Galois

More documents

Recommendations

Info

Introduction Motivation Whole division Prove (a ÷ b) ÷ c = a ÷ (c × b) for b and c ≠ 0. Easy if ÷ is the real number division Also valid in natural numbers but the proof is not so straightforward Paulo Silva (UMinho) Galois PLMMS’09 4 / 28
Introduction Whole division specification Motivation Implicit definition Explicit definition c = x ÷ y ⇔ 〈∃ r : 0 r < y : x = c × y + r〉 x ÷ y = 〈 ∨ z :: z × y x〉 Galois connection z × y x ⇔ z x ÷ y (y > 0) Paulo Silva (UMinho) Galois PLMMS’09 5 / 28
Page 1 and 2: Galois: A Language for Proofs Using
Page 3: Outline Introduction 1 Introduction
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 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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?