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... -calculus. Second, we assume that the following three languages are purely functional: the languagesthat extends the call-by-name -calculus with numbers and addition, and the languages PCF and PPCF (=-=Plotkin, 1977-=-). These assumptions may be challenged but they appear to be consistent with the informal practice. Finally, two of the informal definitions of purity: referential transparency and independence of ord...

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...nceptual. 5.2 Effects as Monadic Operations One of the fundamental properties of continuation-passing style (CPS) terms is that they are independent of the parameter-passing technique (Plotkin, 1975; =-=Reynolds, 1972-=-). This suggests a way to embed computational effects in a purely functional language: force all the imperative parts of the program to be written in CPS or the closely related effect-passing style (E...

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...ce of computational effects in all realistic functional languages, Scheme and SML have an intuitively different character from Haskell. Indeed, Haskell is referred to as a purely functional language (=-=Hudak et al., 1992-=-; Peterson et al. , 1996) to distinguish its treatment of computational effects from the Scheme and SML treatment. Attempts to explain why Haskell is purer than Scheme and SML usually lead to confusio...

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...tic values, have a trivial evaluation, and are allowed to be duplicated and hence re-evaluated several times. Definition 4.1 (Syntactic Value) In , the following subset of terms are syntactic values (=-=Plotkin, 1975-=-): V ::= n j x:M Definition 4.2 The call-by-need evaluator is defined (Ariola et al., 1995; Ariola & Felleisen, 1996) as follows: eval z (M ) = B if M 7\Gamma! A and obs(A) = B, where: Answers A ::= V...

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...The first group G 1 includes C and is Church-Rosser because the reduction forms an orthogonal combinatory reduction system (Klop et al., 1993). The second group G 2 includes fi which is ChurchRosser (=-=Barendregt, 1984-=-). The third group G 3 includes the remaining reductions S and A and is Church-Rosser because the reflexive closure of the reductions satisfies the diamond property (Barendregt, 1984, Ch.3). The resul...

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...nguage like Scheme, it is straightforward to devise a call-by-need or call-by-name evaluator. However, starting from a call-by-name language likes! or Idealized Algol (Reynolds, 1991; Reynolds, 1981; =-=Reynolds, 1988-=-), the design of the call-by-value or call-by-need variant first requires setting a notion of syntactic value. This latter decision affects the purity of the language. Indeed, as we will see in the ne...

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...tational effects in a purely functional language: force all the imperative parts of the program to be written in CPS or the closely related effect-passing style (EPS) based on monads (Filinski, 1994; =-=Filinski, 1996-=-; Wadler, 1990). Intuitively, both CPS and EPS require programmers to explicitly sequence the imperative operations, and hence remove any ambiguity associated with the parameter-passing mechanism. A n...

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... in a purely functional language: force all the imperative parts of the program to be written in CPS or the closely related effect-passing style (EPS) based on monads (Filinski, 1994; Filinski, 1996; =-=Wadler, 1990-=-). Intuitively, both CPS and EPS require programmers to explicitly sequence the imperative operations, and hence remove any ambiguity associated with the parameter-passing mechanism. A naive implement...

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...ky et al., 1993), referential transparency (Launchbury & Peyton Jones, 1995), the confluence of a calculus for the language (Swarup et al., 1991), the preservation of pure observational equivalences (=-=O'Hearn, 1995-=-), and the independence of order of evaluation (Launchbury & Peyton Jones, 1995). The investigation of a formal definition of purity goes beyond settling some differences in opinion. It is crucial at ...

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...Starting from a callby -value language like Scheme, it is straightforward to devise a call-by-need or call-by-name evaluator. However, starting from a call-by-name language likes! or Idealized Algol (=-=Reynolds, 1991-=-; Reynolds, 1981; Reynolds, 1988), the design of the call-by-value or call-by-need variant first requires setting a notion of syntactic value. This latter decision affects the purity of the language. ...

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...y to embed computational effects in a purely functional language: force all the imperative parts of the program to be written in CPS or the closely related effect-passing style (EPS) based on monads (=-=Filinski, 1994-=-; Filinski, 1996; Wadler, 1990). Intuitively, both CPS and EPS require programmers to explicitly sequence the imperative operations, and hence remove any ambiguity associated with the parameter-passin...

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...tion is stuck if the term rewriting machine has no transition from that term. In the remainder of this paper, we will be study the languagesand its extensions. Definition 2.6 (Conservative Extension (=-=Felleisen, 1991-=-)) A language L 1 conservatively extends a language L 2 if: What is a Purely Functional Language? 5 ffl the set of L 1 -terms (programs) includes the set of L 2 -terms (programs), ffl the of L 1 -obse...

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...callby -value language like Scheme, it is straightforward to devise a call-by-need or call-by-name evaluator. However, starting from a call-by-name language likes! or Idealized Algol (Reynolds, 1991; =-=Reynolds, 1981-=-; Reynolds, 1988), the design of the call-by-value or call-by-need variant first requires setting a notion of syntactic value. This latter decision affects the purity of the language. Indeed, as we wi...