Galois

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Theoretical background Point-free transform Point-free definitions Definition (Galois connection) Definition (Indirect equality) f ◦ ◦ ⊑ B = ⊑ A ◦ g f = g ⇔ ≼ ◦ f = ≼ ◦ g f = g ⇔ f ◦ ◦ ≼ = g ◦ ◦ ≼ Paulo Silva (UMinho) Galois PLMMS’09 20 / 28
Outline Galois and Galculator 1 Introduction Motivation Objectives 2 Theoretical background Indirect equality Galois connections Fork algebras Point-free transform 3 Galois and Galculator Galois Galculator 4 Summary Summary Future work Paulo Silva (UMinho) Galois PLMMS’09 21 / 28
Page 1 and 2: Galois: A Language for Proofs Using
Page 3 and 4: Outline Introduction 1 Introduction
Page 5 and 6: Introduction Whole division specifi
Page 7 and 8: Introduction Whole division specifi
Page 9 and 10: Introduction Motivation Proof. n (
Page 11 and 12: Introduction Motivation Proof. n (
Page 13 and 14: Introduction Objectives Objectives
Page 15 and 16: Theoretical background Indirect equ
Page 23 and 24: Properties Theoretical background G
Page 25 and 26: Theoretical background Galois conne
Page 27 and 28: Theoretical background Fork algebra
Page 29 and 30: Theoretical background Fork algebra
Page 31: Theoretical background Point-free t
Page 35 and 36: Galois and Galculator Architecture
Page 37 and 38: Summary Summary Summary Fork algebr
Page 39 and 40: Summary Future work Future work Mec

Galois

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