Galois

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Introduction Motivation Proof. n (a ÷ b) ÷ c ⇔ { z × y x ⇔ z x ÷ y } n × c a ÷ b ⇔ { z × y x ⇔ z x ÷ y } (n × c) × b a ⇔ { multiplication is associative } n × (c × b) a ⇔ { z × y x ⇔ z x ÷ y } n a ÷ (c × b) Paulo Silva (UMinho) Galois PLMMS’09 6 / 28
Introduction Objectives Objectives Galculator = Galois connection + calculator Galois Build a proof assistant based on Galois connections, their algebra and associated tactics Language for mathematical reasoning Equivalent to first-order logic Typed language Front-end for the Galculator Paulo Silva (UMinho) Galois PLMMS’09 7 / 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: Introduction Motivation Proof. n (
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

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