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To: John Harrison <John.Harrison@uk.ac.cam.cl>
Cc: info-hol@edu.uidaho.cs.ted, Tom.Melham@uk.ac.cam.cl
Subject: Re: Completeness proofs
In-Reply-To: Your message of Fri, 19 Feb 93 00:53:04 +0000. <"swan.cl.ca.321:19.02.93.00.53.11"@cl.cam.ac.uk>
Date: Fri, 19 Feb 93 13:25:22 +0000
From: Tom Melham <Tom.Melham@uk.ac.cam.cl>
Message-Id: <"swan.cl.ca.441:19.02.93.13.25.48"@cl.cam.ac.uk>


John Harrison writes:

> As an extremely trivial example of doing metalogical reasoning inside HOL, I
> offer the following proof of the Deduction Theorem ...

See also some of the example applications of the inductive definitions
package that Juanito Camilleri and I developed:

    cl.ml       : Church-Rosser theorem for combinatory logic 
    mil.ml      : minimal intuitionistic logic and Curry-Howard isomorphism

In particular, mil.ml involves *both* an inductive definition of "provable"
as well as a formalization of proof-objects.

They are in contrib/rule-induction.

Tom