diff --git a/src/Bridges/Constraint/map.jl b/src/Bridges/Constraint/map.jl
index 95a6d63e16..38cfbb11d7 100644
--- a/src/Bridges/Constraint/map.jl
+++ b/src/Bridges/Constraint/map.jl
@@ -86,7 +86,7 @@ function Base.getindex(
 end
 
 function Base.delete!(map::Map, ci::MOI.ConstraintIndex)
-    _unregister_for_final_touch(map, map.bridges[_index(ci)])
+    _unregister_for_final_touch(map, map.bridges[_index(ci)]::AbstractBridge)
     map.bridges[_index(ci)] = nothing
     return map
 end
diff --git a/src/Bridges/Variable/map.jl b/src/Bridges/Variable/map.jl
index 9563d0c6f0..7b9e98adb0 100644
--- a/src/Bridges/Variable/map.jl
+++ b/src/Bridges/Variable/map.jl
@@ -208,7 +208,7 @@ function number_with_set(map::Map, S::Type{<:MOI.AbstractSet})
 end
 
 function constraint(map::Map, vi::MOI.VariableIndex)
-    S = constrained_set(map, vi)
+    S = constrained_set(map, vi)::Type{<:MOI.AbstractSet}
     F = MOI.Utilities.variable_function_type(S)
     return MOI.ConstraintIndex{F,S}(-bridge_index(map, vi))
 end
@@ -235,12 +235,14 @@ Return a list of all the different types `(F, S)` of `F`-in-`S` constraints in
 function list_of_constraint_types(map::Map)
     list = Set{Tuple{Type,Type}}()
     for i in eachindex(map.bridges)
-        if map.bridges[i] !== nothing
-            S = map.sets[i]
-            if S != MOI.Reals
-                push!(list, (MOI.Utilities.variable_function_type(S), S))
-            end
+        if map.bridges[i] === nothing
+            continue
+        end
+        S = map.sets[i]
+        if S === nothing || S == MOI.Reals
+            continue
         end
+        push!(list, (MOI.Utilities.variable_function_type(S), S))
     end
     return list
 end
diff --git a/src/Bridges/bridge_optimizer.jl b/src/Bridges/bridge_optimizer.jl
index 22aba001c9..c0af0b3440 100644
--- a/src/Bridges/bridge_optimizer.jl
+++ b/src/Bridges/bridge_optimizer.jl
@@ -1225,7 +1225,7 @@ end
 function MOI.set(
     b::AbstractBridgeOptimizer,
     attr::MOI.AbstractVariableAttribute,
-    index::MOI.Index,
+    index::MOI.VariableIndex,
     value,
 )
     value = bridged_function(b, value)
@@ -1240,7 +1240,7 @@ end
 function MOI.set(
     b::AbstractBridgeOptimizer,
     attr::MOI.AbstractVariableAttribute,
-    indices::Vector{<:MOI.Index},
+    indices::Vector{MOI.VariableIndex},
     values::Vector,
 )
     if any(index -> is_bridged(b, index), indices)
@@ -2004,7 +2004,10 @@ function bridged_variable_function(
     vi::MOI.VariableIndex,
 )
     if is_bridged(b, vi)
-        func = bridged_function(bridge(b, vi), _index(b, vi)...)
+        func = bridged_function(
+            bridge(b, vi)::Variable.AbstractBridge,
+            _index(b, vi)...,
+        )
         # If two variable bridges are chained, `func` may still contain
         # bridged variables.
         return bridged_function(b, func)
diff --git a/src/Bridges/lazy_bridge_optimizer.jl b/src/Bridges/lazy_bridge_optimizer.jl
index daac29de41..fb5c9703f8 100644
--- a/src/Bridges/lazy_bridge_optimizer.jl
+++ b/src/Bridges/lazy_bridge_optimizer.jl
@@ -128,9 +128,12 @@ end
 
 Return the list of `VariableNode` that would be added if `BT` is used in `b`.
 """
-function _variable_nodes(b::LazyBridgeOptimizer, ::Type{BT}) where {BT}
+function _variable_nodes(
+    b::LazyBridgeOptimizer,
+    ::Type{BT},
+) where {BT<:AbstractBridge}
     return VariableNode[
-        node(b, S) for (S,) in added_constrained_variable_types(BT)
+        node(b, S)::VariableNode for (S,) in added_constrained_variable_types(BT)
     ]
 end
 
