| V. C. G. Barthe and O. Pons. Setoids in type theory. Journal of Functional Programming, 13(2):261--293, March 2003. |
....for a signature S = F; ar) consists of a set A, called the carrier of the algebra, and of a function f : A ar(f) A for every f 2 F . To formalise algebras, we therefore need to formalise sets and n ary functions. For the sake of simplicity, we formalise sets as types and not as setoids [7]. The type of n ary functions over a type A is denoted by Fun n A and is dened by the recursive equation Fun[n : N] A : Set] Set = case n of 0 ) A j S m ) A (Fun m A) Denition 2. The type Algebra of algebras over a signature is dened by Algebra[S : Signature] Class = fel : Set; int : ....
G. Barthe, V. Capretta, and O. Pons. Setoids in type theory. Submitted, 2000.
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V. C. G. Barthe and O. Pons. Setoids in type theory. Journal of Functional Programming, 13(2):261--293, March 2003.
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