Mixin Modules and Computational Effects

Abstract

We define a calculus for investigating the interactions between mixin modules and computational effects, by combining the purely functional mixin calculus CMS with a monadic metalanguage supporting the two separate notions of simplification (local rewrite rules) and computation (global evaluation able to modify the store). This distinction is important for smoothly integrating the CMS rules (which are all local) with the rules dealing with the imperative features. In our calculus mixins can contain mutually recursive computational components which are explicitly computed by means of a new mixin operator whose semantics is defined in terms of a Haskell-like recursive monadic binding. Since we mainly focus on the operational aspects, we adopt a simple type system like that for Haskell, that does not detect dynamic errors related to bad recursive declarations involving effects. The calculus serves as a formal basis for defining the semantics of imperative programming languages supporting first class mixins while preserving the CMS equational reasoning.

Modules as Objects in Newspeak

“…Mixin modules ( [8,7,25]) are closely related to the ideas of Jigsaw [14]. Mixin modules compose via inheritance-like operators and naturally support mutual recursion.…”

An abstract monadic semantics for value recursion

“…In special cases [AFMZ02] it is possible to simplify (M.2) by treating X as a stack and enforcing the invariant that FV(E) = ∅, but our aim is an operational semantics that works with arbitrary computational effects. Indeed in the case of continuations (Section 6), neither of these invariants holds.…”

Call-by-Value Mixin Modules

“…In a more recent calculus [1], Ancona et al do distinguish mixins from modules. They propose to handle side effects using monadic operators.…”

“…-Anonymous definitions: Our system features anonymous definitions, that is, definitions that are evaluated, but not exported as components of the final module. 1 The translation-based semantics cannot handle anonymous definitions, because it is type-directed and anonymous definitions do not appear in mixin types.…”