# Recursively find the transitively closed dependencies of the set $1
# of *.vo files, using an accumulating parameter $2 of dependencies
# previously found.  We extract the dependencies from the
# corresponding *.v.d files using sed(1), filter out previously found
# dependencies, sort to remove duplicates, then make a recursive call
# with the deduplicated newly found dependencies.  When $1 becomes
# empty, the result is $2.
ifdef VDFILE
# Coq >= 8.8
read_deps = $(if $(wildcard $(VDFILE).d),$(filter %.vo,$(foreach vo,$1,$(shell grep '^[^:]*$(vo)[^:]*:' $(VDFILE).d | sed -n 's/^[^:]*: // p'))))
else
read_deps = $(if $(wildcard $(1:.vo=.v.d)),$(filter %.vo,$(shell sed -n 's/^[^:]*: // p' $(wildcard $(1:.vo=.v.d)))))
endif
vo_closure = $(if $1,$(call vo_closure,$(sort $(filter-out $1 $2,$(call read_deps,$1))),$1 $2),$2)

# Recursively find the transitively closed reverse dependencies of the
# $2 of *.vo files, using an accumulating parameter $3 of dependencies
# previously found.  The parameter $1 is the full set of *.vo files.
# We use read_deps above to extract the depedencies of each file in
# $1, filtering for files that mention dependencies in $2.  As in
# vo_closure, we filter out previously found dependencies, sort to
# remove duplicates, then make a recursive call with the deduplicated
# newly found dependencies.  When $1 becomes empty, the result is $2.
read_reverse_deps = $(foreach vo,$1,$(if $(filter $2,$(call read_deps,$(vo))),$(vo)))
vo_reverse_closure = $(if $2,$(call vo_reverse_closure,$1,$(sort $(filter-out $2 $3,$(call read_reverse_deps,$1,$2))),$2 $3),$3)