Galois

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Theoretical background Indirect equality Proof. a = b ⇔ { Anti-symmetry } a ⊑ b ∧ b ⊑ a ⇔ { Indirect inequality } 〈∀ x :: x ⊑ a ⇒ x ⊑ b〉 ∧ 〈∀ x :: x ⊑ b ⇒ x ⊑ a〉 ⇔ { Rearranging quantifiers } 〈∀ x :: x ⊑ a ⇒ x ⊑ b ∧ x ⊑ b ⇒ x ⊑ a〉 ⇔ { Mutual implication } 〈∀ x :: x ⊑ a ⇔ x ⊑ b〉 Paulo Silva (UMinho) <strong>Galois</strong> PLMMS’09 10 / 28
Theoretical background Indirect equality Proof. a = b ⇔ { Anti-symmetry } a ⊑ b ∧ b ⊑ a ⇔ { Indirect inequality } 〈∀ x :: x ⊑ a ⇒ x ⊑ b〉 ∧ 〈∀ x :: x ⊑ b ⇒ x ⊑ a〉 ⇔ { Rearranging quantifiers } 〈∀ x :: x ⊑ a ⇒ x ⊑ b ∧ x ⊑ b ⇒ x ⊑ a〉 ⇔ { Mutual implication } 〈∀ x :: x ⊑ a ⇔ x ⊑ b〉 Paulo Silva (UMinho) <strong>Galois</strong> PLMMS’09 10 / 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 17: Theoretical background Indirect equ
Page 21 and 22: 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 and 32: Theoretical background Point-free t
Page 33 and 34: Outline Galois and Galculator 1 Int
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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