Delimiting the Scope of Eeects

Program fragments in functional languages may be observationally congruent in a language without eeects (continuations, state, exceptions) but not in an extension with eeects. We give a generic way to preserve pure functional congruences by means of an eeects delimiter. The eeects delimiter is deened semantically using the retraction techniques of 14], but can also be given an operational semantics. We show that the eeects delim-iter restores observational congruences between purely functional pieces of code, thus achieving a modular separation between the purely functional language and its extensions. 1 Introduction Functional programming is a powerful paradigm, but it has long been recognized that purely functional programs are often ineecient and cumbersome. Many modern functional languages, e.g., SML 9], build in control and state features that strictly fall outside the functional paradigm. For example, SML of New Jersey includes a \call-with-current-continuation" operation callcc, an exception-handling mechanism, and the ability to manipulate state using references, assignment, and deref-erencing operations. The extensions are not simple extensions of underlying semantics of the language: old equivalences between pieces of code not involving the new constructs may fail to be correct in the extension. In order to make the discussion more concrete, consider a call-by-value version of the simply-typed programming language PCF. Call-by-value PCF|VPCF for short|is a functional language with numerals, basic arithmetic operations, recursion, and a conditional test for zero. Section 2 describes the full language for those unfamiliar with the syntax and operational semantics of VPCF. In essence, VPCF is a simpliied form of the purely functional fragment of SML.