Results 1 
2 of
2
A Theory and its Metatheory in FS 0
"... . Feferman has proposed FS 0 , a theory of finitary inductive systems, as a framework theory that allows a user to reason both in and about an encoded theory. I look here at how practical FS 0 really is. To this end I formalise a sequent calculus presentation of classical propositional logic, and sh ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
. Feferman has proposed FS 0 , a theory of finitary inductive systems, as a framework theory that allows a user to reason both in and about an encoded theory. I look here at how practical FS 0 really is. To this end I formalise a sequent calculus presentation of classical propositional logic, and show this can be used for work in both the theory and the metatheory. the latter is illustrated with a discussion of a proof of Gentzen's Hauptsatz. Contents x 1 Introduction 2 x 1.1 Background : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 x 1.2 Outline of paper : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 x 2 The theory FS 0 and notational conventions 4 x 2.1 What is FS 0 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 x 3 An informal description of Gentzen's calculus 5 x 3.1 The language : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 x 3.2 The calculus for classical propositional logic : : : : : : : : : : : : 6 x 4 Formalising the ...
Implementing F S0 in Isabelle: adding structure at the metalevel
 University of Cambridge Computer Laboratory
, 1995
"... Abstract Often the theoretical virtue of simplicity in a theory does not fit with the practical necessities of working with it. We present as a case study an implementation in a generic theorem prover (Isabelle) of a theory (F S0) which at first sight seems to lake all the facilties needed to be pra ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract Often the theoretical virtue of simplicity in a theory does not fit with the practical necessities of working with it. We present as a case study an implementation in a generic theorem prover (Isabelle) of a theory (F S0) which at first sight seems to lake all the facilties needed to be practically usable. However, we show that we can use the facilties available in Isabelle to provide all the structuring facilities (modules, abstraction, etc.) that are needed without compromising the simplicity of the original theory in any way, resulting in a thouroghly practical implementation. We further argue that it would be difficult to build a custom implemenation as effective. A great many logics have been proposed as tools in computer science, especially for all sorts of formal, machine checked reasoning. However, if we try to implement these theories in some practical manner, we find that what has been proposed by theoreticians as a practical tool has to be augmented in all sorts