From 50e91647503314183dda42cd84ae48387b5123b9 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Mon, 26 Jun 2017 16:13:22 +0200
Subject: [PATCH 01/20] Add parent type argument to NullaryType

---
 index.js      | 261 ++++++++++++++++++++++++++++++--------------------
 test/index.js |   8 +-
 2 files changed, 160 insertions(+), 109 deletions(-)

diff --git a/index.js b/index.js
index fce9e36..afdf9c3 100644
--- a/index.js
+++ b/index.js
@@ -353,6 +353,7 @@
     name,       // :: String
     url,        // :: String
     format,     // :: (String -> String, String -> String -> String) -> String
+    parent,     // :: Type
     test,       // :: Any -> Boolean
     keys,       // :: Array String
     types       // :: StrMap { extractor :: a -> Array b, type :: Type }
@@ -362,27 +363,35 @@
     this.keys = keys;
     this.name = name;
     this.type = type;
+    this.parent = parent;
     this.types = types;
     this.url = url;
   }
 
   _Type['@@type'] = 'sanctuary-def/Type';
 
+  _Type.prototype.test = function(x) {
+    return this.parent.test(x) && this._test(x);
+  };
+
   _Type.prototype.validate = function(x) {
-    if (!this._test(x)) return Left({value: x, propPath: []});
-    for (var idx = 0; idx < this.keys.length; idx += 1) {
-      var k = this.keys[idx];
-      var t = this.types[k];
-      for (var idx2 = 0, ys = t.extractor(x); idx2 < ys.length; idx2 += 1) {
-        var result = t.type.validate(ys[idx2]);
-        if (result.isLeft) {
-          var value = result.value.value;
-          var propPath = Z.concat([k], result.value.propPath);
-          return Left({value: value, propPath: propPath});
+    var self = this;
+    return Z.chain(function(x) {
+      if (!self._test(x)) return Left({value: x, propPath: []});
+      for (var idx = 0; idx < self.keys.length; idx += 1) {
+        var k = self.keys[idx];
+        var t = self.types[k];
+        for (var idx2 = 0, ys = t.extractor(x); idx2 < ys.length; idx2 += 1) {
+          var result = t.type.validate(ys[idx2]);
+          if (result.isLeft) {
+            var value = result.value.value;
+            var propPath = Z.concat([k], result.value.propPath);
+            return Left({value: value, propPath: propPath});
+          }
         }
       }
-    }
-    return Right(x);
+      return Right(x);
+    }, self.parent.validate(x));
   };
 
   _Type.prototype.toString = function() {
@@ -398,10 +407,6 @@
   var UNKNOWN       = 'UNKNOWN';
   var VARIABLE      = 'VARIABLE';
 
-  //  Inconsistent :: Type
-  var Inconsistent =
-  new _Type(INCONSISTENT, '', '', always2('???'), K(false), [], {});
-
   //  typeEq :: String -> a -> Boolean
   function typeEq(name) {
     return function(x) {
@@ -424,9 +429,9 @@
            '#' + stripNamespace(name);
   }
 
-  //  NullaryTypeWithUrl :: (String, Any -> Boolean) -> Type
-  function NullaryTypeWithUrl(name, test) {
-    return NullaryType(name, functionUrl(name), test);
+  //  NullaryTypeWithUrl :: (String, Type, Any -> Boolean) -> Type
+  function NullaryTypeWithUrl(name, parent, test) {
+    return NullaryType(name, functionUrl(name), parent, test);
   }
 
   //  EnumTypeWithUrl :: (String, Array Any) -> Type
@@ -456,17 +461,29 @@
   //# Any :: Type
   //.
   //. Type comprising every JavaScript value.
-  var Any = NullaryTypeWithUrl('sanctuary-def/Any', K(true));
+  var Any = NullaryTypeWithUrl('sanctuary-def/Any', null, null);
+  Any.parent = Any;
+  Any.test = K(true);
+  Any.validate = Right;
+
+  //# None :: Type
+  //.
+  //. Type with no members.
+  var None = NullaryTypeWithUrl('sanctuary-def/None', Any, K(false));
+
+  //  Inconsistent :: Type
+  var Inconsistent =
+  new _Type(INCONSISTENT, '', '', always2('???'), None, K(false), [], {});
 
