TLAPS: how to take a \beta-reduction step?

[Marko Schuetz-Schmuck]

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

[Stephan Merz]

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

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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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[Marko Schuetz-Schmuck]

Dear Stephan,

Stephan Merz <stepha...@gmail.com> writes:

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

thanks!!! That did it.

Best regards,

Marko

> To view this discussion on the web visit https://groups.google.com/d/msgid/tlaplus/944861DF-5AC1-4DEA-A37E-6D581E5A0F04%40gmail.com.

> For more options, visit https://groups.google.com/d/optout.

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Prof. Dr. Marko Schütz-Schmuck
Department of Mathematical Sciences
University of Puerto Rico at Mayagüez
Mayagüez, PR 00681