Add property checks for Nat (#1175)

test_workspace/Nat.bosatsu

@@ -1,37 +1,72 @@
 package Bosatsu/Nat
 
 from Bosatsu/Predef import add as operator +, times as operator *
-export Nat(), times2, add, mult, exp, to_Int, to_Nat, is_even, div2
+export Nat(), times2, add, sub_Nat, mult, exp, to_Int, to_Nat, is_even, div2, cmp_Nat
 
 # This is the traditional encoding of natural numbers
 # it is useful when you are iterating on all values
 enum Nat: Zero, Succ(prev: Nat)
 
+def cmp_Nat(a: Nat, b: Nat) -> Comparison:
+    recur a:
+        case Zero:
+            match b:
+                case Zero: EQ
+                case _: LT
+        case Succ(n):
+            match b:
+                case Zero: GT
+                case Succ(m): cmp_Nat(n, m)
+
 # This is an O(n) operation
 def times2(n: Nat) -> Nat:
-  recur n:
-    Zero: Zero
-    Succ(prev):
-      # 2*(n + 1) = 2*n + 1 + 1
-      Succ(Succ(times2(prev)))
+  def loop(n: Nat, acc: Nat):
+      recur n:
+        Zero: acc
+        Succ(prev):
+          # 2*(n + 1) = 2*n + 1 + 1
+          loop(prev, Succ(Succ(acc)))
+  loop(n, Zero)
 
 def add(n1: Nat, n2: Nat) -> Nat:
-  recur n1:
-    Zero: n2
-    Succ(prev_n1):
-      match n2:
-        Zero: n1
-        Succ(prev_n2): Succ(Succ(add(prev_n1, prev_n2)))
-
-# (n1 + 1) * (n2 + 1) = n1 * n2 + n1 + n2 + 1
+  def loop(n1: Nat, n2: Nat):
+    recur n1:
+      Zero: n2
+      Succ(prev_n1): loop(prev_n1, Succ(n2))
+
+  if n2 matches Zero: n1
+  else: loop(n1, n2)
+
+def sub_Nat(n1: Nat, n2: Nat) -> Nat:
+  recur n2:
+    Zero: n1
+    Succ(prev_n2):
+      # (n1 + 1) - (n2 + 1) == (n1 - n2)
+      match n1:
+        case Zero: Zero
+        case Succ(prev_n1):
+          sub_Nat(prev_n1, prev_n2)
+
 def mult(n1: Nat, n2: Nat) -> Nat:
-  recur n1:
-    Zero: Zero
-    Succ(n1):
-      match n2:
-        Zero: Zero
-        Succ(n2):
-          Succ(mult(n1, n2).add(add(n1, n2)))
+  # return n1 * n2 + c
+  # note: (n1 + 1) * (n2 + 1) + c ==
+  # n1 * n2 + (n1 + n2 + 1 + c)
+  def loop(n1: Nat, n2: Nat, c: Nat):
+    recur n1:
+      Zero: c
+      Succ(n1):
+        match n2:
+          Zero: c
+          Succ(n2):
+            c1 = Succ(add(add(n1, n2), c))
+            loop(n1, n2, c1)
+
+  # we repeatedly do add(n, m)
+  # where we keep stepping down by one on both sides.
+  # add is more efficient if the lhs is smaller
+  # so we check that first
+  if cmp_Nat(n1, n2) matches GT: loop(n2, n1, Zero)
+  else: loop(n1, n2, Zero)
 
 def is_even(n: Nat) -> Bool:
     def loop(n: Nat, res: Bool) -> Bool:

