Explicit dispatch

src/models/ModelInterface.jl

@@ -45,15 +45,16 @@ in the theory.
 module ModelInterface
 
 export implements, impl_type, TypeCheckFail, SignatureMismatchError, 
-       @model, @instance, @withmodel, @fail, migrate_model
+       @model, @instance, @withmodel, @fail, migrate_model, @default_model,
+       Dispatch
 
 using ...Syntax
 using ...Util.MetaUtils
 using ...Util.MetaUtils: JuliaFunctionSigNoWhere
 
 import ...Syntax.TheoryMaps: migrator 
 using ...Syntax.TheoryMaps: dom, codom
-using ...Syntax.TheoryInterface: GAT_MODULE_LOOKUP
+using ...Syntax.TheoryInterface: GAT_MODULE_LOOKUP, Dispatch
 
 using MLStyle
 using DataStructures: DefaultDict, OrderedDict
@@ -80,15 +81,18 @@ implements(m, ::Type{Val{tag}}) where {tag} = nothing
 
 implements(m, tag::ScopeTag) = implements(m, Val{tag})
 
-impl_type(m, tag::ScopeTag) = impl_type(m, Val{tag})
-
-impl_type(m, mod::Module, name::Symbol) = 
-  impl_type(m, gettag(ident(mod.Meta.theory; name)))
-
-
 implements(m, theory_module::Module) =
   all(!isnothing(implements(m, gettag(scope))) for scope in theory_module.Meta.theory.segments.scopes)
 
+"""
+If `m` implements a GAT with a type constructor (identified by ident `id`), 
+mapped to a Julia type, this function returns that Julia type.
+"""
+impl_type(m, id::Ident) = impl_type(m, Val{gettag(id)}, Val{getlid(id)})
+
+impl_type(m, mod::Module, name::Symbol) = 
+  impl_type(m, ident(mod.Meta.theory; name))
+
 struct TypeCheckFail <: Exception
   model::Any
   theory::GAT
@@ -600,17 +604,17 @@ end
 function impl_type_declaration(model_type, whereparams, sort, jltype)
   quote 
     if !hasmethod($(GlobalRef(ModelInterface, :impl_type)), 
-      ($(model_type) where {$(whereparams...)}, Type{Val{$(gettag(getdecl(sort)))}}))
+      ($(model_type) where {$(whereparams...)}, Type{Val{$(gettag(getdecl(sort)))}}, Type{Val{$(getlid(getdecl(sort)))}}))
       $(GlobalRef(ModelInterface, :impl_type))(
-          ::$(model_type), ::Type{Val{$(gettag(getdecl(sort)))}}
+          ::$(model_type), ::Type{Val{$(gettag(getdecl(sort)))}}, ::Type{Val{$(getlid(getdecl(sort)))}}
         ) where {$(whereparams...)} = $(jltype)
     end
   end
 end
 
 function implements_declaration(model_type, scope, whereparams)
   notes = ImplementationNotes(nothing)
-  m = only(methods(implements, (Any, Type{Val{1}})))
+  _, m = methods(implements, (Any, Type{Val{1}})) # first method is for Dispatch
   quote
     if $m == only(methods($(GlobalRef(ModelInterface, :implements)), 
         ($(model_type) where {$(whereparams...)}, Type{Val{$(gettag(scope))}})))
@@ -679,7 +683,7 @@ function migrate_model(F::AbsTheoryMap, m::Any, new_model_name::Union{Nothing,Sy
 
   # Expressions which evaluate to the correct Julia type
   jltype_by_sort = Dict(map(sorts(dom_theory)) do v
-    v => :(impl_type($m, gettag(getdecl(AlgSort($F($v.method).val)))))
+    v => :(impl_type($m, getdecl(AlgSort($F($v.method).val))))
   end)
 
   _x = gensym("val")
@@ -802,4 +806,121 @@ function to_call_accessor(t::AlgTerm, x::Symbol, mod::Module)
   Expr(:call, Expr(:ref, :($mod.$(nameof(headof(b)))), :(model.model)), rest)
 end
 
