J. H. Williams. On the development of the algebra of funtcional programs. ACM Transactions on Programming Languages and Systems, 4(4):733 -- 757, October 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... axiomatic calculi allow to compute assertions on programs formalized through pre and postconditions, and inference rules are defined on individual syntactic units [53] In the last two decades, algebraic specification has frequently been used to study denotational semantics of functional [6, 55] and imperative [7] languages. Algebraic specification languages inherently provide algebraic semantics and thus mathematical objects denoting syntactical constructs (c.f. 8, 27, 21, 12, 5, 57, 25] Algebraic semantics are also used in the field of abstract state machines to formalize the ....

J. H. Williams. On the development of the algebra of funtcional programs. ACM Transactions on Programming Languages and Systems, 4(4):733 -- 757, October 1982.

....that, according to the FP style, we are manipulating functions and not objects. Thus in general, the function variables used in equations stand for arbitrary functional forms which greatly extends the applicability of laws. 4 Optimization The existence of an algebra of programs [Bac78, Bac85, Wil82] is founded on the combining forms being the only means for constructing programs and queries. This algebra can be used to reason about programs, and we will describe part of it by giving several equations containing combining forms and function variables. Apart from the laws defining the algebra ....

....giving several equations containing combining forms and function variables. Apart from the laws defining the algebra of programs, there are derived rules (identities that can be inferred directly from the laws) and theorems (giving nonrecursive definitions for recursively defined functions, see [Wil82, KS81] for details) It has turned out that derived rules are suited best for our purpose. The completeness of a set of rules can be judged from three different points of view: First, a complete set of rules in the sense that it explicitly contains all valid rules is impossible to give since ....

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WILLIAMS, J.H.: on the Development of the Algebra of Functional Programs, ACM Transactions on Programming Languages and Systems Vol. 4, No. 4, 1982, pp. 733-757.

....a FARM leaves many implementation issues still to be resolved, in particular whether the environment is to be accessed remotely or passed to each processor. An inter skeleton transformation which relies heavily on fine tuning is DC to PIPE. By assuming that an application of DC is overrun tolerant[19], we can obtain the equivalence[18] 6] map ( DC t s d c ) j PIPE ( rept q ( map n c ) map s . PIPE ( rept q ( foldr1 ( map d ) rept : Int ff [ff] rept n = take n . repeat map : Int ( ff] fi) ff] fi] map n f xs j length xs n = f ( take n xs ) map n f ( drop ....

J.H. Williams, On the Development of the Algebra of Functional Programs, ACM Transactions on Programming Languages and Systems vol. 4, pp. 733-57, 1982.

....The Backus Naur Form (bnf) Bac59, N 60] originally developed for the definition of the syntax of Algol, is a commonly used notation for context free grammars, but it does not have the status of a standard. Several standard notations for syntax definition have been proposed [Wir77, Wil82] None of these has been convincing, instead a number of similar or overlapping formalisms exist. Proceedings of ASF SDF95. A workshop on Generating Tools from Algebraic Specifications. May 11 12, 1995, CWI, Amsterdam, M.G.J. van den Brand, A. van Deursen, T.B. Dinesh, J.F.Th. Kamperman E. ....

....production has the form A : A 0 j : jAn , where j has the meaning of or. Extended bnf (ebnf) is the canonical extension of bnf with regular operators. In one formulation, Wirth [Wir77] adds the operators fAg for iteration and [A] for optionality. Variations on this notation appear in [Lee72, Wil82] Sdf provides Kleene iteration A and A and fA Lg Phi iteration for abbreviation of lists of A s separated by a literal L. In this section we give an extension of context free productions by a set of regular operators on symbols. In all the approaches mentioned above regular operators are ....

M. H. Williams. A flexible notation for syntactic definitions. ACM Transactions on Programming Languages and Systems, 4(1):113--119, 1982.

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