Questions tagged [isabelle]

Use this tag with the proof assistant Isabelle, if your question is specific to a certain object logic please use the corresponding tag (eg. questions specific to Isabelle/HOL should also be tagged with (isabelle-hol)).

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18 votes
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How can all functions be total in Isabelle?

Isabelle/HOL’s logic is called a logic of “total functions”, yet there are functions that are obviously not total, such as division div. How does this make sense?
Joachim Breitner's user avatar
19 votes
2 answers

Why is Isabelle usually not just Isabelle but Isabelle/<xyz>?

For most proof assistants the name alone is common, E.g. Coq, Lean but with Isabelle it is often seen as Isabelle/<xyz>? Why the two parts? What is Isabelle/HOL Isabelle/FOL Isabelle/ZF ...
Guy Coder's user avatar
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8 votes
2 answers

How to prove Gauss summation of integers with proof assistants using forward reasoning?

As shown in an exercise here, we can prove the Gauss summation (that $\Sigma_{i=0..n}{i} = n \cdot (n + 1)/2$ ) in Isabelle/Isar using mathematical induction, as follows. ...
tinlyx's user avatar
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5 votes
1 answer

Architecture of Isabelle: What parts are written in SML? What parts are written in Scala? What does the boundary look like?

My question is based on this question, which asks about swapping out different SML implementations when building Isabelle. I've read on Wikipedia that Isaballe is written in Scala and SML. Based on ...
Greg Nisbet's user avatar
  • 2,711
5 votes
2 answers

Standard ML is used for many proof systems. Is there a recommended implementation to use for Isabelle?

Is there a recommended implementation of Standard ML to use for Isabelle? Note: An answer should strive to include why that implementation (noted in build instructions is acceptable). While not needed ...
Guy Coder's user avatar
  • 2,836
2 votes
0 answers

Disjoint unions in Isabelle/HOL

In mathematics there is a notion of a "disjoint union" in which you "consider" all of the sets to be disjoint even if they are not. For instance, you might want to take the ...
Charles Staats's user avatar