   //# AnyFunction :: Type
   //.
   //. Type comprising every Function value.
-  var AnyFunction = NullaryTypeWithUrl('Function', typeofEq('function'));
+  var AnyFunction = NullaryTypeWithUrl('Function', Any, typeofEq('function'));
 
   //# Arguments :: Type
   //.
   //. Type comprising every [`arguments`][arguments] object.
-  var Arguments = NullaryTypeWithUrl('Arguments', typeEq('Arguments'));
+  var Arguments = NullaryTypeWithUrl('Arguments', Any, typeEq('Arguments'));
 
   //# Array :: Type -> Type
   //.
@@ -476,18 +493,32 @@
   //# Boolean :: Type
   //.
   //. Type comprising `true` and `false`.
-  var Boolean_ = NullaryTypeWithUrl('Boolean', typeofEq('boolean'));
+  var Boolean_ = NullaryTypeWithUrl('Boolean', Any, typeofEq('boolean'));
 
   //# Date :: Type
   //.
   //. Type comprising every Date value.
-  var Date_ = NullaryTypeWithUrl('Date', typeEq('Date'));
+  var Date_ = NullaryTypeWithUrl('Date', Any, typeEq('Date'));
 
   //# Error :: Type
   //.
   //. Type comprising every Error value, including values of more specific
   //. constructors such as [`SyntaxError`][] and [`TypeError`][].
-  var Error_ = NullaryTypeWithUrl('Error', typeEq('Error'));
+  var Error_ = NullaryTypeWithUrl('Error', Any, typeEq('Error'));
+
+  //# Number :: Type
+  //.
+  //. Type comprising every primitive Number value (including `NaN`).
+  var Number_ = NullaryTypeWithUrl('Number', Any, typeofEq('number'));
+
+  //# ValidNumber :: Type
+  //.
+  //. Type comprising every [`Number`][] value except `NaN`.
+  var ValidNumber = NullaryTypeWithUrl(
+    'sanctuary-def/ValidNumber',
+    Number_,
+    function(x) { return !isNaN(x); }
+  );
 
   //# FiniteNumber :: Type
   //.
@@ -495,7 +526,8 @@
   //. `-Infinity`.
   var FiniteNumber = NullaryTypeWithUrl(
     'sanctuary-def/FiniteNumber',
-    function(x) { return ValidNumber._test(x) && isFinite(x); }
+    ValidNumber,
+    isFinite
   );
 
   //# Function :: Array Type -> Type
@@ -522,8 +554,6 @@
                           last(xs));
     }
 
-    var test = AnyFunction._test;
-
     var $keys = [];
     var $types = {};
     types.forEach(function(t, idx) {
@@ -532,9 +562,21 @@
       $types[k] = {extractor: K([]), type: t};
     });
 
-    return new _Type(FUNCTION, '', '', format, test, $keys, $types);
+    return new _Type(FUNCTION,
+                     '',
+                     '',
+                     format,
+                     AnyFunction,
+                     K(true),
+                     $keys,
+                     $types);
   }
 
+  //# RegExp :: Type
+  //.
+  //. Type comprising every RegExp value.
+  var RegExp_ = NullaryTypeWithUrl('RegExp', Any, typeEq('RegExp'));
+
   //# GlobalRegExp :: Type
   //.
   //. Type comprising every [`RegExp`][] value whose `global` flag is `true`.
@@ -542,7 +584,8 @@
   //. See also [`NonGlobalRegExp`][].
   var GlobalRegExp = NullaryTypeWithUrl(
     'sanctuary-def/GlobalRegExp',
-    function(x) { return RegExp_._test(x) && x.global; }
+    RegExp_,
+    function(x) { return x.global; }
   );
 
