16 files changed, 157 insertions(+), 2 deletions(-)

M lib/dhall/ast.rb
M lib/dhall/builtins.rb
M lib/dhall/normalize.rb
A test/normalization/beta/FunctionApplicationCaptureA.dhallb
A test/normalization/beta/FunctionApplicationCaptureB.dhallb
A test/normalization/beta/FunctionApplicationNoSubstituteA.dhallb
A test/normalization/beta/FunctionApplicationNoSubstituteB.dhallb
A test/normalization/beta/FunctionApplicationNormalizeArgumentsA.dhallb
A test/normalization/beta/FunctionApplicationNormalizeArgumentsB.dhallb
A test/normalization/beta/FunctionApplicationSubstituteA.dhallb
A test/normalization/beta/FunctionApplicationSubstituteB.dhallb
A test/normalization/beta/FunctionNormalizeArgumentsA.dhallb
A test/normalization/beta/FunctionNormalizeArgumentsB.dhallb
A test/normalization/beta/FunctionTypeNormalizeArgumentsA.dhallb
A test/normalization/beta/FunctionTypeNormalizeArgumentsB.dhallb
M test/test_normalization.rb

@@ 129,6 129,14 @@ module Dhall
 		def map_subexpressions(&block)
 			with(var: var, type: type.nil? ? nil : block[type], body: block[body])
 		end
+
+		def call(*args)
+			return super if args.length > 1
+			body.substitute(
+				Variable.new(name: var),
+				args.first.shift(1, var, 0)
+			).shift(-1, var, 0).normalize
+		end
 	end
 
 	class Forall < Function; end


@@ 279,6 287,10 @@ module Dhall
 		def map_subexpressions(&block)
 			with(value: block[value], type: type.nil? ? type : block[type])
 		end
+
+		def reduce(_, &block)
+			block[value]
+		end
 	end
 
 	class OptionalNone < Optional


@@ 289,6 301,10 @@ module Dhall
 		def map_subexpressions(&block)
 			with(type: block[@type])
 		end
+
+		def reduce(z)
+			z
+		end
 	end
 
 	class Merge < Expression

@@ 154,6 154,10 @@ module Dhall
 		end
 
 		class List_build < Builtin
+			def initialize(type=nil)
+				@type = type
+			end
+
 			def fusion(*args)
 				_, arg, = args
 				if arg.is_a?(Application) &&


@@ 165,6 169,37 @@ module Dhall
 					super
 				end
 			end
+
+			def call(arg)
+				if @type.nil?
+					self.class.new(arg)
+				else
+					arg.call(
+						Application.new(
+							function: Variable.new(name: "List"),
+							arguments: [@type]
+						),
+						Function.new(
+							var: "_",
+							type: @type,
+							body: Function.new(
+								var:  "_",
+								type: Application.new(
+									function: Variable.new(name: "List"),
+									arguments: [@type.shift(1, "_", 0)]
+								),
+								body: Operator::ListConcatenate.new(
+									lhs: List.new(
+										elements: [Variable.new(name: "_", index: 1)]
+									),
+									rhs: Variable.new(name: "_")
+								)
+							),
+						),
+						EmptyList.new(type: @type)
+					)
+				end
+			end
 		end
 
 		class List_fold < Builtin


@@ 249,6 284,10 @@ module Dhall
 		end
 
 		class Optional_build < Builtin
+			def initialize(type=nil)
+				@type = type
+			end
+
 			def fusion(*args)
 				_, arg, = args
 				if arg.is_a?(Application) &&


@@ 260,9 299,54 @@ module Dhall
 					super
 				end
 			end
+
+			def call(arg)
+				if @type.nil?
+					self.class.new(arg)
+				else
+					arg.call(
+						Application.new(
+							function: Variable.new(name: "Optional"),
+							arguments: [@type]
+						),
+						Function.new(
+							var: "_",
+							type: @type,
+							body: Optional.new(
+								value: Variable.new(name: "_"),
+								type: @type
+							)
+						),
+						OptionalNone.new(type: @type)
+					)
+				end
+			end
+
 		end
 
 		class Optional_fold < Builtin
+			def initialize(type=nil, optional=nil, ztype=nil, f=nil)
+				@type = type
+				@optional = optional
+				@ztype = ztype
+				@f = f
+			end
+
+			def call(arg)
+				if @type.nil?
+					self.class.new(arg)
+				elsif arg.is_a?(Optional)
+					self.class.new(@type, arg)
+				elsif !@optional.nil? && @ztype.nil?
+					self.class.new(@type, @optional, arg)
+				elsif !@optional.nil? && @f.nil?
+					self.class.new(@type, @optional, @ztype, arg)
+				elsif !@optional.nil?
+					@optional.reduce(arg, &@f)
+				else
+					super
+				end
+			end
 		end
 
 		class Text_show < Builtin

@@ 12,6 12,10 @@ module Dhall
 			map_subexpressions { |expr| expr.shift(amount, name, min_index) }
 		end
 
+		def substitute(var, with_expr)
+			map_subexpressions { |expr| expr.substitute(var, with_expr) }
+		end
+
 		def fusion(*); end
 	end
 


@@ 21,7 25,8 @@ module Dhall
 			normalized = super
 			return normalized.fuse if normalized.fuse
 
-			if normalized.function.is_a?(Builtin)
+			if normalized.function.is_a?(Builtin) ||
+			   normalized.function.is_a?(Function)
 				return normalized.function.call(*normalized.arguments)
 			end
 


@@ 46,6 51,15 @@ module Dhall
 				body: body.shift(amount, name, min_index + 1)
 			)
 		end
+
+		def substitute(svar, with_expr)
+			with_expr = with_expr.shift(1, var, 0)
+			if var == svar.name
+				super(svar.with(index: svar.index + 1), with_expr)
+			else
+				super(svar, with_expr)
+			end
+		end
 	end
 
 	class Forall; end


@@ 58,6 72,10 @@ module Dhall
 			return self if self.name != name || min_index > index
 			with(index: index + amount)
 		end
+
+		def substitute(var, with_expr)
+			self == var ? with_expr : self
+		end
 	end
 
 	class Operator


@@ 293,7 311,7 @@ module Dhall
 		end
 
 		def desugar
-			lets.reduce(body) { |inside, let|
+			lets.reverse.reduce(body) { |inside, let|
 				Application.new(
 					function: Function.new(
 						var: let.var,

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@@ 78,4 78,34 @@ class TestParser < Minitest::Test
 			).shift(1, "x", 0)
 		)
 	end
+
+	def test_substitute_variable
+		assert_equal(
+			Dhall::Natural.new(value: 1),
+			Dhall::Variable.new(name: "x", index: 0).substitute(
+				Dhall::Variable.new(name: "x", index: 0),
+				Dhall::Natural.new(value: 1)
+			)
+		)
+	end
+
+	def test_substitute_variable_different_name
+		assert_equal(
+			Dhall::Variable.new(name: "y", index: 0),
+			Dhall::Variable.new(name: "y", index: 0).substitute(
+				Dhall::Variable.new(name: "x", index: 0),
+				Dhall::Natural.new(value: 1)
+			)
+		)
+	end
+
+	def test_substitute_variable_different_index
+		assert_equal(
+			Dhall::Variable.new(name: "x", index: 1),
+			Dhall::Variable.new(name: "x", index: 1).substitute(
+				Dhall::Variable.new(name: "x", index: 0),
+				Dhall::Natural.new(value: 1)
+			)
+		)
+	end
 end