Results 1 
2 of
2
A Formalisation Of Weak Normalisation (With Respect To Permutations) Of Sequent Calculus Proofs
, 1999
"... rule). This is also the case for NJ and LJ as defined in this formalisation. This is due to the particular nature of the logics in question, and does not necessarily generalise to other logics. In particular, a formalisation of linear logic would not work in this fashion, and a more complex variable ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
rule). This is also the case for NJ and LJ as defined in this formalisation. This is due to the particular nature of the logics in question, and does not necessarily generalise to other logics. In particular, a formalisation of linear logic would not work in this fashion, and a more complex variablereferencing mechanism would be required. See Section 6 for a further discussion of this problem. Other operations, such as substitutions (sub in Table 2) and weakening, require lift and drop operations as defined in [27] to ensure the correctness of the de Bruijn indexing.
MetaTheory of SequentStyle Calculi in Coq
, 1997
"... We describe a formalisation of proof theory about sequentstyle calculi, based on informal work in [DP96]. The formalisation uses de Bruijn nameless dummy variables (also called de Bruijn indices) [dB72], and is performed within the proof assistant Coq [BB + 96]. We also present a description of ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We describe a formalisation of proof theory about sequentstyle calculi, based on informal work in [DP96]. The formalisation uses de Bruijn nameless dummy variables (also called de Bruijn indices) [dB72], and is performed within the proof assistant Coq [BB + 96]. We also present a description of some of the other possible approaches to formal metatheory, particularly an abstract named syntax and higher order abstract syntax. 1 Introduction Formal proof has developed into a significant area of mathematics and logic. Until recently, however, such proofs have concentrated on proofs within logical systems, and metatheoretic work has continued to be done informally. Recent developments in proof assistants and automated theorem provers have opened up the possibilities for machinesupported metatheory. This paper presents a formalisation of a large theory comprising of over 200 definitions and more than 500 individual theorems about three different deductive system. 1 The central dif...