⋌

Hendriks, Dimitri; Oostrom, Vincent van

doi:10.1007/978-3-540-45085-6_11

“…[AMV11] furthermore study the so-called rational fixed point, again over Set F , as a semantic universe for solutions of higher-order recursion schemes. In [HvO03], the authors define a calculus with an operator called adbmal to deal with α-conversion. This operator removes the scope of a variable.…”

Section: Related and Future Workmentioning

confidence: 99%

Nominal Coalgebraic Data Types with Applications to Lambda Calculus

Kurz

¹

,

Petrişan

²

,

Severi

³

et al. 2013

Logical Methods in Computer Science

View full text Add to dashboard Cite

show abstract

“…In the generalised form, due to Patterson and Bird [3], the symbol S can occur anywhere between a variable occurrence and its binding abstraction. The idea to view S as a scope delimiter was employed by Hendriks and van Oostrom, who defined an end-of-scope symbol λ [18]. This approach is also used in the translation of pure λ-terms (without letrec) into Lambdascope-graphs (interaction nets) on which van Oostrom defines an optimal evaluator for the λ-calculus [27].…”

Section: Contribution Of This Paper In Contextmentioning

confidence: 99%

Maximal sharing in the Lambda calculus with letrec

GrabmayerClemens¹,

RochelJan

²

2014

View full text Add to dashboard Cite

Increasing sharing in programs is desirable to compactify the code, and to avoid duplication of reduction work at run-time, thereby speeding up execution. We show how a maximal degree of sharing can be obtained for programs expressed as terms in the lambda calculus with letrec. We introduce a notion of 'maximal compactness' for λ letrec -terms among all terms with the same infinite unfolding. Instead of defined purely syntactically, this notion is based on a graph semantics. λ letrec -terms are interpreted as first-order term graphs so that unfolding equivalence between terms is preserved and reflected through bisimilarity of the term graph interpretations. Compactness of the term graphs can then be compared via functional bisimulation.We describe practical and efficient methods for the following two problems: transforming a λ letrec -term into a maximally compact form; and deciding whether two λ letrec -terms are unfolding-equivalent. The transformation of a λ letrec -term L into maximally compact form L0 proceeds in three steps: (i) translate L into its term graph G = L ; (ii) compute the maximally shared form of G as its bisimulation collapse G0 ; (iii) read back a λ letrec -term L0 from the term graph G0 with the property L0 = G0. This guarantees that L0 and L have the same unfolding, and that L0 exhibits maximal sharing.The procedure for deciding whether two given λ letrec -terms L1 and L2 are unfolding-equivalent computes their term graph interpretations L1 and L2 , and checks whether these term graphs are bisimilar.For illustration, we also provide a readily usable implementation.

show abstract

“…The term enriched by abdmals [18]. The adbmal ( λ) is to be read as a scope delimiter that explicitly includes the name of the λ-variable whose scope it delimits.…”

Section: B Implementation Showcasementioning

confidence: 99%

Maximal sharing in the Lambda calculus with letrec

Grabmayer¹,

Rochel

²

2014

Proceedings of the 19th ACM SIGPLAN International Conference on Functional Programming

View full text Add to dashboard Cite

Increasing sharing in programs is desirable to compactify the code, and to avoid duplication of reduction work at run-time, thereby speeding up execution. We show how a maximal degree of sharing can be obtained for programs expressed as terms in the lambda calculus with letrec. We introduce a notion of 'maximal compactness' for λ letrec -terms among all terms with the same infinite unfolding. Instead of defined purely syntactically, this notion is based on a graph semantics. λ letrec -terms are interpreted as first-order term graphs so that unfolding equivalence between terms is preserved and reflected through bisimilarity of the term graph interpretations. Compactness of the term graphs can then be compared via functional bisimulation.We describe practical and efficient methods for the following two problems: transforming a λ letrec -term into a maximally compact form; and deciding whether two λ letrec -terms are unfolding-equivalent. The transformation of a λ letrec -term L into maximally compact form L0 proceeds in three steps: (i) translate L into its term graph G = L ; (ii) compute the maximally shared form of G as its bisimulation collapse G0 ; (iii) read back a λ letrec -term L0 from the term graph G0 with the property L0 = G0. This guarantees that L0 and L have the same unfolding, and that L0 exhibits maximal sharing.The procedure for deciding whether two given λ letrec -terms L1 and L2 are unfolding-equivalent computes their term graph interpretations L1 and L2 , and checks whether these term graphs are bisimilar.For illustration, we also provide a readily usable implementation.

show abstract

⋌

Cited by 21 publications

References 18 publications

Nominal Coalgebraic Data Types with Applications to Lambda Calculus

Nominal Coalgebraic Data Types with Applications to Lambda Calculus

Maximal sharing in the Lambda calculus with letrec

Maximal sharing in the Lambda calculus with letrec

Contact Info

Product

Resources

About