Please see the JuMP readme regarding support for Julia v1.0.
The latest release of JuMP (based on MathProgBase) is not compatible with Julia 0.7 or 1.0. We encourage users to continue to use Julia 0.6 for a stable environment. The development version of JuMP (based on MOI) supports both Julia 0.6 and Julia 0.7 but is alpha-quality with breaking changes in still progress. See the Discourse post for more information on Julia 0.7/1.0 support.