragments. The frameworks of type, region, and effect inference, and monadic state are technologies that have been used to state and enforce the property that an expression has no visible side-effects. This property has been exploited to justify the deallocation of memory regions despite the presence of dangling pointers. Starting from an idea developed in the context of monadic state in Haskell, we develop an ML-like language with full assignments and an operator that enforces the encapsulation of effects. Using this language, we formalize and prove the folklore connection between effect masking and monadic encapsulation. Then, by employing a novel set of reductions to deal with dangling pointers, we establish the soundness of the type-based encapsulation with a proof based on a standard subject reduction argument. 1 Introduction Two of the recurring theme...

This paper proposes a non-standard way to combine lazy functional languages with I/O. In order to demonstrate the usefulness of the approach, a tiny lazy functional core language “FUNDIO”, which is also a call-by-need lambda calculus, is investigated. The syntax of “FUNDIO ” has case, letrec, constructors and an IO-interface: its operational semantics is described by small-step reductions. A contextual approximation and equivalence depending on the input-output behavior of normal order reduction sequences is defined and a context lemma is proved. This enables to study a semantics of “FUNDIO ” and its semantic properties. The paper demonstrates that the technique of complete reduction diagrams enables to show a considerable set of program transformations to be correct. Several optimizations of evaluation are given, including strictness optimizations and an abstract machine, and shown to be correct w.r.t. contextual equivalence. Correctness of strictness optimizations also justifies correctness of parallel evaluation. Thus this calculus has a potential to integrate non-strict functional programming with a non-deterministic approach to input-output and also to provide a useful semantics for this combination. It is argued that monadic IO and unsafePerformIO can be combined in Haskell, and that the result is reliable, if all reductions and transformations are correct w.r.t. to the FUNDIO-semantics. Of course, we do not address the typing problems the are involved in the usage of Haskell’s unsafePerformIO. The semantics can also be used as a novel semantics for strict functional languages with IO, where the sequence of IOs is not fixed.

This paper proves several generic variants of context lemmas and thus contributes to improving the tools for observational semantics of deterministic and non-deterministic higher-order calculi that use a small-step reduction semantics. The generic (sharing) context lemmas are provided for may- as well as two variants of must-convergence, which hold in a broad class of extended process- and extended lambda calculi, if the calculi satisfy certain natural conditions. As a guide-line, the proofs of the context lemmas are valid in call-by-need calculi, in call-by-value calculi if substitution is restricted to variable-by-variable and in process calculi like variants of the π-calculus. For calculi employing beta-reduction using a call-by-name or call-by-value strategy or similar reduction rules, some iu-variants of ciu-theorems are obtained from our context lemmas. Our results reestablish several context lemmas already proved in the literature, and also provide some new context lemmas as well as some new variants of the ciu-theorem. To make the results widely applicable, we use a higher-order abstract syntax that allows untyped calculi as well as certain simple typing schemes. The approach may lead to a unifying view of higher-order calculi, reduction, and observational equality.

Region-based memory management is a scheme for managing dynamically allocated data. A defining characteristic of region-based memory management is the bulk deallocation of data, which avoids both the tedium of malloc/free and the overheads of a garbage collector. Type systems for region-based memory manag-ment enhance the utility of this scheme by statically determining when a program is guaranteed to not perform any erroneous region operations. We describe three type systems for region-based memory management: • a type-and-effect system (à la the Tofte-Talpin region calculus); • a novel monadic type system; • a novel substructural type system. We demonstrate how to successively encode the type-and-effect system into the monadic type system and the monadic type system into the substructural type system. These type systems and encodings support the argument that the type-and-effect systems that have traditionally been used to ensure the safety of region-based memory management are neither the simplest nor the most expressive type

Abstract. In this paper we analyze the semantics of a higher-order functional language with concurrent threads, monadic IO and synchronizing variables as in Concurrent Haskell. To assure declarativeness of concurrent programming we extend the language by implicit, monadic, and concurrent futures. As semantic model we introduce and analyze the process calculus CHF, which represents a typed core language of Concurrent Haskell extended by concurrent futures. Evaluation in CHF is defined by a small-step reduction relation. Using contextual equivalence based on may- and should-convergence as program equivalence, we show that various transformations preserve program equivalence. We establish a context lemma easing those correctness proofs. An important result is that call-by-need and call-by-name evaluation are equivalent in CHF, since they induce the same program equivalence. Finally we show that the monad laws hold in CHF under mild restrictions on Haskell’s seq-operator, which for instance justifies the use of the do-notation. 1