diff --git a/src/models/ModelInterface.jl b/src/models/ModelInterface.jl
index f532d2b0..b4f25eff 100644
--- a/src/models/ModelInterface.jl
+++ b/src/models/ModelInterface.jl
@@ -145,18 +145,10 @@ macro instance(head, model, body)
   theory = macroexpand(__module__, :($theory_module.Meta.@theory))
 
   # A dictionary to look up the Julia type of a type constructor from its name (an ident)
-  i = 0
-  jltype_by_sort = Dict(map(sorts(theory)) do s 
-    sorttype = getvalue(theory[methodof(s)])
-    s => if sorttype isa AlgTypeConstructor 
-      i += 1
-      instance_types[i]
-    elseif sorttype isa AlgStruct
-      nameof(sorttype.declaration)
-    end
-  end)
-  i == length(instance_types) || error("Did not use all types ($i): $instance_types")
-
+  jltype_by_sort = Dict{AlgSort,Expr0}([
+    zip(primitive_sorts(theory), instance_types)..., 
+    [s => nameof(headof(s)) for s in struct_sorts(theory)]...
+  ]) 
 
   # Get the model type that we are overloading for, or nothing if this is the
   # default instance for `instance_types`
diff --git a/src/syntax/GATs.jl b/src/syntax/GATs.jl
index c7db9c82..3d451eb2 100644
--- a/src/syntax/GATs.jl
+++ b/src/syntax/GATs.jl
@@ -5,8 +5,8 @@ export Constant, AlgTerm, AlgType, AlgAST,
   AlgTypeConstructor, AlgAccessor, AlgAxiom, AlgStruct, AlgDot, AlgFunction,
   typesortsignature, sortsignature, getdecl,
   GATSegment, GAT, GATContext, gettheory, gettypecontext, allmethods, 
-  resolvemethod, resolvefield,
-  termcons,typecons, accessors, structs,
+  resolvemethod,
+  termcons,typecons, accessors, structs, primitive_sorts, struct_sorts,
   equations, build_infer_expr, compile, sortcheck, allnames, sorts, sortname,
   InCtx, TermInCtx, TypeInCtx, headof, argsof, methodof, bodyof, argcontext,
   infer_type
diff --git a/src/syntax/gats/gat.jl b/src/syntax/gats/gat.jl
index e62a0181..eba4b2cd 100644
--- a/src/syntax/gats/gat.jl
+++ b/src/syntax/gats/gat.jl
@@ -163,6 +163,12 @@ function allnames(theory::GAT; aliases=false)
 end
 
 sorts(theory::GAT) = theory.sorts
+primitive_sorts(theory::GAT) = 
+  filter(s->getvalue(theory[methodof(s)]) isa AlgTypeConstructor, sorts(theory))
+
+# NOTE: AlgStruct is the only derived sort this returns.
+struct_sorts(theory::GAT) = 
+  filter(s->getvalue(theory[methodof(s)]) isa AlgStruct, sorts(theory))
 
 function termcons(theory::GAT)
   xs = Tuple{Ident, Ident}[]
@@ -231,20 +237,5 @@ else
   Scopes.unsafe_pushbinding!(theory, Binding{Judgment}(name, AlgDeclaration()))
 end
 
-"""Get type associated with a field of a struct"""
-function resolvefield(t::Context, method::Ident, field::Symbol)
-  str = getvalue(t[method])
-  str.fields[ident(str.fields; name=field)] |> getvalue
-end
-
 """Get all structs in a theory"""
-function structs(t::GAT)
-  res = AlgStruct[]
-  for s in sorts(t)
-    v = getvalue(t[methodof(s)])
-    if v isa AlgStruct 
-      push!(res, v)
-    end
-  end
-  res
-end
+structs(t::GAT) = AlgStruct[getvalue(t[methodof(s)]) for s in struct_sorts(t)]
\ No newline at end of file
diff --git a/src/syntax/gats/judgments.jl b/src/syntax/gats/judgments.jl
index a3ad371c..6bc28b36 100644
--- a/src/syntax/gats/judgments.jl
+++ b/src/syntax/gats/judgments.jl
@@ -66,7 +66,7 @@ A declaration of a type constructor.
   args::Vector{LID}
 end
 
-Scopes.getcontext(tc::AlgTypeConstructor) = tc.localcontext
+Scopes.getcontext(tc::TrmTypConstructor) = tc.localcontext
 
 abstract type AccessorField <: Judgment end
 
@@ -87,7 +87,6 @@ exist.
   arg::Int
 end
 
-Scopes.getcontext(::AccessorField) = EmptyContext{AlgType}()
 
 getdecl(acc::AccessorField) = acc.declaration
 
@@ -106,7 +105,6 @@ A declaration of a term constructor as a method of an `AlgFunction`.
   type::Union{TypeScope,AlgType}
 end
 
-Scopes.getcontext(tc::AlgTermConstructor) = tc.localcontext
 
 sortsignature(tc::TrmTypConstructor) =
   AlgSort.(getvalue.(argsof(tc)))
@@ -122,7 +120,6 @@ A declaration of an axiom
   equands::Vector{AlgTerm}
 end
 
-Scopes.getcontext(t::AlgAxiom) = t.localcontext
 
 """
 `AlgSorts`
@@ -175,8 +172,6 @@ typesortsignature(tc::AlgStruct) =
   AlgSort.(getvalue.(typeargsof(tc)))
 argsof(t::AlgStruct) = getbindings(t.fields)
 
-Scopes.getcontext(tc::AlgStruct) = tc.localcontext
-
 """
 A shorthand for a function, such as "square(x) := x * x".  It is relevant for 
 models but can be ignored by theory maps, as it is fully determined by other 
@@ -188,5 +183,3 @@ judgments in the theory.
   args::Vector{LID}
   value::AlgTerm
 end
-
-Scopes.getcontext(tc::AlgFunction) = tc.localcontext
diff --git a/test/nonstdlib/Pushouts.jl b/test/nonstdlib/Pushouts.jl
index 76597ef5..7b2b2a98 100644
--- a/test/nonstdlib/Pushouts.jl
+++ b/test/nonstdlib/Pushouts.jl
@@ -28,4 +28,5 @@ Universal input:                    Output
   @test cospan(res) == Cospan(4, [1,1,2,3], [1,2,4])
   @test ι₁(res) == [1,1,2,3]
   @test universal(res, Cospan(4, [3,3,2,2],[3,2,1])) == [3,2,2,1]
+  @test_throws ErrorException universal(PushoutInt(4, [1,1,2,3],[1,2,3]), Cospan(4, [3,3,2,2],[3,2,1]))
 end
diff --git a/test/syntax/GATs.jl b/test/syntax/GATs.jl
index fe34251d..7640d69f 100644
--- a/test/syntax/GATs.jl
+++ b/test/syntax/GATs.jl
@@ -64,6 +64,7 @@ ob_decl = getvalue(thcat[O])
 
 ObT = fromexpr(thcat, :Ob, AlgType)
 ObS = AlgSort(ObT)
+@test headof(ObS) == O
 @test toexpr(GATContext(thcat), ObS) == :Ob