scholarly journals Study of the subtyping machine of nominal subtyping with variance

2021 ◽  
Vol 5 (OOPSLA) ◽  
pp. 1-27
Author(s):  
Ori Roth
Keyword(s):  
Type System ◽  
Computing Power ◽  
Tree Languages ◽  
Software Artifact ◽  
Context Free

This is a study of the computing power of the subtyping machine behind Kennedy and Pierce's nominal subtyping with variance. We depict the lattice of fragments of Kennedy and Pierce's type system and characterize their computing power in terms of regular, context-free, deterministic, and non-deterministic tree languages. Based on the theory, we present Treetop---a generator of C# implementations of subtyping machines. The software artifact constitutes the first feasible (yet POC) fluent API generator to support context-free API protocols in a decidable type system fragment.

PROPERTIES OF QUASI-RELABELING TREE BIMORPHISMS

2010 ◽  
Vol 21 (03) ◽  
pp. 257-276 ◽  
Author(s):  
ANDREAS MALETTI ◽  
CĂTĂLIN IONUŢ TÎRNĂUCĂ
Keyword(s):  
Cartesian Product ◽  
Canonical Representation ◽  
Finite Union ◽  
Top Down ◽  
Tree Language ◽  
Regular Tree ◽  
Fundamental Properties ◽  
Tree Transducers ◽  
Tree Languages ◽  
Context Free

The fundamental properties of the class QUASI of quasi-relabeling relations are investigated. A quasi-relabeling relation is a tree relation that is defined by a tree bimorphism (φ, L, ψ), where φ and ψ are quasi-relabeling tree homomorphisms and L is a regular tree language. Such relations admit a canonical representation, which immediately also yields that QUASI is closed under finite union. However, QUASI is not closed under intersection and complement. In addition, many standard relations on trees (e.g., branches, subtrees, v-product, v-quotient, and f-top-catenation) are not quasi-relabeling relations. If quasi-relabeling relations are considered as string relations (by taking the yields of the trees), then every Cartesian product of two context-free string languages is a quasi-relabeling relation. Finally, the connections between quasi-relabeling relations, alphabetic relations, and classes of tree relations defined by several types of top-down tree transducers are presented. These connections yield that quasi-relabeling relations preserve the regular and algebraic tree languages.

scholarly journals IO and OI

1975 ◽  
Vol 4 (47) ◽  
Author(s):  
Joost Engelfriet ◽  
Erik Meineche Schmidt
Keyword(s):  
Fixed Point ◽  
Program Scheme ◽  
Closure Properties ◽  
Recursive Program ◽  
Tree Languages ◽  
Emptiness Problem ◽  
Free Tree ◽  
Context Free ◽  
Inside Out

A fixed point characterization of the inside-out (IO) and the outside- in (OI) context-free tree languages is given. This characterization is used to obtain a theory of nondeterministic systems of context-free equations with parameters. Several ''Mezei and Wright like'' results are obtained which relate to context-free tree languages, to recognizable tree languages and to nondeterministic recursive program(scheme)s (called by value and called by name). The emptiness problem and closure properties of the context-free tree languages are discussed. Hierarchies of higher level equational subsets of an algebra are considered.

scholarly journals Linear context-free tree languages and inverse homomorphisms

2019 ◽  
Vol 269 ◽  
pp. 104454 ◽  
Author(s):  
Johannes Osterholzer ◽  
Toni Dietze ◽  
Luisa Herrmann
Keyword(s):  
Tree Languages ◽  
Free Tree ◽  
Context Free

A bottom-up parsing method for complete context-free tree languages

1986 ◽  
Vol 17 (3) ◽  
pp. 66-74
Author(s):  
Kyota Aoki ◽  
Kazumi Matsuura
Keyword(s):  
Bottom Up ◽  
Tree Languages ◽  
Free Tree ◽  
Context Free
Sign in / Sign up

Export Citation Format

Share Document