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Alphastructural recursion and induction
 Journal of the ACM
, 2006
"... The nominal approach to abstract syntax deals with the issues of bound names and αequivalence by considering constructions and properties that are invariant with respect to permuting names. The use of permutations gives rise to an attractively simple formalisation of common, but often technically i ..."
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Cited by 56 (6 self)
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incorrect uses of structural recursion and induction for abstract syntax modulo αequivalence. At the heart of this approach is the notion of finitely supported mathematical objects. This paper explains the idea in as concrete a way as possible and gives a new derivation within higherorder logic
Structural Recursion as a Query Language
 In Proceedings of 3rd International Workshop on Database Programming Languages
, 1991
"... We propose a programming paradigm that tries to get close to both the semantic simplicity of relational algebra, and the expressive power of unrestricted programming languages. Its main computational engine is structural recursion on sets. All programming is done within a "nicely" typed la ..."
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Cited by 116 (12 self)
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We propose a programming paradigm that tries to get close to both the semantic simplicity of relational algebra, and the expressive power of unrestricted programming languages. Its main computational engine is structural recursion on sets. All programming is done within a "nicely" typed
Using structural recursion for corecursion
 In Types for Proofs and Programs, International Conference, TYPES 2008, volume 5497 of LNCS
, 2009
"... Abstract. We propose a (limited) solution to the problem of constructing stream values defined by recursive equations that do not respect the guardedness condition. The guardedness condition is imposed on definitions of corecursive functions in Coq, AGDA, and other higherorder proof assistants. In ..."
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Cited by 6 (1 self)
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. In this paper, we concentrate in particular on those nonguarded equations where recursive calls appear under functions. We use a correspondence between streams and functions over natural numbers to show that some classes of nonguarded definitions can be modelled through the encoding as structural recursive
Structurally Recursive Descent Parsing
, 2008
"... Recursive descent parsing does not terminate for left recursive grammars. We turn recursive descent parsing into structurally recursive descent parsing, acceptable by total dependently typed languages like Agda, by using the type system to rule out left recursion. The resulting library retains much ..."
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Cited by 2 (0 self)
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Recursive descent parsing does not terminate for left recursive grammars. We turn recursive descent parsing into structurally recursive descent parsing, acceptable by total dependently typed languages like Agda, by using the type system to rule out left recursion. The resulting library retains much
A Predicative Analysis of Structural Recursion
, 1999
"... We introduce a language based upon lambda calculus with products, coproducts and strictly positive inductive types that allows the definition of recursive terms. We present the implementation (foetus) of a syntactical check that ensures that all such terms are structurally recursive, i.e., recursive ..."
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Cited by 43 (20 self)
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We introduce a language based upon lambda calculus with products, coproducts and strictly positive inductive types that allows the definition of recursive terms. We present the implementation (foetus) of a syntactical check that ensures that all such terms are structurally recursive, i
Nominal Structures and Structural Recursion
"... It is possible within Tree Adjoining Grammar to reproduce many of the syntactic analyses originally formulated by linguists in transformational terms. Tothe extent that these analyses are wellmotivated empirically, this fact makes TAG interesting for use in developing computational learning and ..."
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Cited by 5 (3 self)
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It is possible within Tree Adjoining Grammar to reproduce many of the syntactic analyses originally formulated by linguists in transformational terms. Tothe extent that these analyses are wellmotivated empirically, this fact makes TAG interesting for use in developing computational learning and processing models (Joshi 1990, Frank 1992, Rambow 1994), since the use of other nontransformational formalisms sometimes forces choices of linguistic description different from those ordinarily made by descriptive syntacticians. Thus, using TAG, one can takeadvantage in the construction of parsers and learners of the computational tractability of a mathematically restrictive formalism without having to reinvent empirical syntax in order to do so. At the same time, TAG analyses are not identical in every detail to their transformational counterparts; and it is interesting to compare them where they diverge. The differences arise because of a fundamental difference in the way that synt...
A Transformation System for Developing Recursive Programs
, 1977
"... A system of rules for transforming programs is described, with the programs in the form of recursion equations An initially very simple, lucid. and hopefully correct program IS transformed into a more efficient one by altering the recursion structure Illustrative examples of program transformations ..."
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Cited by 649 (3 self)
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A system of rules for transforming programs is described, with the programs in the form of recursion equations An initially very simple, lucid. and hopefully correct program IS transformed into a more efficient one by altering the recursion structure Illustrative examples of program transformations
On Two Forms of Structural Recursion
 in &quot;LNCS 893: Proceedings of 5th International Conference on Database Theory,&quot; 111124
, 1995
"... . We investigate and compare two forms of recursion on sets for querying nested collections. The first one is called sri and it corresponds to sequential processing of data. The second one is called sru and it corresponds to dataparallel processing. A uniform firstorder translation from sru into s ..."
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Cited by 17 (11 self)
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. We investigate and compare two forms of recursion on sets for querying nested collections. The first one is called sri and it corresponds to sequential processing of data. The second one is called sru and it corresponds to dataparallel processing. A uniform firstorder translation from sru
Structural recursion for querying ordered graphs
 In ICFP 2013
, 2013
"... Structural recursion, in the form of, for example, folds on lists and catamorphisms on algebraic data structures including trees, plays an important role in functional programming, by providing a systematic way for constructing and manipulating functional programs. It is, however, a challenge to de ..."
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Cited by 2 (1 self)
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Structural recursion, in the form of, for example, folds on lists and catamorphisms on algebraic data structures including trees, plays an important role in functional programming, by providing a systematic way for constructing and manipulating functional programs. It is, however, a challenge
Unifying structured recursion schemes
 in International Conference on Functional Programming. ACM
"... Folds over inductive datatypes are well understood and widely used. In their plain form, they are quite restricted; but many disparate generalisations have been proposed that enjoy similar calculational benefits. There have also been attempts to unify the various generalisations: two prominent su ..."
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Cited by 2 (2 self)
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such unifications are the ‘recursion schemes from comonads ’ of Uustalu, Vene and Pardo, and our own ‘adjoint folds’. Until now, these two unified schemes have appeared incompatible. We show that this appearance is illusory: in fact, adjoint folds subsume recursion schemes from comonads. The proof of this claim
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