   //# Integer :: Type
@@ -551,9 +594,9 @@
   //. [[`Number.MIN_SAFE_INTEGER`][min] .. [`Number.MAX_SAFE_INTEGER`][max]].
   var Integer = NullaryTypeWithUrl(
     'sanctuary-def/Integer',
+    ValidNumber,
     function(x) {
-      return ValidNumber._test(x) &&
-             Math.floor(x) === x &&
+      return Math.floor(x) === x &&
              x >= MIN_SAFE_INTEGER &&
              x <= MAX_SAFE_INTEGER;
     }
@@ -564,7 +607,8 @@
   //. Type comprising every [`FiniteNumber`][] value less than zero.
   var NegativeFiniteNumber = NullaryTypeWithUrl(
     'sanctuary-def/NegativeFiniteNumber',
-    function(x) { return FiniteNumber._test(x) && x < 0; }
+    FiniteNumber,
+    function(x) { return x < 0; }
   );
 
   //# NegativeInteger :: Type
@@ -572,7 +616,8 @@
   //. Type comprising every [`Integer`][] value less than zero.
   var NegativeInteger = NullaryTypeWithUrl(
     'sanctuary-def/NegativeInteger',
-    function(x) { return Integer._test(x) && x < 0; }
+    Integer,
+    function(x) { return x < 0; }
   );
 
   //# NegativeNumber :: Type
@@ -580,7 +625,8 @@
   //. Type comprising every [`Number`][] value less than zero.
   var NegativeNumber = NullaryTypeWithUrl(
     'sanctuary-def/NegativeNumber',
-    function(x) { return Number_._test(x) && x < 0; }
+    Number_,
+    function(x) { return x < 0; }
   );
 
   //# NonEmpty :: Type -> Type
@@ -607,7 +653,8 @@
   //. See also [`GlobalRegExp`][].
   var NonGlobalRegExp = NullaryTypeWithUrl(
     'sanctuary-def/NonGlobalRegExp',
-    function(x) { return RegExp_._test(x) && !x.global; }
+    RegExp_,
+    function(x) { return !x.global; }
   );
 
   //# NonZeroFiniteNumber :: Type
@@ -615,7 +662,8 @@
   //. Type comprising every [`FiniteNumber`][] value except `0` and `-0`.
   var NonZeroFiniteNumber = NullaryTypeWithUrl(
     'sanctuary-def/NonZeroFiniteNumber',
-    function(x) { return FiniteNumber._test(x) && x !== 0; }
+    FiniteNumber,
+    function(x) { return x !== 0; }
   );
 
   //# NonZeroInteger :: Type
@@ -623,7 +671,8 @@
   //. Type comprising every [`Integer`][] value except `0` and `-0`.
   var NonZeroInteger = NullaryTypeWithUrl(
     'sanctuary-def/NonZeroInteger',
-    function(x) { return Integer._test(x) && x !== 0; }
+    Integer,
+    function(x) { return x !== 0; }
   );
 
   //# NonZeroValidNumber :: Type
@@ -631,13 +680,14 @@
   //. Type comprising every [`ValidNumber`][] value except `0` and `-0`.
   var NonZeroValidNumber = NullaryTypeWithUrl(
     'sanctuary-def/NonZeroValidNumber',
-    function(x) { return ValidNumber._test(x) && x !== 0; }
+    ValidNumber,
+    function(x) { return x !== 0; }
   );
 
   //# Null :: Type
   //.
   //. Type whose sole member is `null`.
-  var Null = NullaryTypeWithUrl('Null', typeEq('Null'));
+  var Null = NullaryTypeWithUrl('Null', Any, typeEq('Null'));
 
   //# Nullable :: Type -> Type
   //.
@@ -651,11 +701,6 @@
     }
   );
 
-  //# Number :: Type
-  //.
-  //. Type comprising every primitive Number value (including `NaN`).
-  var Number_ = NullaryTypeWithUrl('Number', typeofEq('number'));
-
   //# Object :: Type
   //.
   //. Type comprising every "plain" Object value. Specifically, values
@@ -665,7 +710,7 @@
   //.   - [`Object.create`][]; or
   //.   - the `new` operator in conjunction with `Object` or a custom
   //.     constructor function.
-  var Object_ = NullaryTypeWithUrl('Object', typeEq('Object'));
+  var Object_ = NullaryTypeWithUrl('Object', Any, typeEq('Object'));
 
