Galois
Galois: A Language for Proofs Using Galois connections and ... - ALFA
Galois: A Language for Proofs Using Galois connections and ... - ALFA
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Theoretical background<br />
<strong>Galois</strong> connections — Algebra<br />
<strong>Galois</strong> connections<br />
Identity connection<br />
(id,id)<br />
(A, ⊑ A ) (A, ⊑ A )<br />
Composition<br />
(f ,g)<br />
(h,k)<br />
(h◦f ,g◦k)<br />
if (A, ⊑) (B, ≼) and (B, ≼) (C, ) then (A, ⊑) (C, )<br />
Composition is associative and the identity is its unit.<br />
<strong>Galois</strong> connections form a category.<br />
Paulo Silva (UMinho) <strong>Galois</strong> PLMMS’09 14 / 28
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