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Make Interleave agree with the rest of the module on the empty sequence #129

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Merged
lemmy merged 1 commit into from
Sep 9, 2026
Merged

Make Interleave agree with the rest of the module on the empty sequence #129

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6 changes: 5 additions & 1 deletion modules/SequencesExt.tla
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Original file line number Diff line number Diff line change
Expand Up @@ -446,7 +446,11 @@ Interleave(s, t) ==
ELSE u[i-1] \o << <<s[i]>> >> \o << <<t[i]>> >>
IN Last(u)
\* error "Interleave: sequences must have same length"
[] Len(s) = Len(t) /\ Len(s) = 0 -> << <<>>, <<>> >>
\* <<>> is the identity of \o, which is what the arm above builds the
\* result with, so Len(Interleave(s, t)) = 2 * Len(s) holds for the empty
\* sequence as well. It also matches the other operators of this module
\* on an empty argument, such as Zip, FlattenSeq, and Reverse.
[] Len(s) = Len(t) /\ Len(s) = 0 -> << >>

(**************************************************************************)
(* The set of all subsequences of the sequence s . Note that the empty *)
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10 changes: 9 additions & 1 deletion tests/SequencesExtTests.tla
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Expand Up @@ -172,7 +172,7 @@ ASSUME FlattenSeq(<<"a", "b">>) = "ab"

-----------------------------------------------------------------------------

ASSUME Interleave(<<>>, <<>>) = << <<>>, <<>> >>
ASSUME Interleave(<<>>, <<>>) = << >>
ASSUME Interleave(<< <<>> >>, <<1>>) = << << <<>> >>, <<1>> >>
ASSUME Interleave(<<1>>, << <<>> >>) = << <<1>>, << <<>> >> >>
ASSUME Interleave(<<2>>,<<2>>) = << <<2>>, <<2>> >>
Expand All @@ -184,6 +184,14 @@ ASSUME AssertEq(FlattenSeq(Interleave(<<1,3>>,<<2,4>>)), <<1, 2, 3, 4>>)
ASSUME Interleave(<<"a", "c">>, <<"b", "d">>) = <<<<"a">>, <<"b">>, <<"c">>, <<"d">>>>
ASSUME AssertEq(FlattenSeq(Interleave(<<"a", "c">>, <<"b", "d">>)), <<"a", "b", "c", "d">>)

\* Two entries per position of s, the odd ones from s and the even ones from
\* t. The empty case is the one this used to fail, with a length of 2.
ASSUME \A s \in BoundedSeq(1..3, 3) :
\A t \in {u \in BoundedSeq(1..3, 3) : Len(u) = Len(s)} :
/\ Len(Interleave(s, t)) = 2 * Len(s)
/\ \A i \in 1..Len(s) : /\ Interleave(s, t)[2*i - 1] = <<s[i]>>
/\ Interleave(s, t)[2*i] = <<t[i]>>

-----------------------------------------------------------------------------

ASSUME Zip(<<>>, <<>>) = << >>
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