+
+# Default models
+
+"""
+Create an @instance for a model `M` whose methods are determined by type 
+dispatch, e.g.:
+
+```
+@instance ThCategory{O,H} [model::M] begin
+  id(x::O) = id(x)
+  compose(f::H, g::H)::H = compose(f, g)
+end
+```
+
+Use this with caution! For example, using this with two different models of 
+the same theory with the same types would cause a conflict.
+"""
+function default_instance(theorymodule, theory, jltype_by_sort, model)
+  acc = Iterators.flatten(values.(values(theory.accessors)))
+
+  termcon_funs = map(last.(termcons(theory)) ∪ acc) do x 
+    generate_function(use_dispatch_method_impl(x, theory, jltype_by_sort))
+  end
+  generate_instance(
+    theory, theorymodule, jltype_by_sort, model, [], 
+    Expr(:block, termcon_funs...); typecheck=true, escape=true)
+end
+
+"""
+Create an @instance for a model `M` whose methods are determined by the 
+implementation of another model, `M2`, e.g.:
+
+```
+@instance ThCategory{O,H} [model::M] begin
+  id(x::O) = id[M2](x)
+  compose(f::H, g::H)::H = compose[M2](f, g)
+end
+```
+"""
+function default_model(theorymodule, theory, jltype_by_sort, model)
+  acc = Iterators.flatten(values.(values(theory.accessors)))
+  termcon_funs = map(last.(termcons(theory)) ∪ acc) do x 
+    generate_function(use_model_method_impl(x, theory, jltype_by_sort, model))
+  end
+  generate_instance(
+    theory, theorymodule, jltype_by_sort, nothing, [], 
+    Expr(:block, termcon_funs...); typecheck=true, escape=true)
+end
+
+macro default_model(head, model)
+  # Parse the head of @instance to get theory and instance types
+  (theory_module, instance_types) = @match head begin
+    :($ThX{$(Ts...)}) => (ThX, Ts)
+    _ => error("invalid syntax for head of @instance macro: $head")
+  end
+
+  # Get the underlying theory
+  theory = macroexpand(__module__, :($theory_module.Meta.@theory))
+
+  # A dictionary to look up the Julia type of a type constructor from its name (an ident)
+  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`
+  m = parse_model_param(model)[1]
+
+  # Create the actual instance
+  default_model(theory_module, theory, jltype_by_sort, m)
+end
+
+"""
+A canonical implementation that just calls the method with the implementation
+of another model, `m`.
+"""
+function use_model_method_impl(x::Ident, theory::GAT, 
+                               jltype_by_sort::Dict{AlgSort}, m::Expr0)
+  op = getvalue(theory[x])
+  name = nameof(getdecl(op))
+  return_type = op isa AlgAccessor ? nothing : jltype_by_sort[AlgSort(op.type)]
+  args = args_from_sorts(sortsignature(op), jltype_by_sort)
+  impl = :(return $(name)[$m()]($(args...)))
+  JuliaFunction(name=name, args=args, return_type=return_type, impl=impl)
+end
+
+"""
+A canonical implementation that just calls the method with type dispatch.
+"""
+function use_dispatch_method_impl(x::Ident, theory::GAT, 
+                                  jltype_by_sort::Dict{AlgSort})
+  op = getvalue(theory[x])
+  name = nameof(getdecl(op))
+  return_type = op isa AlgAccessor ? nothing : jltype_by_sort[AlgSort(op.type)]
+  args = args_from_sorts(sortsignature(op), jltype_by_sort)
+  impl = :(return $(name)($(args...)))
+  JuliaFunction(name=name, args=args, return_type=return_type, impl=impl)
+end
+
+# Special model for any theory which uses dispatch
+##################################################
+
+"""
+Check whether a dispatch model implements a particular scope of a theory.
+This could be more rigorous, like actually checking whether certain methods 
+exist, but for now users will be assuming that the dispatch methods exist when
+using a Dispatch model.
+"""
+function implements(d::Dispatch, ::T) where {X,T <: Type{Val{X}}}
+  hastag(d.t, X) ? true : nothing
+end
+
+function impl_type(d::Dispatch, x::Ident)
+  d.types[AlgSort(x, only(d.t.resolvers[x])[2])]
+end
+
 end # module

src/models/SymbolicModels.jl

@@ -8,6 +8,7 @@ using ...Util
 using ...Syntax
 import ...Syntax: invoke_term
 using ..ModelInterface
+using ..ModelInterface: args_from_sorts, default_instance
 
 using Base.Meta: ParseError
 using MLStyle
@@ -262,6 +263,10 @@ macro symbolic_model(decl, theoryname, body)
 
   module_structs = symbolic_structs(theory, abstract_types, __module__)
 
