Division

src/num.ts

@@ -1,6 +1,6 @@
 import { toNative as $$, L, P, _, fromNative as __, id } from './core';
 import { EQ, GT, LT, Ord } from './ord';
-import { Bool, False, True } from './bool';
+import { Bool, False, iif, True } from './bool';
 
 export type Num = L<<T extends P>(z: T) => L<(n: L<(p: Num) => T>) => T>>;
 
@@ -52,6 +52,12 @@ export const sub: L<(l: Num) => L<(r: Num) => Num>>
 export const mul: L<(l: Num) => L<(r: Num) => Num>>
   = _(l => _(r => l._(Zero)._(_(pl => sum._(r)._(mul._(pl)._(r))))));
 
+export const div: L<(l: Num) => L<(r: Num) => Num>>
+  = _(l => _(r => iif._(lt._(l)._(r))._(Zero)._(succ._(div._(sub._(l)._(r))._(r)))));
+
+export const mod: L<(l: Num) => L<(r: Num) => Num>>
+= _(l => _(r => iif._(lt._(l)._(r))._(l)._(mod._(sub._(l)._(r))._(r))));
+
 export const fromNumber: (n: number) => Num
   = n => !n ? Zero : Succ._(new L(() => fromNumber(n - 1).value));
 

test/num.spec.ts

@@ -2,7 +2,7 @@ import { describe, expect, it } from '@jest/globals';
 import { L, undef } from '../src/core';
 import { toNOrd as $o, NOrd } from '../src/ord';
 import { toBoolean as $b, fromBoolean as _b } from '../src/bool';
-import { toNumber as $, Num, Succ, Zero, fromNumber as _, cmp, eq, ge, gt, ifz, le, lt, mul, pred, sub, succ, sum } from '../src/num';
+import { toNumber as $, Num, Succ, Zero, fromNumber as _, cmp, div, eq, ge, gt, ifz, le, lt, mod, mul, pred, sub, succ, sum } from '../src/num';
 
 describe('Num', () => {
   const infinity: Num = new L(() => Succ._(infinity).value);
@@ -332,4 +332,56 @@ describe('Num', () => {
       expect($(mul._(_(0))._(undef))).toBe(0);
     });
   });
+
+  describe('div', () => {
+    it('0 div 10 is 0', () => {
+      expect($(div._(_(0))._(_(10)))).toBe(0);
+    });
+
+    it('1 div 10 is 0', () => {
+      expect($(div._(_(1))._(_(10)))).toBe(0);
+    });
+
+    it('10 div 1 is 10', () => {
+      expect($(div._(_(10))._(_(1)))).toBe(10);
+    });
+
+    it('10 div 5 is 2', () => {
+      expect($(div._(_(10))._(_(5)))).toBe(2);
+    });
+
+    it('10 div 3 is 3', () => {
+      expect($(div._(_(10))._(_(3)))).toBe(3);
+    });
+
+    it.failing('0 div ignores second argument', () => {
+      expect($(div._(_(0))._(undef))).toBe(0);
+    });
+  });
+
+  describe('mod', () => {
+    it('0 mod 10 is 0', () => {
+      expect($(mod._(_(0))._(_(10)))).toBe(0);
+    });
+
+    it('1 mod 10 is 1', () => {
+      expect($(mod._(_(1))._(_(10)))).toBe(1);
+    });
+
+    it('10 mod 1 is 0', () => {
+      expect($(mod._(_(10))._(_(1)))).toBe(0);
+    });
+
+    it('10 mod 5 is 0', () => {
+      expect($(mod._(_(10))._(_(5)))).toBe(0);
+    });
+
+    it('10 mod 3 is 1', () => {
+      expect($(mod._(_(10))._(_(3)))).toBe(1);
+    });
+
+    it.failing('0 mod ignores second argument', () => {
+      expect($(mod._(_(0))._(undef))).toBe(0);
+    });
+  });
 });