   //# Pair :: Type -> Type -> Type
   //.
@@ -683,7 +728,8 @@
   //. Type comprising every [`FiniteNumber`][] value greater than zero.
   var PositiveFiniteNumber = NullaryTypeWithUrl(
     'sanctuary-def/PositiveFiniteNumber',
-    function(x) { return FiniteNumber._test(x) && x > 0; }
+    FiniteNumber,
+    function(x) { return x > 0; }
   );
 
   //# PositiveInteger :: Type
@@ -691,7 +737,8 @@
   //. Type comprising every [`Integer`][] value greater than zero.
   var PositiveInteger = NullaryTypeWithUrl(
     'sanctuary-def/PositiveInteger',
-    function(x) { return Integer._test(x) && x > 0; }
+    Integer,
+    function(x) { return x > 0; }
   );
 
   //# PositiveNumber :: Type
@@ -699,14 +746,10 @@
   //. Type comprising every [`Number`][] value greater than zero.
   var PositiveNumber = NullaryTypeWithUrl(
     'sanctuary-def/PositiveNumber',
-    function(x) { return Number_._test(x) && x > 0; }
+    Number_,
+    function(x) { return x > 0; }
   );
 
-  //# RegExp :: Type
-  //.
-  //. Type comprising every RegExp value.
-  var RegExp_ = NullaryTypeWithUrl('RegExp', typeEq('RegExp'));
-
   //# RegexFlags :: Type
   //.
   //. Type comprising the canonical RegExp flags:
@@ -732,7 +775,7 @@
   //. `{foo: 1, bar: 2, baz: 'XXX'}` is not.
   var StrMap = UnaryTypeWithUrl(
     'sanctuary-def/StrMap',
-    Object_._test,
+    Object_.test.bind(Object_),
     function(strMap) {
       return Z.reduce(function(xs, x) { return xs.concat([x]); }, [], strMap);
     }
@@ -741,28 +784,31 @@
   //# String :: Type
   //.
   //. Type comprising every primitive String value.
-  var String_ = NullaryTypeWithUrl('String', typeofEq('string'));
+  var String_ = NullaryTypeWithUrl('String', Any, typeofEq('string'));
 
   //# Symbol :: Type
   //.
   //. Type comprising every Symbol value.
-  var Symbol_ = NullaryTypeWithUrl('Symbol', typeofEq('symbol'));
+  var Symbol_ = NullaryTypeWithUrl('Symbol', Any, typeofEq('symbol'));
 
   //# Type :: Type
   //.
   //. Type comprising every `Type` value.
-  var Type = NullaryTypeWithUrl('Type', typeEq('sanctuary-def/Type'));
+  var Type = NullaryTypeWithUrl('Type', Any, typeEq('sanctuary-def/Type'));
 
   //# TypeClass :: Type
   //.
   //. Type comprising every [`TypeClass`][] value.
-  var TypeClass =
-  NullaryTypeWithUrl('TypeClass', typeEq('sanctuary-type-classes/TypeClass'));
+  var TypeClass = NullaryTypeWithUrl(
+    'TypeClass',
+    Any,
+    typeEq('sanctuary-type-classes/TypeClass')
+  );
 
   //# Undefined :: Type
   //.
   //. Type whose sole member is `undefined`.
-  var Undefined = NullaryTypeWithUrl('Undefined', typeEq('Undefined'));
+  var Undefined = NullaryTypeWithUrl('Undefined', Any, typeEq('Undefined'));
 
   //# Unknown :: Type
   //.
@@ -780,22 +826,16 @@
   //.   - `List (List (List Number))`
   //.   - `List (List (List String))`
   //.   - `...`
-  var Unknown = new _Type(UNKNOWN, '', '', always2('???'), K(true), [], {});
+  var Unknown =
+  new _Type(UNKNOWN, '', '', always2('???'), Any, K(true), [], {});
 