test_workspace/NumberProps.bosatsu

@@ -0,0 +1,111 @@
+package Bosatsu/NumberProps
+
+from Bosatsu/BinNat import (BinNat, toBinNat as int_to_BinNat)
+from Bosatsu/Nat import (Nat, Zero as NZero, Succ as NSucc, to_Nat as int_to_Nat, is_even as is_even_Nat,
+  times2 as times2_Nat, div2 as div2_Nat, cmp_Nat, to_Int as nat_to_Int, add as add_Nat,
+  mult as mult_Nat, exp as exp_Nat, sub_Nat)
+from Bosatsu/Properties import (Prop, suite_Prop, forall_Prop, run_Prop)
+from Bosatsu/Rand import (Rand, from_pair, geometric_Int, int_range, map_Rand, prod_Rand)
+
+export (rand_Int, rand_Nat, rand_BinNat)
+
+# Property checks for Nat, BinNat, Int
+
+#external def todo(ignore: x) -> forall a. a
+
+rand_Int: Rand[Int] = from_pair(int_range(128), geometric_Int)
+rand_Nat: Rand[Nat] = rand_Int.map_Rand(int_to_Nat)
+rand_BinNat: Rand[BinNat] = rand_Int.map_Rand(int_to_BinNat)
+
+eq_Int = (a, b) -> a.cmp_Int(b) matches EQ
+
+int_props = suite_Prop(
+  "Int props",
+  [
+    forall_Prop(prod_Rand(rand_Int, rand_Int), "divmod law", ((a, b)) -> (
+      adivb = a.div(b)
+      amodb = a.mod_Int(b)
+      a1 = adivb.times(b).add(amodb)
+      Assertion(eq_Int(a1, a), "check")
+    )),
+  ]
+)
+
+def cmp_Comparison(c1: Comparison, c2: Comparison) -> Comparison:
+    match c1:
+        case LT:
+            match c2:
+                case LT: EQ
+                case _: LT
+        case EQ:
+            match c2:
+                case LT: GT
+                case EQ: EQ
+                case GT: LT
+        case GT:
+            match c2:
+                case GT: EQ
+                case _: GT
+
+def exp_Int(base: Int, power: Int) -> Int:
+  int_loop(power, 1, (p, acc) -> (p.sub(1), acc.times(base)))
+
+small_rand_Nat: Rand[Nat] = int_range(7).map_Rand(int_to_Nat)
+
+nat_props = suite_Prop(
+  "Nat props",
+  [
+    forall_Prop(rand_Nat, "if is_even(n) then times2(div2(n)) == n", n -> (
+      if is_even_Nat(n):
+        n1 = times2_Nat(div2_Nat(n))
+        Assertion(cmp_Nat(n1, n) matches EQ, "times2/div2")
+      else:
+        # we return the previous number
+        n1 = times2_Nat(div2_Nat(n))
+        Assertion(cmp_Nat(NSucc(n1), n) matches EQ, "times2/div2")
+    )),
+    forall_Prop(prod_Rand(rand_Nat, rand_Nat), "cmp_Nat matches cmp_Int", ((n1, n2)) -> (
+      cmp_n = cmp_Nat(n1, n2)
+      cmp_i = cmp_Int(n1.nat_to_Int(), n2.nat_to_Int())
+      Assertion(cmp_Comparison(cmp_n, cmp_i) matches EQ, "cmp_Nat")
+    )),
+    forall_Prop(prod_Rand(rand_Nat, rand_Nat), "add homomorphism", ((n1, n2)) -> (
+      n3 = add_Nat(n1, n2)
+      i3 = add(n1.nat_to_Int(), n2.nat_to_Int())
+      Assertion(cmp_Int(n3.nat_to_Int(), i3) matches EQ, "add homomorphism")
+    )),
+    forall_Prop(prod_Rand(rand_Nat, rand_Nat), "sub_Nat homomorphism", ((n1, n2)) -> (
+      n3 = sub_Nat(n1, n2)
+      i1 = n1.nat_to_Int()
+      i2 = n2.nat_to_Int()
+      match cmp_Int(i1, i2):
+        case EQ | GT:
+          i3 = sub(i1, i2)
+          Assertion(cmp_Int(n3.nat_to_Int(), i3) matches EQ, "sub_Nat homomorphism")
+        case LT:
+          Assertion(n3 matches NZero, "sub to zero")
+    )),
+    forall_Prop(prod_Rand(rand_Nat, rand_Nat), "mult homomorphism", ((n1, n2)) -> (
+      n3 = mult_Nat(n1, n2)
+      i3 = times(n1.nat_to_Int(), n2.nat_to_Int())
+      Assertion(cmp_Int(n3.nat_to_Int(), i3) matches EQ, "mult homomorphism")
+    )),
+    forall_Prop(prod_Rand(small_rand_Nat, small_rand_Nat), "exp homomorphism", ((n1, n2)) -> (
+      n3 = exp_Nat(n1, n2)
+      i3 = exp_Int(n1.nat_to_Int(), n2.nat_to_Int())
+      Assertion(cmp_Int(n3.nat_to_Int(), i3) matches EQ, "exp homomorphism")
+    )),
+    forall_Prop(rand_Nat, "times2 == x -> mult(2, x)", n -> (
+      t2 = n.times2_Nat()
+      t2_2 = mult_Nat(n, NSucc(NSucc(NZero)))
+      Assertion(cmp_Nat(t2, t2_2) matches EQ, "times2 == mult(2, _)")
+    )),
+  ]
+)
+
+all_props = [int_props, nat_props]
+
+seed = 123456
+test = TestSuite("properties", [
+  run_Prop(p, 100, seed) for p in all_props
+])

test_workspace/Properties.bosatsu

@@ -73,5 +73,5 @@ all_props = suite_Prop(
     shift_unshift_law,
     positive_and_law,
   ])
-
-all_laws = run_Prop(all_props, 100, 42)
+  
+test = run_Prop(all_props, 100, 42)

test_workspace/Rand.bosatsu

@@ -7,7 +7,7 @@ from Bosatsu/BinNat import (BinNat, Zero as BZero, Odd, Even,
   next as next_BinNat, prev as prev_BinNat, toInt as binNat_to_Int)
 
 export (Rand, run_Rand, prod_Rand, map_Rand, flat_map_Rand, const_Rand,
-  int_range, sequence_Rand, bool_Rand, geometric_Int, from_pair, one_of)
+  int_range, nat_range, sequence_Rand, bool_Rand, geometric_Int, from_pair, one_of)
 
 struct State(s0: Int, s1: Int, s2: Int, s3: Int)
 struct UInt64(toInt: Int)
@@ -171,6 +171,9 @@ def int_range(high: Int) -> Rand[Int]:
       resample(rand_Int, high, uint_count)
   else: const0
 
+def nat_range(high: Nat) -> Rand[Nat]:
+  int_range(nat_to_Int(high)).map_Rand(int_to_Nat)
+
 def geometric(depth: Nat, acc: Int) -> Rand[Int]:
     recur depth:
         case Zero: const_Rand(acc)
@@ -182,6 +185,7 @@ def geometric(depth: Nat, acc: Int) -> Rand[Int]:
                   case False: geometric(prev, acc + 1)
           ))
 
+# geometric distribution with mean 1
 geometric_Int: Rand[Int] = geometric(nat30, 0)
 
 def len[a](list: List[a]) -> BinNat: