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making comment more precise
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aleksnanevski committed Aug 21, 2023
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13 changes: 10 additions & 3 deletions theories/model.v
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Expand Up @@ -1159,19 +1159,26 @@ Qed.
(* standalone theory, where you can show that all functions that can be *)
(* produced using the syntax are monotone in the model. That proof *)
(* relied on a significant subset of Coq, but still a subset. *)

(* The paper is: *)
(* Partiality, State and Dependent Types *)
(* Kasper Svendsen, Lars Birkedal and Aleksandar Nanevski *)
(* International Conference on Typed Lambda Calculi and Applications (TLCA), pages 198-212, 2011. *)
(* International Conference on Typed Lambda Calculi and Applications (TLCA) *)
(* pages 198-212, 2011. *)

(* The model in that paper, and the one we use here, are quite different *)
(* however, and we can't exclude concocting a *)
(* non-monotone program using the syntax we export here, *)
(* though we have so far failed to do that. *)
(* based on the results of that other paper. *)
(* That said, we have so far failed to do produce such a non-monotone function. *)
(* But if such a case arises, we should switch to using Fix' *)
(* and ask for explicit proofs of monotonicity. *)
(* For all the examples we did so far, such a proof is easily *)
(* constructed, along the lines of above (and maybe can even be automated). *)
(* constructed, along the above lines (moreover, such proofs ought to be automatable) *)
(* Perhaps a proof, in the theory of Coq, that all functions are monotone *)
(* can be produced if we worked from parametricity properties of Coq, *)
(* which have been established in the past work, and even internalized *)
(* into Coq by means of parametricity axioms. But that remains future work. *)

End MonotonicityExamples.

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