   //# ValidDate :: Type
   //.
   //. Type comprising every [`Date`][] value except `new Date(NaN)`.
   var ValidDate = NullaryTypeWithUrl(
     'sanctuary-def/ValidDate',
-    function(x) { return Date_._test(x) && !isNaN(x.valueOf()); }
-  );
-
-  //# ValidNumber :: Type
-  //.
-  //. Type comprising every [`Number`][] value except `NaN`.
-  var ValidNumber = NullaryTypeWithUrl(
-    'sanctuary-def/ValidNumber',
-    function(x) { return Number_._test(x) && !isNaN(x); }
+    Date_,
+    function(x) { return !isNaN(x.valueOf()); }
   );
 
   //# env :: Array Type
@@ -834,7 +874,7 @@
   ];
 
   //  Unchecked :: String -> Type
-  function Unchecked(s) { return NullaryType(s, '', K(true)); }
+  function Unchecked(s) { return NullaryType(s, '', Any, K(true)); }
 
   var def = _create({checkTypes: true, env: env});
 
@@ -1267,20 +1307,9 @@
   //. The environment is only significant if the type contains
   //. [type variables][].
   //.
-  //. One may define a more restrictive type in terms of a more general one:
-  //.
-  //. ```javascript
-  //. //    NonNegativeInteger :: Type
-  //. const NonNegativeInteger = $.NullaryType(
-  //.   'my-package/NonNegativeInteger',
-  //.   'http://example.com/my-package#NonNegativeInteger',
-  //.   x => $.test([], $.Integer, x) && x >= 0
-  //. );
-  //. ```
-  //.
-  //. Using types as predicates is useful in other contexts too. One could,
-  //. for example, define a [record type][] for each endpoint of a REST API
-  //. and validate the bodies of incoming POST requests against these types.
+  //. Using types as predicates is powerful. One could, for example,
+  //. define a [record type][] for each endpoint of a REST API and
+  //. validate the bodies of incoming POST requests against these types.
   function test(env, t, x) {
     var typeInfo = {name: 'name', constraints: {}, types: [t]};
     return satisfactoryTypes(env, typeInfo, {}, t, 0, [], [x]).isRight;
@@ -1290,7 +1319,7 @@
   //.
   //. sanctuary-def provides several functions for defining types.
 
-  //# NullaryType :: String -> String -> (Any -> Boolean) -> Type
+  //# NullaryType :: String -> String -> Type -> (Any -> Boolean) -> Type
   //.
   //. Type constructor for types with no type variables (such as [`Number`][]).
   //.
@@ -1300,6 +1329,8 @@
   //.
   //.   - the documentation URL of `t` (exposed as `t.url`); and
   //.
+  //.   - the parent of `t` (exposed as `t.parent`);
+  //.
   //.   - a predicate which accepts any JavaScript value and returns `true` if
   //.     (and only if) the value is a member of `t`.
   //.
@@ -1310,8 +1341,8 @@
   //. const Integer = $.NullaryType(
   //.   'my-package/Integer',
   //.   'http://example.com/my-package#Integer',
-  //.   x => typeof x === 'number' &&
-  //.        Math.floor(x) === x &&
+  //.   $.ValidNumber,
+  //.   x => Math.floor(x) === x &&
   //.        x >= Number.MIN_SAFE_INTEGER &&
   //.        x <= Number.MAX_SAFE_INTEGER
   //. );
@@ -1320,7 +1351,8 @@
   //. const NonZeroInteger = $.NullaryType(
   //.   'my-package/NonZeroInteger',
   //.   'http://example.com/my-package#NonZeroInteger',
-  //.   x => $.test([], Integer, x) && x !== 0
+  //.   Integer,
+  //.   x => x !== 0
   //. );
   //.
   //. //    rem :: Integer -> NonZeroInteger -> Integer
@@ -1352,17 +1384,17 @@
   //. //
   //. //   The value at position 1 is not a member of ‘NonZeroInteger’.
   //. ```
-  function NullaryType(name, url, test) {
+  function NullaryType(name, url, parent, test) {
     function format(outer, inner) {
       return outer(stripNamespace(name));
     }
-    return new _Type(NULLARY, name, url, format, test, [], {});
+    return new _Type(NULLARY, name, url, format, parent, test, [], {});
   }
 
   var CheckedNullaryType =
   def('NullaryType',
       {},
-      [String_, String_, Function_([Any, Boolean_]), Type],
+      [String_, String_, Type, Function_([Any, Boolean_]), Type],
       NullaryType);
 
