## ON THE MATHEMATICAL SYNTHESIS OF EQUATIONAL LOGICS

### BibTeX

@MISC{Fiore_onthe,

author = {Marcelo Fiore and Chung-kil Hur},

title = {ON THE MATHEMATICAL SYNTHESIS OF EQUATIONAL LOGICS},

year = {}

}

### OpenURL

### Abstract

Birkhoff [1935] initiated the general study of algebraic structure. Importantly for our concerns here, his development was from (universal) algebra to (equational) logic. Birkhoff’s starting point was the informal conception of algebra based on familiar concrete examples. Abstracting from these, he introduced the concepts of signature and equational presentation,

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- Clouston, Pitts
(Show Context)
Citation Context ... X] has action π · 〈a〉 x = 〈π · a〉 π · x Note that supp(〈a〉 x) is supp(x)\{a}. 6.2. Nominal Equational Systems. We specify a class of MESs on Nom, called Nominal Equational Systems (NESs). Following [=-=Clouston and Pitts, 2007-=-] we define a nominal signature Σ to be a family of nominal sets { Σ(n) }n∈N, each of which consists of the operators of arity n. Example 6.1. The nominal signature Σλ for the untyped λ-calculus is gi... |

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(Show Context)
Citation Context ...y a pair of nominal terms t and t ′ in the same nominal context [a]V. A NEP T = (Σ,E) consists of a nominal signature Σ and a set of nominal equations E. Example 5.2 (continued from Example 5.1, cf. (=-=Gabbay and Mathijssen, 2007-=-) and (Clouston and Pitts, 2007)). The NEP Tλ = (Σλ,Eλ) for αβη-equivalence of untyped λ-terms has the following equations: (α) (βκ) [a,b] x : 1 ⊢ La.x(a) ≡ Lb.x(b) [a] x : 0,y : 1 ⊢ A ( La.x, y(a) ) ... |

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- 2006
(Show Context)
Citation Context ... ⊢ t ≡ [a]V ⊢ t ′ : A # n → TΣV } ( [a]V ⊢t≡t ′ ) ∈ A where [a]V ⊢ t is the Kleisli map corresponding to 〈a〉 t via the above bijection.April 18, 2010 13 Example 6.2 (continued from Example 6.1, cf. [=-=Gabbay and Mathijssen, 2007-=-] and [Clouston and Pitts, 2007]). The NEP Tλ = (Σλ, Aλ) for αβη-equivalence of untyped λterms has the following equations: (α) [a, b] x : 1 ⊢ La. x(a) ≡ Lb. x(b) (βκ) [a] x : 0, y : 1 ⊢ A ( La. x , y... |

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