[Relay] Add hd,tl,nth for list in Prelude (apache#2771)

python/tvm/relay/prelude.py

@@ -18,6 +18,50 @@ def define_list_adt(self):
         self.cons = Constructor("cons", [a, self.l(a)], self.l)
         self.mod[self.l] = TypeData(self.l, [a], [self.nil, self.cons])
 
+    def define_list_hd(self):
+        """Defines a function to get the head of a list. Assume the list has at least one
+        element.
+
+        hd(l) : list[a] -> a
+        """
+        self.hd = GlobalVar("hd")
+        a = TypeVar("a")
+        x = Var("x", self.l(a))
+        y = Var("y")
+        z = Var("z")
+        # Don't match nil() since it will break type checking
+        cons_case = Clause(PatternConstructor(self.cons, [PatternVar(y), PatternVar(z)]), y)
+        self.mod[self.hd] = Function([x], Match(x, [cons_case]), a, [a])
+
+    def define_list_tl(self):
+        """Defines a function to get the tail of a list.
+
+        tl(l) : list[a] -> list[a]
+        """
+        self.tl = GlobalVar("tl")
+        a = TypeVar("a")
+        x = Var("x", self.l(a))
+        y = Var("y")
+        z = Var("z")
+        nil_case = Clause(PatternConstructor(self.nil, []), self.nil())
+        cons_case = Clause(PatternConstructor(self.cons, [PatternVar(y), PatternVar(z)]), z)
+        self.mod[self.tl] = Function([x], Match(x, [nil_case, cons_case]), self.l(a), [a])
+
+    def define_list_nth(self):
+        """Defines a function to get the nth element of a list.
+
+        nth(l) : list[a] -> a
+        """
+        self.nth = GlobalVar("nth")
+        a = TypeVar("a")
+        x = Var("x", self.l(a))
+        n = Var("n", self.nat())
+
+        y = Var("y")
+        z_case = Clause(PatternConstructor(self.z), self.hd(x))
+        s_case = Clause(PatternConstructor(self.s, [PatternVar(y)]), self.nth(self.tl(x), y))
+        self.mod[self.nth] = Function([x, n], Match(n, [z_case, s_case]), a, [a])
+
     def define_list_map(self):
         """Defines a function for mapping a function over a list's
         elements. That is, map(f, l) returns a new list where
@@ -405,6 +449,8 @@ def define_iterate(self):
     def __init__(self, mod):
         self.mod = mod
         self.define_list_adt()
+        self.define_list_hd()
+        self.define_list_tl()
         self.define_list_map()
         self.define_list_foldl()
         self.define_list_foldr()
@@ -423,6 +469,7 @@ def __init__(self, mod):
         self.define_nat_double()
         self.define_nat_add()
         self.define_list_length()
+        self.define_list_nth()
         self.define_list_sum()
 
         self.define_tree_adt()

tests/python/relay/test_adt.py

@@ -23,6 +23,9 @@
 nil = p.nil
 cons = p.cons
 l = p.l
+hd = p.hd
+tl = p.tl
+nth = p.nth
 length = p.length
 map = p.map
 foldl = p.foldl
@@ -120,6 +123,30 @@ def test_list_constructor():
     a = relay.TypeVar("a")
     assert relay.ir_pass.infer_type(cons(z(), nil()), mod).checked_type == l(nat())
 
+def test_hd_tl():
+    expected = list(range(10))
+    l = nil()
+    for i in reversed(expected):
+        l = cons(build_nat(i), l)
+
+    got = []
+    for i in range(len(expected)):
+        got.append(count(intrp.evaluate(hd(l))))
+        l = tl(l)
+
+    assert got == expected
+
+def test_nth():
+    expected = list(range(10))
+    l = nil()
+    for i in reversed(expected):
+        l = cons(build_nat(i), l)
+
+    got = []
+    for i in range(len(expected)):
+        got.append(count(intrp.evaluate(nth(l, build_nat(i)))))
+
+    assert got == expected
 
 def test_length():
     a = relay.TypeVar("a")