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[Thorsten Altenkirch <Thorsten.Altenkirch AT nottingham.ac.uk>]

What is nice about this conceptual confusion?

On 16/11/2015 11:14, "Freek Wiedijk" 
<freek AT cs.ru.nl>
 wrote:

>Hi Yasuaki and Yves,
>
>>If I remember correctly, early version of Automath
>>(starting around 1968 and into the 1970s) used lambda
>>terms to describe the type of lambda terms.
>
>*All* versions of Automath.  In Automath there has never
>been a difference between lambda and Pi, both "fun x :
>A =>" and "forall x : A," are written as [x:A].  You get
>very nice typing rules that way:
>
>        Gamma |- M : A   Gamma |- N : B
>        -------------------------------
>               Gamma |- MN : AN
>
>             Gamma, x : A |- M : B
>            ------------------------
>            Gamma |- [x:A]M : [x:A]B
>
>But of course Automath still has the ugliness of the
>conversion rule, so nothing is perfect :-)
>
>Freek





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