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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: sci.logic
Subject: Re: What are Simple Types (Was: Proofs as programs)
Date: Thu, 19 Dec 2024 00:33:07 +0100
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Hi,

The typing rules for WE3 are similar to WE2.
The changes are:

- WE2 doesn't require a context
- WE3 requires a context
- WE2 has only modus ponense and constants
- WE3 has additionally deduction theorem and variables

See also here what WE3 requires:

https://en.wikipedia.org/wiki/Simply_typed_lambda_calculus#Typing_rules

Bye

Mild Shock schrieb:
> The requirement for week 3 is explicitly lambda expressions:
> 
>> Create a proof search in Simple Types,
>> that finds Lambda Expressions as proof,
>> for a given formula in propositional logic.
>>
>> The logic is the same as in Weekend 2. 
> 
> 
> For Affine Logic the lambda expressions should have a funny property:
> 
> - A variable occurs only once unbound in the bound scope.
> 
> For example this here, although it has a simple type:
> 
> λ y:A λ x:A->A. x (x y)
> 
> It cannot be a proof term of Affine Logic, since x occurs twice.
> 
> Some testing showed you don't produce lambda expressions:
> 
> You produce:
> 
>> But I am not familiar with this proof display:
>>
>> [
>>    impI((p->0))
>>    impI((p->0))
>>    [
>>      impE1(1:(p->q))
>>      impI(p)
>>      [
>>        impE1(1:p)
>>        unif(2:p)
>>      ]
>>      [
>>        impE2(1:0)
>>        botE(3:0)
>>      ]
>>    ]
>>    [
>>      impE2(1:p)
>>      [
>>        impE1(1:p)
>>        unif(2:p)
>>      ]
>>      [
>>        impE2(1:0)
>>        unif(3:0)
>>      ]
>>    ]
>> ] 
> 
> Julio Di Egidio schrieb:
>> On 18/12/2024 15:30, Mild Shock wrote:
>>
>>> Maybe your work qualifies for Weekend 3.
>>
>> In fact, I have replied to the WE3 announcement.
>>
>>> I don't know yet. You have to tell us. Do
>>> you think it implements a Natural Deduction
>>> with Simple Types proof extraction?
>>
>> It implements "affine intuitionistic propositional logic", and I am 
>> getting to evaluation/compilation which is the functional side (more 
>> details in my initial reply): so, sure, I even classify my reduction 
>> rules as intros vs elims...
>>
>> What is the deadline?  I don't know what WE is 3.
>>
>> -Julio
>>
>