Christopher Wadsworth, Semantics and Pragmatics of the Lambda Calculus, Ph.D. Thesis, Oxford University, 1971.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....format can be given a dependent type, since the type of the returned function depends upon the value of the string argument. 43 A. The LP program A.1. Data structures and algorithms The core of the LP program is a reduction engine for typed X terms. Terms are represented as graphs, much as in [Wadsworth 1971], and reduction is performed by a closure based algorithm similar to that of [Aiello Prini 1981] Once reduction is implemented, it is a simple matter to implement a type derivation algorithm that computes the type, if any, of an arbitrary term. Due to the type conversion (tc) rule, the proof ....

Christopher P. Wadsworth. Semantics and Pragmatics of the Lambda-Calculus. Ph.D. thesis, Oxford University, 1971.

.... for term graphs (such as in some functional programming languages) often use names bound by e.g. where clauses to express sharing; this kind of binding is perceived as different from that introduced by l abstractions as represented in term graphs e.g. by Wadsworth, the inventor of graph reduction [12], the difference being that the names bound by where clauses do not appear in the graph, but those bound by l abstractions do. In previouswork [3]we took the step to consider both uses of bound variable names only as coding of structure that can be made explicit with an appropriate definition of ....

Christopher Peter Wadsworth. Semantics and Pragmatics of the Lambda Calculus. Ph.D. thesis, Oxford University, September 1971.

....has to be considered. In the term t 1 : x : y , the variable x is not a subterm of t 1 ; the only nontrivial subterm is y . Therefore, in the tree representation there should be no node representing x . x y One way to achieve this was already used by Wadsworth, the inventor of graph reduction [27], who would have represented t 1 by a two node term graph with the root labelled x and its successor y . The problem with this approach is, that the variable binding, which is an essential ingredient of the structure of the term, is not reflected in the structure of the graph, but has ....

....the horizontal embeddings in a much less constrained way than the V variables via the vertical homomorphisms of Def. 4.3.8; the image intervals of these V variables are indicated in the drawing. The construction of the host graph takes care of eventual duplication of the non abstractable parts [27] of the body of the abstraction. 4.4 Unique Encapsulation The problem whether there is a matching of a rule s left hand side into a given application graph, limited to the case where the images of the rule tips are given, is decidable and finitary on finite graph, i.e. it has mostly finitely ....

Christopher Peter Wadsworth. Semantics and Pragmatics of the Lambda Calculus. D.Phil. thesis, Oxford University, September 1971.

.... for term graphs (such as in some functional programming languages) often use names bound by e.g. where clauses to express sharing; this kind of binding is perceived as different from that introduced by l abstractions as represented in term graphs e.g. by Wadsworth, the inventor of graph reduction [25], the difference being that the namesbound by where clauses do not appear in the graph, but those bound by l abstractions do. In previous work [13] we took the step to consider both uses of bound variable names only as coding of structure that can be made explicit with an appropriate definition ....

Christopher Peter Wadsworth. Semantics and Pragmatics of the Lambda Calculus. Ph.D. thesis, Oxford University, September 1971.

....on graph reduction, and since the G machine was chosen as a basis for the Freja implementation, we will not consider environment based implementations further. 2.3. 5 Graph Reduction Graph reduction is a much newer technique than the environment based scheme and was first invented by Wadsworth [Wad71]. The basic idea is to represent lambda expressions as graphs, since graphs are much more convenient for computers to manipulate than text, and then evaluate the expressions in much the same way as the lambda expression in section 2.3.2 was evaluated. Consider the lambda expression (x. 1 x) 4 ....

Christopher Wadsworth. Semantics and Pragmatics of the Lambda Calculus. Phd thesis, Oxford, 1971.

....[BvEG 87] i.e. the delayed equations may be viewed as shared subterms. It should be noted that the strategy may not be optimal as defined in [HL91] neither concerning the number of R reductions nor fi reductions. The notion of need considered here is similar to the notion of call by need in [Wad71]. Let us now come back from evaluation to the context of narrowing. Consider for instance the Lazy Narrowing step with the above rule ff (t 1 ; t 2 ) g(a; Z )g )LN ft 1 X ; t 2 Y ; g(X ; X ) g(a; Z )g In contrast to evaluation as in functional languages, solving the goals ....

Christopher Peter Wadsworth. Semantics and Pragmatics of the Lambda Calculus. Phd thesis, University of Oxford, Oxford, September 1971.

....resp. term trees as a special case of term graphs and still have the full power of (second order) substitution available. Keywords: Term graph rewriting, relational matching, relation calculus, # calculus 1 Introduction Term graphs have probably been introduced into the literature by Wadsworth [43], the inventor of graph reduction, which is an important implementation technique for functional programming languages. Since then, term graphs have been used as an e#cient implementation of terms, and various flavours of term graph rewriting have been investigated mainly as implementations of ....

....binding has to be considered. In the # term t 1 : #x. y, the variable x is not a subterm of t 1 ; the only nontrivial subterm is y. Therefore, in the tree representation there should be no node representing x. One way to achieve this was already used by Wadsworth, the inventor of graph reduction [43], who would have represented t 1 by a two node term graph with the root labelled #x and its successor y : #x y The problem with this approach is, that the variable binding, which is an essential ingredient of the structure of the # term, is not reflected in the structure of the graph, but has ....

