I searched on the internet, but I could not find anything useful about applications of forcing in constructive set theories.
Are there any developments of forcing in CZF or IZF?


Thanks in advance. 



Forcing in Constructive Set Theories
See 


[Forcing for IZF in sheaf toposes](https://www.researchgate.net/publication/228380851_Forcing_for_IZF_in_sheaf_toposes)


Also 


[Toposes from Forcing for Intuitionistic ZF with Atoms.](https://arxiv.org/abs/1702.03399)




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Edit:


Maybe more references:


[Heyting-valued models for intuitionistic set theory](https://link.springer.com/chapter/10.1007%2FBFb0061825)


The book "Intuitionistic logic, model theory and forcing" by Fitting.


see also the following web-page where some references are also given:


[Constructive Set Theory: Forcing, Large Sets, and Mathematics](https://www.nsf.gov/awardsearch/showAward?AWD_ID=0301162)


[Topological forcing semantics with settling](http://www.sciencedirect.com/science/article/pii/S0168007211001369?via%3Dihub).


