scholarly journals Factorising folds for faster functions

2010 ◽  
Vol 20 (3-4) ◽  
pp. 353-373 ◽  
Author(s):  
GRAHAM HUTTON ◽  
MAURO JASKELIOFF ◽  
ANDY GILL
Keyword(s):  
Fixed Point ◽  
New Technique ◽  
General Technique ◽  
Initial Algebra ◽  
Recursive Programs ◽  
Fixed Point Semantics ◽  
Initial Algebra Semantics ◽  
Structured Approach

AbstractThe worker/wrapper transformation is a general technique for improving the performance of recursive programs by changing their types. The previous formalisation (A. Gill & G. Hutton, J. Funct. Program., vol. 19, 2009, pp. 227–251) was based upon a simple fixed-point semantics of recursion. In this paper, we develop a more structured approach, based upon initial-algebra semantics. In particular, we show how the worker/wrapper transformation can be applied to programs defined using the structured pattern of recursion captured by fold operators, and illustrate our new technique with a number of examples.

Initial Algebra Semantics and Continuous Algebras

1977 ◽  
Vol 24 (1) ◽  
pp. 68-95 ◽  
Author(s):  
J. A. Goguen ◽  
J. W. Thatcher ◽  
E. G. Wagner ◽  
J. B. Wright
Keyword(s):  
Initial Algebra ◽  
Initial Algebra Semantics

scholarly journals Crisp-determinization of weighted tree automata over strong bimonoids

2021 ◽  
Vol vol. 23 no. 1 (Automata, Logic and Semantics) ◽  
Author(s):  
Zoltán Fülöp ◽  
Dávid Kószó ◽  
Heiko Vogler
Keyword(s):  
Finite Order ◽  
Positive Answer ◽  
Order Property ◽  
Sufficient Condition ◽  
Tree Automata ◽  
Weighted Tree ◽  
Bottom Up ◽  
Initial Algebra ◽  
Initial Algebra Semantics ◽  
Weighted Tree Automata

We consider weighted tree automata (wta) over strong bimonoids and their initial algebra semantics and their run semantics. There are wta for which these semantics are different; however, for bottom-up deterministic wta and for wta over semirings, the difference vanishes. A wta is crisp-deterministic if it is bottom-up deterministic and each transition is weighted by one of the unit elements of the strong bimonoid. We prove that the class of weighted tree languages recognized by crisp-deterministic wta is the same as the class of recognizable step mappings. Moreover, we investigate the following two crisp-determinization problems: for a given wta ${\cal A}$, (a) does there exist a crisp-deterministic wta which computes the initial algebra semantics of ${\cal A}$ and (b) does there exist a crisp-deterministic wta which computes the run semantics of ${\cal A}$? We show that the finiteness of the Nerode algebra ${\cal N}({\cal A})$ of ${\cal A}$ implies a positive answer for (a), and that the finite order property of ${\cal A}$ implies a positive answer for (b). We show a sufficient condition which guarantees the finiteness of ${\cal N}({\cal A})$ and a sufficient condition which guarantees the finite order property of ${\cal A}$. Also, we provide an algorithm for the construction of the crisp-deterministic wta according to (a) if ${\cal N}({\cal A})$ is finite, and similarly for (b) if ${\cal A}$ has finite order property. We prove that it is undecidable whether an arbitrary wta ${\cal A}$ is crisp-determinizable. We also prove that both, the finiteness of ${\cal N}({\cal A})$ and the finite order property of ${\cal A}$ are undecidable.

scholarly journals Equivalence of two fixed-point semantics for definitional higher-order logic programs

2017 ◽  
Vol 668 ◽  
pp. 27-42 ◽  
Author(s):  
Angelos Charalambidis ◽  
Panos Rondogiannis ◽  
Ioanna Symeonidou
Keyword(s):  
Fixed Point ◽  
Higher Order ◽  
Order Logic ◽  
Logic Programs ◽  
Higher Order Logic ◽  
Fixed Point Semantics

scholarly journals Denotational fixed-point semantics for constructive scheduling of synchronous concurrency

2015 ◽  
Vol 52 (4-5) ◽  
pp. 393-442 ◽  
Author(s):  
Joaquín Aguado ◽  
Michael Mendler ◽  
Reinhard von Hanxleden ◽  
Insa Fuhrmann
Keyword(s):  
Fixed Point ◽  
Fixed Point Semantics

scholarly journals Stratified, Weak Stratified, and Three-Valued Semantics1

1990 ◽  
Vol 13 (1) ◽  
pp. 19-33
Author(s):  
Melvin Fitting ◽  
Marion Ben-Jacob
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Horn Clause ◽  
Logic Programs ◽  
The Family ◽  
Fixed Point Semantics ◽  
Truth Value ◽  
The Relationship ◽  
Classical Truth

We investigate the relationship between three-valued Kripke/Kleene semantics and stratified semantics for stratifiable logic programs. We first show these are compatible, in the sense that if the three-valued semantics assigns a classical truth value, the stratified approach will assign the same value. Next, the familiar fixed point semantics for pure Horn clause programs gives both smallest and biggest fixed points fundamental roles. We show how to extend this idea to the family of stratifiable logic programs, producing a semantics we call weak stratified. Finally, we show weak stratified semantics coincides exactly with the three-valued approach on stratifiable programs, though the three-valued version is generally applicable, and does not require stratification assumptions.

Sign in / Sign up

Export Citation Format

Share Document