TITLE: Forcing in Constructive Set Theories
QUESTION [8 upvotes]: 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.

REPLY [8 votes]: See 
Forcing for IZF in sheaf toposes
Also 
Toposes from Forcing for Intuitionistic ZF with Atoms.

Edit:
Maybe more references:
Heyting-valued models for intuitionistic set theory
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
Topological forcing semantics with settling.