   //# UnaryType :: String -> String -> (Any -> Boolean) -> (t a -> Array a) -> (Type -> Type)
@@ -1450,7 +1482,7 @@
                inner('$1')(String($1)) + outer(')');
       }
       var types = {$1: {extractor: _1, type: $1}};
-      return new _Type(UNARY, name, url, format, test, ['$1'], types);
+      return new _Type(UNARY, name, url, format, Any, test, ['$1'], types);
     };
   }
 
@@ -1471,7 +1503,7 @@
 
   //  fromUnaryType :: Type -> (Type -> Type)
   function fromUnaryType(t) {
-    return UnaryType(t.name, t.url, t._test, t.types.$1.extractor);
+    return UnaryType(t.name, t.url, t.test.bind(t), t.types.$1.extractor);
   }
 
   //# BinaryType :: String -> String -> (Any -> Boolean) -> (t a b -> Array a) -> (t a b -> Array b) -> (Type -> Type -> Type)
@@ -1533,14 +1565,16 @@
   //. const Rank = $.NullaryType(
   //.   'my-package/Rank',
   //.   'http://example.com/my-package#Rank',
-  //.   x => typeof x === 'string' && /^([A23456789JQK]|10)$/.test(x)
+  //.   $.String,
+  //.   x => /^([A23456789JQK]|10)$/.test(x)
   //. );
   //.
   //. //    Suit :: Type
   //. const Suit = $.NullaryType(
   //.   'my-package/Suit',
   //.   'http://example.com/my-package#Suit',
-  //.   x => typeof x === 'string' && /^[\u2660\u2663\u2665\u2666]$/.test(x)
+  //.   $.String,
+  //.   x => /^[\u2660\u2663\u2665\u2666]$/.test(x)
   //. );
   //.
   //. //    Card :: Type
@@ -1573,7 +1607,14 @@
       }
       var types = {$1: {extractor: _1, type: $1},
                    $2: {extractor: _2, type: $2}};
-      return new _Type(BINARY, name, url, format, test, ['$1', '$2'], types);
+      return new _Type(BINARY,
+                       name,
+                       url,
+                       format,
+                       Any,
+                       test,
+                       ['$1', '$2'],
+                       types);
     };
   }
 
@@ -1597,7 +1638,7 @@
   function xprod(t, $1s, $2s) {
     var specialize = BinaryType(t.name,
                                 t.url,
-                                t._test,
+                                t.test.bind(t),
                                 t.types.$1.extractor,
                                 t.types.$2.extractor);
     var $types = [];
@@ -1632,7 +1673,7 @@
   //. );
   //. ```
   function EnumType(name, url, members) {
-    return NullaryType(name, url, memberOf(members));
+    return NullaryType(name, url, Any, memberOf(members));
   }
 
   var CheckedEnumType =
@@ -1710,7 +1751,7 @@
       $types[k] = {extractor: function(x) { return [x[k]]; }, type: fields[k]};
     });
 
-    return new _Type(RECORD, '', '', format, test, keys, $types);
+    return new _Type(RECORD, '', '', format, Object_, test, keys, $types);
   }
 
   var CheckedRecordType =
@@ -1770,7 +1811,7 @@
   //. //   Since there is no type of which all the above values are members, the type-variable constraint has been violated.
   //. ```
   function TypeVariable(name) {
-    return new _Type(VARIABLE, name, '', always2(name), K(true), [], {});
+    return new _Type(VARIABLE, name, '', always2(name), Any, K(true), [], {});
   }
 
   var CheckedTypeVariable =
@@ -1828,7 +1869,14 @@
         return outer('(' + name + ' ') + inner('$1')(String($1)) + outer(')');
       }
       var types = {$1: {extractor: K([]), type: $1}};
-      return new _Type(VARIABLE, name, '', format, K(true), ['$1'], types);
+      return new _Type(VARIABLE,
+                       name,
+                       '',
+                       format,
+                       Any,
+                       K(true),
+                       ['$1'],
+                       types);
     };
   }
 