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Christopher Peter Wadsworth. Semantics and Pragmatics of the Lambda Calculus. D.Phil. thesis, Oxford University, September 1971.

....usage of a parameterized set has its own distinct parameter. Of course, more space efficient cyclic graphs can still be used to implement self containing sets which do not introduce quantifiers. Related Work Graph reduction was first suggested as a language implementation technique by Wadsworth [12]. The first use of graph reduction for functional logic programming in particular seems to have been by Reddy [10] In his system the various occurrences of a subexpression arising from multiple uses of an abstraction parameter in a function body within a single nondeterministic choice branch are ....

Christopher P. Wadsworth. Semantics and Pragmatics of the Lambda Calculus. PhD thesis, Oxford University, 1971.

....transformation, also known as graph rewriting or graph reduction, combines the potentials and advantages of both, graphs and rules, into a single computational paradigm. More than 25 years ago, Rosenfeld et al. PR69, RM72] in the USA, and Schneider, Ehrig, Pfender, and Wadsworth [Sch70, Sch71, Wad71, EPS73] in Europe introduced graph transformation for the generation, manipulation, recognition, and evaluation of graphs. Since then graph transformation has been studied in a variety of approaches, motivated by application domains such as pattern recognition, semantics of programming languages, ....

....graphs and infinite computations [FW90, KKSdV94] and with term graph rewriting for logic programming and equation solving [CMR 91, CR93, CW94, HP96] An area related to term graph rewriting is graph reduction for the lambda calculus. From the numerous literature of this area we mention only [Wad71, Lam90, AL95] 3.2 Specification of an Interactive Graphical Tool Often, the objects of an interactive graphical tool can be represented as graphs, and its operations can be modelled by graph transformation. Here we consider the Agg system being developed at TU Berlin, a tool for editing and ....

Christopher P. Wadsworth. Semantics and Pragmatics of the Lambda Calculus. PhD thesis, University of Oxford, 1971.

....transformation, also known as graph rewriting or graph reduction, combines the potentials and advantages of both, graphs and rules, into a single computational paradigm. More than 25 years ago, Rosenfeld et al. PR69, RM72] in the USA, and Schneider, Ehrig, Pfender, and Wadsworth [Sch70, Sch71, Wad71, EPS73] in Europe introduced graph transformation for the generation, manipulation, recognition, and evaluation of This work was partially supported by the Deutsche Forschungsgemeinschaft and the ESPRIT Basic Research Working Group No. 7183: Computing by Graph Transformation (COMPUGRAPH II) ....

....cyclic term graphs and infinite computations [FW90, KKSdV91] and with term graph rewriting for logic programming and equation solving [CR93, CW94, HP96] An area related to term graph rewriting is graph reduction for the lambda calculus. From the numerous literature of this area we mention only [Wad71, Lam90, AL95] 3.2 Specification of an Interactive Graphical Tool Often, the objects of an interactive graphical tool can be represented as graphs, and its operations can be modelled by graph transformation. Here we consider the Agg system 7 being developed at TU Berlin, a tool for editing ....

Christopher P. Wadsworth. Semantics and Pragmatics of the Lambda Calculus. PhD thesis, University of Oxford, 1971.

....between call by name lambda calculi and lazy functional languages (such as Miranda or Haskell) is not so good. Call by name re evaluates an argument each time it is used, which is prohibitively expensive. So lazy languages are implemented using the callby need mechanism proposed by Wadsworth [Wad71] which overwrites an argument with its value the first time it is evaluated, avoiding the need for any subsequent evaluation [Tur79, Joh84, KL89, Pey92] Call by need reduction implements the observational behavior of call by name in a way that requires no more substitution steps than ....

Christopher P. Wadsworth. Semantics and Pragmatics of the Lambda Calculus. PhD thesis, Oxford University, 1971.

....a name one will. Similarly, even if the argument of an application does terminate, if it is a large, expensive computation and the result is thrown away (by K, for example) the effort is wasted. Writers of compilers and interpreters for functional languages noticed this, and in 1971 Wadsworth [Wad71] proposed the mechanism now known as call by need, and implemented in so called lazy functional languages: only evaluate the argument of an application when its value is required, and memoize the result so that if the argument s value is required again it need not be recalculated. This of ....

Christopher P. Wadsworth. Semantics and Pragmatics of the Lambda Calculus. PhD thesis, Oxford University, 1971.

....subterms. This is why we use the subscript G, for graph. In the next section we will use the fi G rule as the core of a new calculus, let . The idea of sharing subexpressions to make normal order reduction efficient was first tackled by Wadsworth in his D.Phil. Thesis as far back as 1971 [13]. In his seminal work, which came to be known as graph reduction, he used an explicit graph notation instead of a textual term notation. Since the source language was standard calculus, there was no issue of recursive or cyclic terms the sharing he obtained was just a way to avoid duplicating ....

Christopher P. Wadsworth. Semantics and Pragmatics of the Lambda-calculus, 1971. D.Phil. thesis, University of Oxford.

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Christopher Wadsworth, Semantics and Pragmatics of the Lambda Calculus, Ph.D. Thesis, Oxford University, 1971.

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Christopher P. Wadsworth. Semantics and Pragmatics of the Lambda-Calculus. PhD thesis, Oxford University, 1971. 16

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Christopher P. Wadsworth. Semantics and pragmatics of the lambda calculus. PhD thesis, Oxford, 1971.

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