Even LF included beta eta hence has a non-trivial judgemental equality. Not to mention the equations for substitution.
Thorsten
On 09/02/2019, 11:38, "homotopyt...@googlegroups.com on behalf of Thomas Streicher" <homotopyt...@googlegroups.com on behalf of stre...@mathematik.tu-darmstadt.de > wrote:
Working without any judgemental equality was the aim of the original
LF where elements of a type A correspond to formal derivations of A in
abstract syntax. Also Isabelle works a bit like that.
So with a modicum of judgemental equality one uses dependent types for
having a syntax for formal derivations. But, of course, this is
absolutely useless when you want to execute your proofs!
Thomas
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