A Proof Description Language and Its Reduction System
Masamichi Hagiya · Publications of the Research Institute for Mathematical Sciences · 1983
The normalization of a natural deduction proof of a closed existential formula ∃xA gives a term t and a proof of A_x[t] . This allows us to regard a proof as a program (Goad [9] [10] etc.). But it is not always necessary to completely normalize the given proof to obtain t . We analyze the situation by introducing the notions called minimal I -reduct, proper reduction etc.; in a word, we define the normal order of proof reduction and study its proof-theoretical property. Then, we present an experimental proof-checker-reducer system that actually uses those principles. In designing a proof-checker (or rather a proof description language ), we focussed our attention on the readability of proofs.