Re: [TYPES] What are congruence rules called?

[ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list ]

Hello,
Not really that common in literature, but in Hindley and Selding’s book,
Lambda Calculus and Combinators, they use respectively ν and μ
to name those congruence rules, both in the untyped and the typed case.
They claim to have taken that from Curry & Feys.

Best regards

-- 
Filippo Sestini
[email protected]
(+39) 333 6757668

> On Jul 3, 2017, at 8:04 PM, Philip Wadler <[email protected]> wrote:
> 
> [ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list ]
> 
> Reduction for the simply-typed call-by-value lambda calculus consists of
> the β rule,
> 
>  (λx.N)V ⟹ N[x:=V]
> 
> and the congruence rules
> 
>  L ⟹ L′
>  ------------
>  L M ⟹ L′ M
> 
>  M ⟹ M′
>  ------------
>  V M ⟹ V M′
> 
> Question: Is there a standard greek letter for naming the congruence rules,
> such as κ or γ? Or any other relevant naming convention?
> 
> Cheers, -- P
> 
> 
> .   \ Philip Wadler, Professor of Theoretical Computer Science
> .   /\ School of Informatics, University of Edinburgh
> .  /  \ http://homepages.inf.ed.ac.uk/wadler/
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