Re: [tlaplus] TLAPS: how to take a \beta-reduction step?

Hello,

TLAPS only supports functions of one argument. It’s probably best to replace your function of type

[ Elems \X SUBSET Elems -> SUBSET Elems ]

by a “curried” function

[ Elems -> [ SUBSET Elems -> SUBSET Elems ] ]

and correspondingly write

ASSUME ...

PROVE x \in [new \in Elems |-> [set_1 \in SUBSET Elems |-> set_1 \cup {new}]][x][set]

Regards,

Stephan

On 20 Jun 2019, at 18:39, 'Marko Schuetz-Schmuck' via tlaplus <tlaplus@xxxxxxxxxxxxxxxx> wrote:

Dear All,

I have a function Insert and an operator InsertOp as in the attached
file. When I make the definition of the operator available TLAPS proves
the corresponding theorem, but when I make the definition of the
function available the function gets rewritten leading to the goal

ASSUME NEW CONSTANT Elems,
      NEW CONSTANT x \in Elems,
      NEW CONSTANT set \in SUBSET Elems
PROVE x
      \in [new \in Elems, set_1 \in SUBSET Elems |-> set_1 \cup {new}][x,
                                                                   set]

How do I tell TLAPS to take the \beta-reduction step?

I was unable to find this in all the TLAPS documentation I checked.

Thanks and best regards,

Marko

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------------------------------- MODULE Dummy -------------------------------
EXTENDS TLAPS
CONSTANT Elems
ASSUME \E x : x \in Elems

Insert[new \in Elems, set \in SUBSET Elems] ==
set \cup {new}

InsertOp(new, set) ==
set \cup {new}

THEOREM \A x \in Elems, set \in SUBSET Elems:
x \in Insert[x, set]
<1> SUFFICES ASSUME NEW x \in Elems, NEW set \in SUBSET Elems
              PROVE x \in Insert[x, set]
   OBVIOUS
<1> QED
   BY DEF Insert

THEOREM \A x \in Elems, set \in SUBSET Elems:
x \in InsertOp(x, set)
<1>a SUFFICES ASSUME NEW x \in Elems, NEW set \in SUBSET Elems
              PROVE x \in InsertOp(x, set)
   OBVIOUS
<1>b QED
   BY DEF InsertOp
=============================================================================
\* Modification History
\* Last modified Thu Jun 20 12:30:32 AST 2019 by marko
\* Created Thu Jun 13 13:34:49 AST 2019 by marko

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