Add tests for composition of head/tail and init/last

Author: penelopeysm

src/varname.jl

@@ -967,8 +967,11 @@ string_to_varname(str::AbstractString) = dict_to_varname(JSON.parse(str))
 
 Get the innermost layer of an optic.
 
+For all (normalised) optics, we have that `normalise(_tail(optic) ∘
+_head(optic) == optic)`.
+
 !!! note
-    Does not perform optic normalisation. You may wish to call
+    Does not perform optic normalisation on the input. You may wish to call
     `normalise(optic)` before using this function if the optic you are passing
     was not obtained from a VarName.
 
@@ -999,8 +1002,11 @@ _head(::typeof(identity)) = identity
 
 Get everything but the innermost layer of an optic.
 
+For all (normalised) optics, we have that `normalise(_tail(optic) ∘
+_head(optic) == optic)`.
+
 !!! note
-    Does not perform optic normalisation. You may wish to call
+    Does not perform optic normalisation on the input. You may wish to call
     `normalise(optic)` before using this function if the optic you are passing
     was not obtained from a VarName.
 
@@ -1031,8 +1037,11 @@ _tail(::typeof(identity)) = identity
 
 Get the outermost layer of an optic.
 
+For all (normalised) optics, we have that `normalise(_last(optic) ∘
+_init(optic)) == optic`.
+
 !!! note
-    Does not perform optic normalisation. You may wish to call
+    Does not perform optic normalisation on the input. You may wish to call
     `normalise(optic)` before using this function if the optic you are passing
     was not obtained from a VarName.
 
@@ -1063,8 +1072,11 @@ _last(::typeof(identity)) = identity
 
 Get everything but the outermost layer of an optic.
 
+For all (normalised) optics, we have that `normalise(_last(optic) ∘
+_init(optic)) == optic`.
+
 !!! note
-    Does not perform optic normalisation. You may wish to call
+    Does not perform optic normalisation on the input. You may wish to call
     `normalise(optic)` before using this function if the optic you are passing
     was not obtained from a VarName.
 
@@ -1084,7 +1096,9 @@ identity (generic function with 1 method)
 julia> AbstractPPL._init(Accessors.@o _)
 identity (generic function with 1 method)
 """
-_init(o::ComposedFunction{Outer,Inner}) where {Outer,Inner} = _init(o.outer) ∘ o.inner
+# This one needs normalise because it's going 'against' the direction of the
+# linked list (otherwise you will end up with identities scattered throughout)
+_init(o::ComposedFunction{Outer,Inner}) where {Outer,Inner} = normalise(_init(o.outer) ∘ o.inner)
 _init(::Accessors.PropertyLens) = identity
 _init(::Accessors.IndexLens) = identity
 _init(::typeof(identity)) = identity

test/varname.jl

@@ -252,6 +252,54 @@ end
         @test string_to_varname(varname_to_string(vn)) == vn
     end
 
+    @testset "head, tail, init, last" begin
+        @testset "specification" begin
+            @test AbstractPPL._head(@o _.a.b.c) == @o _.a
+            @test AbstractPPL._tail(@o _.a.b.c) == @o _.b.c
+            @test AbstractPPL._init(@o _.a.b.c) == @o _.a.b
+            @test AbstractPPL._last(@o _.a.b.c) == @o _.c
+
+            @test AbstractPPL._head(@o _[1][2][3]) == @o _[1]
+            @test AbstractPPL._tail(@o _[1][2][3]) == @o _[2][3]
+            @test AbstractPPL._init(@o _[1][2][3]) == @o _[1][2]
+            @test AbstractPPL._last(@o _[1][2][3]) == @o _[3]
+
+            @test AbstractPPL._head(@o _.a) == @o _.a
+            @test AbstractPPL._tail(@o _.a) == identity
+            @test AbstractPPL._init(@o _.a) == identity
+            @test AbstractPPL._last(@o _.a) == @o _.a
+
+            @test AbstractPPL._head(@o _[1]) == @o _[1]
+            @test AbstractPPL._tail(@o _[1]) == identity
+            @test AbstractPPL._init(@o _[1]) == identity
+            @test AbstractPPL._last(@o _[1]) == @o _[1]
+
+            @test AbstractPPL._head(identity) == identity
+            @test AbstractPPL._tail(identity) == identity
+            @test AbstractPPL._init(identity) == identity
+            @test AbstractPPL._last(identity) == identity
+        end
+
+        @testset "composition" begin
+            varnames = (
+                @varname(x),
+                @varname(x[1]),
+                @varname(x.a),
+                @varname(x.a.b),
+                @varname(x[1].a),
+            )
+            for vn in varnames
+                optic = getoptic(vn)
+                @test AbstractPPL.normalise(
+                    AbstractPPL._last(optic) ∘ AbstractPPL._init(optic)
+                ) == optic
+                @test AbstractPPL.normalise(
+                    AbstractPPL._tail(optic) ∘ AbstractPPL._head(optic)
+                ) == optic
+            end
+        end
+    end
+
     @testset "prefix and unprefix" begin
         @testset "basic cases" begin
             @test prefix(@varname(y), @varname(x)) == @varname(x.y)