+  # Part 1.5: Generate a model  
+  imp = Expr(:import, Expr(:(:), Expr(:., :., :., name), [
+    Expr(:., x) for x in [name, theoryname, name, nameof.(sorts(theory))...]]...))
+
   # Part 2: Generating internal methods
 
   module_methods = [internal_accessors(theory)..., 
@@ -271,15 +276,20 @@ macro symbolic_model(decl, theoryname, body)
     export $(nameof.(sorts(theory))...)
     using ..($(nameof(__module__)))
     import ..($(nameof(__module__))): $theoryname
+
+    $(module_structs...)
+
+    $(generate_function.(module_methods)...)
+
     module $(esc(:Meta))
-      import ..($(name)): $theoryname
+      $imp
       const $(esc(:theory_module)) = $(esc(theoryname))
       const $(esc(:theory)) = $(theory)
       const $(esc(:theory_type)) = $(esc(theoryname)).Meta.T
+      # Canonical symbolic model
+      $(esc(:M)) = Dispatch($(esc(:theory)), [$(esc.(nameof.(theory.sorts))...)])
     end
 
-    $(module_structs...)
-    $(generate_function.(module_methods)...)
   end)
 
   # Part 3: Generating instance of theory
@@ -731,4 +741,4 @@ function show_latex_script(io::IO, expr::GATExpr, head::String;
   print(io, "}")
 end
 
-end
+end # module

src/syntax/TheoryInterface.jl

@@ -184,11 +184,27 @@ function theory_impl(head, body, __module__)
   )
 end
 
+"""
+The Dispatch type is a model of every theory.
+"""
+@struct_hash_equal struct Dispatch 
+  t::GAT
+  types::Dict{AlgSort,Type}
+end
+
+Dispatch(t::GAT, v::AbstractVector{<:Type}) = 
+  Dispatch(t, Dict(zip(sorts(t), v)))
+
+# WARNING: if any other package play with indexing methodnames with their own 
+# structs, then this code could be broken because it assumes we are the only  
+# ones to use this trick.
 function juliadeclaration(name::Symbol)
   quote
     function $name end
+    # we expect just one method because of Dispatch type
+    if isempty(Base.methods(Base.getindex, [typeof($name), Any]))
+      Base.getindex(f::typeof($name), ::$(GlobalRef(TheoryInterface, :Dispatch))) = f
 
-    if Base.isempty(Base.methods(Base.getindex, [typeof($name), Any]))
       function Base.getindex(::typeof($name), m::Any) 
         (args...; context=nothing) -> $name($(GlobalRef(TheoryInterface, :WithModel))(m), args...; context)
       end

src/syntax/gats/gat.jl

@@ -36,6 +36,8 @@ fancier.
   bysignature::Dict{AlgSorts, Ident}
 end
 
+Base.iterate(m::MethodResolver, i...) = iterate(m.bysignature, i...)
+
 function MethodResolver()
   MethodResolver(Dict{AlgSorts, Ident}())
 end

test/models/ModelInterface.jl

@@ -56,7 +56,7 @@ end
 @test !implements(FinSetC(), ThNatPlus)
 
 # Todo: get things working where Ob and Hom are the same type (i.e. binding dict not monic)
-struct TypedFinSetC
+@struct_hash_equal struct TypedFinSetC
   ntypes::Int
 end
 
@@ -214,4 +214,19 @@ end
 # this will fail unless WithModel accepts subtypes
 @test ThSet.default[MyVect([1,2,3])](1) == 1
 
+# Test default model + dispatch model
+#####################################
+@test_throws MethodError id(2)
+
+@default_model ThCategory{Int, Vector{Int}} [model::FinSetC]
+
+d = Dispatch(ThCategory.Meta.theory, [Int, Vector{Int}])
+@test implements(d, ThCategory)
+@test !implements(d, ThNatPlus)
+@test impl_type(d, ThCategory, :Ob) == Int 
+@test impl_type(d, ThCategory, :Hom) == Vector{Int} 
+
+@test id(2) == [1,2] == ThCategory.id[d](2)
+@test compose([1,2,3], [2,1,3]) == [2,1,3]
+
 end # module

test/models/SymbolicModels.jl

@@ -19,6 +19,15 @@ f = FreeCategory.Hom{:generator}([:f], [x, y])
 @test ThCategory.id(x) isa HomExpr{:id}
 @test ThCategory.compose(ThCategory.id(x), f) == f
 
+M = FreeCategory.Meta.M
+@test M isa Dispatch
+@test implements(M, ThCategory)
+@test !implements(M, ThNatPlus)
+@test impl_type(M, ThCategory, :Ob) == FreeCategory.Ob
+@test impl_type(M, ThCategory, :Hom) == FreeCategory.Hom
+@test ThCategory.id[M](x) isa HomExpr{:id}
+@test ThCategory.compose[M](ThCategory.id(x), f) == f
+
 # Monoid
 ########