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Title:  Sufficient completeness of parameterized specifications in CafeOBJ 
Authors:  Nakamura, Masaki Gaina, Daniel Ogata, Kazuhiro Futatsugi, Kokichi 
Issue Date:  20141215 
Publisher:  北陸先端科学技術大学院大学情報科学研究科 
Magazine name:  Research report (School of Information Science, Japan Advanced Institute of Science and Technology) 
Volume:  ISRR2014005 
Start page:  1 
End page:  4 
Abstract:  CafeOBJ is a specification language which supports several kinds of specifications [1] . In this study, we focus on constructorbased ordersorted (CBOS) equational specifications. A signature (S,≤, Σ, Σ^C) (abbr. Σ) consists of a set S of sorts, a poset ≤ on S, a S^+ sorted set Σ of operators, and a set Σ^C ⊆ Σ of constructors. We use the notation for the complement set Σ' = E ＼ E', constrained sorts S^<cs> = {s ∈ S  f ∈ Σ^C_<ωs>) ∨ (f ∈Σ^C_<ωs'> ∧ s' ≤ s)}, loose sorts S^<ls> = S ＼ S^<cs>, and constrained operators Σ^<S^<cs>> = {f ∈ Σ_<ωs >  ω ∈ S^* ,s ∈ S^<cs>}, A specification SP is a pair of a signature Σ and a set of equations on Σ. We use the subscript A_<SP> to refer the element of SP, e.g. S_<SP>, Σ_<SP>, E_<SP>, etc. Sufficient completeness is an important property which guarantees the existence of the initial model [3]. A sufficient condition of sufficient completeness is given in [2] as follows: SP = ((S,≤, Σ, Σ^C), E) is sufficiently complete if for each S^<ls>sorted set Y of variables of loose sorts and each term t ∈ T_<Σ ^<S^<cs>> (Y), there exists a term u ∈ T_<Σ^C>(Y) such that t = _Eu. We call the above condition SCE. The theory of term rewriting systems (TRS) is useful to prove sufficient completeness, where equations are regarded as lefttoright rewrite rules. A term is Ereducible if it has a subterm which can be rewritten by some rewrite rule in E. It is known that the notion of basic terms is useful to show ground reducibility. We give a variant of basic terms for CBOS specifications. 
URI:  http://hdl.handle.net/10119/12301 
Material Type:  publisher 
Appears in Collections:  ISRR2014

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