Ground term confluence in parametric conditional equational specifications

Author(s):  
Harald Ganzinger
Author(s):  
Mauricio Ayala-Rincón ◽  
Maribel Fernández ◽  
Daniele Nantes-Sobrinho ◽  
Deivid Vale

AbstractWe define nominal equational problems of the form $$\exists \overline{W} \forall \overline{Y} : P$$ ∃ W ¯ ∀ Y ¯ : P , where $$P$$ P consists of conjunctions and disjunctions of equations $$s\approx _\alpha t$$ s ≈ α t , freshness constraints $$a\#t$$ a # t and their negations: $$s \not \approx _\alpha t$$ s ≉ α t and "Equation missing", where $$a$$ a is an atom and $$s, t$$ s , t nominal terms. We give a general definition of solution and a set of simplification rules to compute solutions in the nominal ground term algebra. For the latter, we define notions of solved form from which solutions can be easily extracted and show that the simplification rules are sound, preserving, and complete. With a particular strategy for rule application, the simplification process terminates and thus specifies an algorithm to solve nominal equational problems. These results generalise previous results obtained by Comon and Lescanne for first-order languages to languages with binding operators. In particular, we show that the problem of deciding the validity of a first-order equational formula in a language with binding operators (i.e., validity modulo $$\alpha $$ α -equality) is decidable.


1998 ◽  
Vol 36 (4) ◽  
pp. 367-413 ◽  
Author(s):  
Sándor Vágvölgyi
Keyword(s):  

2007 ◽  
Vol 17 (3) ◽  
pp. 439-484 ◽  
Author(s):  
CLEMENS GRABMAYER

This paper presents a proof-theoretic observation about two kinds of proof systems for bisimilarity between cyclic term graphs.First we consider proof systems for demonstrating that μ term specifications of cyclic term graphs have the same tree unwinding. We establish a close connection between adaptations for μ terms over a general first-order signature of the coinductive axiomatisation of recursive type equivalence by Brandt and Henglein (Brandt and Henglein 1998) and of a proof system by Ariola and Klop (Ariola and Klop 1995) for consistency checking. We show that there exists a simple duality by mirroring between derivations in the former system and formalised consistency checks, which are called ‘consistency unfoldings', in the latter. This result sheds additional light on the axiomatisation of Brandt and Henglein: it provides an alternative soundness proof for the adaptation considered here.We then outline an analogous duality result that holds for a pair of similar proof systems for proving that equational specifications of cyclic term graphs are bisimilar.


1987 ◽  
Vol 42 (6) ◽  
pp. 597-602
Author(s):  
H. N. v. Allwörden ◽  
W. Preetz

The vibrational and electronic resonance Raman spectra of the solid tetraalkylammonium salts of [RuClnBr6-n]2-, n = 0 . . . 6, are measured at 80 K. The observed electronic Raman bands in the regions of 640-740 cm-1 and 1560-1790 cm-1 are assigned to the intraconfigurational transitions Γ1 → Γ4 and Γ1 → Γ3, Γ5 within the 3T1g(Oh) ground term. The observed splittings and shifts, due to spin orbit coupling and lowered symmetry, are interpreted qualitatively according to the point groups D4h, C4V, C3V and C2V. The O-O-transitions are deduced from vibrational fine structure. The electronic Raman bands of [RuCl6]2- and [RuBr6]2- are assigned in detail by polarisation measurements.


1981 ◽  
Vol 14 (4) ◽  
pp. L135-L139 ◽  
Author(s):  
R New ◽  
J A R Griffith ◽  
G R Isaak ◽  
M P Ralls
Keyword(s):  

1970 ◽  
Vol 53 (3) ◽  
pp. 1247-1257 ◽  
Author(s):  
D. E. Wortman ◽  
David Sanders

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