| Groupoid of Equational Proofs (2007) | |||||||||||||||
Abstract | |||||||||||||||
| h\Omega; V; E i induces a graph GP of terms and equations, while proof figures in P induces an\Omega1712 AP on groupoids. Although the construction of AP is quite syntactic, it is not free over G P. In order to make the meaning of freeness precise, we introduce a notion of\Omega3924 and show that AP is freely generated by the\Omegae342 GP induced by P. Incidentally, this construction introduces a congruence on proof figures, by which `logically equivalent ' proof figures are equalized. 3 The authors gratefully acknowledge the support from Monbu-sho Kaken-hi, Suri-ronri oyobi sono shuhen-bun'ya no kenkyu (04302009). (axiom) s = t ax ("s = t " 2 E) (reflexivity) t = t refl | |||||||||||||||
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