@@ -139,7 +142,10 @@ end
 
 Return the list of `ConstraintNode` that would be added if `BT` is used in `b`.
 """
-function _constraint_nodes(b::LazyBridgeOptimizer, ::Type{BT}) where {BT}
+function _constraint_nodes(
+    b::LazyBridgeOptimizer,
+    ::Type{BT},
+) where {BT<:AbstractBridge}
     return ConstraintNode[
         node(b, F, S) for (F, S) in added_constraint_types(BT)
     ]
@@ -168,10 +174,10 @@ function _edge(
 )
     return ObjectiveEdge(
         index,
-        _variable_nodes(b, BT),
-        _constraint_nodes(b, BT),
-        node(b, set_objective_function_type(BT)),
-        bridging_cost(BT),
+        _variable_nodes(b, BT)::Vector{VariableNode},
+        _constraint_nodes(b, BT)::Vector{ConstraintNode},
+        node(b, set_objective_function_type(BT))::ObjectiveNode,
+        bridging_cost(BT)::Float64,
     )
 end
 
@@ -321,7 +327,7 @@ function node(b::LazyBridgeOptimizer, F::Type{<:MOI.AbstractFunction})
     push!(b.objective_types, (F,))
     for (i, BT) in enumerate(b.objective_bridge_types)
         if Objective.supports_objective_function(BT, F)
-            bridge_type = Objective.concrete_bridge_type(BT, F)
+            bridge_type = Objective.concrete_bridge_type(BT, F)::Type{<:Objective.AbstractBridge}
             edge = _edge(b, i, bridge_type)::ObjectiveEdge
             add_edge(b.graph, objective_node, edge)
         end
diff --git a/src/Utilities/functions.jl b/src/Utilities/functions.jl
index 3c436b43a7..53fefc8da8 100644
--- a/src/Utilities/functions.jl
+++ b/src/Utilities/functions.jl
@@ -150,7 +150,7 @@ function eval_variables(value_fn::Function, f::MOI.ScalarQuadraticFunction)
 end
 
 function eval_variables(value_fn::Function, f::MOI.VectorOfVariables)
-    return value_fn.(f.variables)
+    return map(value_fn, f.variables)
 end
 
 function eval_variables(value_fn::Function, f::MOI.VectorAffineFunction)
diff --git a/src/Utilities/matrix_of_constraints.jl b/src/Utilities/matrix_of_constraints.jl
index 10bdac499f..843f2262cc 100644
--- a/src/Utilities/matrix_of_constraints.jl
+++ b/src/Utilities/matrix_of_constraints.jl
@@ -271,7 +271,7 @@ function rows end
 
 MOI.is_empty(v::MatrixOfConstraints) = MOI.is_empty(v.sets)
 
-function MOI.empty!(v::MatrixOfConstraints{T}) where {T}
+function MOI.empty!(v::MatrixOfConstraints{T,AT,BT,ST}) where {T,AT,BT,ST}
     MOI.empty!(v.coefficients)
     empty!(v.constants)
     MOI.empty!(v.sets)
diff --git a/src/Utilities/objective_container.jl b/src/Utilities/objective_container.jl
index d8fd4db793..59f046d8a0 100644
--- a/src/Utilities/objective_container.jl
+++ b/src/Utilities/objective_container.jl
@@ -123,12 +123,12 @@ function MOI.get(
     T,
     F<:Union{
         MOI.VariableIndex,
-        MOI.ScalarAffineFunction{T},
-        MOI.ScalarQuadraticFunction{T},
+        MOI.ScalarAffineFunction,
+        MOI.ScalarQuadraticFunction,
         MOI.ScalarNonlinearFunction,
         MOI.VectorOfVariables,
-        MOI.VectorAffineFunction{T},
-        MOI.VectorQuadraticFunction{T},
+        MOI.VectorAffineFunction,
+        MOI.VectorQuadraticFunction,
         MOI.VectorNonlinearFunction,
     },
 }
diff --git a/src/Utilities/struct_of_constraints.jl b/src/Utilities/struct_of_constraints.jl
index 41d6f83cda..b383ceeb5c 100644
--- a/src/Utilities/struct_of_constraints.jl
+++ b/src/Utilities/struct_of_constraints.jl
@@ -283,7 +283,7 @@ function struct_of_constraint_code(struct_name, types, field_types = nothing)
     typed_struct = :($(struct_name){$T})
     type_parametrized = field_types === nothing
     if type_parametrized
-        field_types = [Symbol("C$i") for i in eachindex(types)]
+        field_types = Symbol[Symbol("C$i") for i in eachindex(types)]
         append!(typed_struct.args, field_types)
     end
     code = quote
diff --git a/src/Utilities/universalfallback.jl b/src/Utilities/universalfallback.jl
index db1e624867..0c90656c41 100644
--- a/src/Utilities/universalfallback.jl
+++ b/src/Utilities/universalfallback.jl
@@ -579,7 +579,7 @@ function MOI.modify(
     if uf.objective === nothing
         MOI.modify(uf.model, obj, change)
     else
-        uf.objective = modify_function(uf.objective, change)
+        uf.objective = modify_function(something(uf.objective), change)
     end
     return
 end