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

Why do you use strings for variables? Why isn't term dependent on the scope?

Is this how people still work in coq?

Thorsten

On 13/03/2020, 13:27, 
"coq-club-request AT inria.fr
 on behalf of Louis Noizet" 
<coq-club-request AT inria.fr
 on behalf of 
louis.noizet AT irisa.fr>
 wrote:

    Sorry for hitting send too fast !
    
    
    Hi, I'm trying to implement some kind of non-deterministic λ-calculus.
    Anyway, the terms are something like that
    
    Inductive term :=
    | var: string -> term
    | func: var -> body -> term
    with body :=
    | choose: list body -> body
    | ret: term -> body
    | apply: var -> term -> body
    | letin: var -> body -> body -> body
    
    And now I'm trying to define the type of values.
    So a functional value is a relation between values, because it takes a 
value and produces some number of values.
    
    I would like to write something like that :
    
    Inductive value : Type :=
    | base: forall t: Type, t -> value
    | func: (value -> value -> Prop) -> value.
    
    
    Of course, this is not working because of non-positivity. 
    
    The obvious solution would be to use closures, but we want to be able to 
externally define functions (directly in gallina, via a relation) without 
having to explicitly define a body for it.
    
    I thought for sure somebody must have already had a similar issue.
    
    By the way, we did a version using step-indexing, but it's not entirely 
satisfactory, because it makes the definition hard to use to make a proof.
    
    Thanks in advance !
    
    -- 
    Louis
    
    




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