Galois

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Summary Summary Summary Galois Follows the mathematical concepts Alternative to first-order languages Typed approach Galculator Proof assistance prototype based on Galois connections Innovative approach Uses a point-free equational approach Paulo Silva (UMinho) Galois PLMMS’09 26 / 28
Summary Future work Future work Mechanization of point-free transform Automated proofs Extension of the type system Free-theorems Evaluation of the language Integration with host theorem provers (e.g., Coq) Paulo Silva (UMinho) Galois PLMMS’09 27 / 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 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: Summary Summary Summary Fork algebr

Galois

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