@@ -1863,7 +1911,7 @@
       var keys = ['$1', '$2'];
       var types = {$1: {extractor: K([]), type: $1},
                    $2: {extractor: K([]), type: $2}};
-      return new _Type(VARIABLE, name, '', format, K(true), keys, types);
+      return new _Type(VARIABLE, name, '', format, Any, K(true), keys, types);
     };
   }
 
@@ -2495,7 +2543,7 @@
   function fromUncheckedUnaryType(typeConstructor) {
     var t = typeConstructor(Unknown);
     var _1 = t.types.$1.extractor;
-    return CheckedUnaryType(t.name, t.url, t._test, _1);
+    return CheckedUnaryType(t.name, t.url, t.test.bind(t), _1);
   }
 
   //  fromUncheckedBinaryType :: ((Type, Type) -> Type) ->
@@ -2504,7 +2552,7 @@
     var t = typeConstructor(Unknown, Unknown);
     var _1 = t.types.$1.extractor;
     var _2 = t.types.$2.extractor;
-    return CheckedBinaryType(t.name, t.url, t._test, _1, _2);
+    return CheckedBinaryType(t.name, t.url, t.test.bind(t), _1, _2);
   }
 
   return {
@@ -2528,6 +2576,7 @@
     NonZeroFiniteNumber: NonZeroFiniteNumber,
     NonZeroInteger: NonZeroInteger,
     NonZeroValidNumber: NonZeroValidNumber,
+    None: None,
     Null: Null,
     Nullable: fromUncheckedUnaryType(Nullable),
     Number: Number_,
diff --git a/test/index.js b/test/index.js
index 9716b4a..be3b194 100644
--- a/test/index.js
+++ b/test/index.js
@@ -69,6 +69,7 @@ var MIN_SAFE_INTEGER = -MAX_SAFE_INTEGER;
 var Integer = $.NullaryType(
   'my-package/Integer',
   'http://example.com/my-package#Integer',
+  $.Any,
   function(x) {
     return $.Number._test(x) &&
            Math.floor(x) === Number(x) &&
@@ -3025,6 +3026,7 @@ describe('def', function() {
     var Void = $.NullaryType(
       'my-package/Void',
       'http://example.com/my-package#Void',
+      $.Any,
       function(x) { count += 1; return false; }
     );
 
@@ -3097,10 +3099,10 @@ describe('test', function() {
 
 describe('NullaryType', function() {
 
-  it('is a ternary function', function() {
+  it('is a quaternary function', function() {
     eq(typeof $.NullaryType, 'function');
-    eq($.NullaryType.length, 3);
-    eq($.NullaryType.toString(), 'NullaryType :: String -> String -> (Any -> Boolean) -> Type');
+    eq($.NullaryType.length, 4);
+    eq($.NullaryType.toString(), 'NullaryType :: String -> String -> Type -> (Any -> Boolean) -> Type');
   });
 
 });

From e983ea251bd8e26dd067d65d4974afd1f86ba2af Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Tue, 27 Jun 2017 11:00:12 +0200
Subject: [PATCH 02/20] Reorder types based on new ordering scheme

The sheme has been discussed in #162
---
 index.js | 365 +++++++++++++++++++++++++++----------------------------
 1 file changed, 180 insertions(+), 185 deletions(-)

diff --git a/index.js b/index.js
index afdf9c3..50838d3 100644
--- a/index.js
+++ b/index.js
@@ -466,15 +466,6 @@
   Any.test = K(true);
   Any.validate = Right;
 
-  //# None :: Type
-  //.
-  //. Type with no members.
-  var None = NullaryTypeWithUrl('sanctuary-def/None', Any, K(false));
-
-  //  Inconsistent :: Type
-  var Inconsistent =
-  new _Type(INCONSISTENT, '', '', always2('???'), None, K(false), [], {});
-
   //# AnyFunction :: Type
   //.
   //. Type comprising every Function value.
@@ -500,15 +491,34 @@
   //. Type comprising every Date value.
   var Date_ = NullaryTypeWithUrl('Date', Any, typeEq('Date'));
 
+  //# ValidDate :: Type
+  //.
+  //. Type comprising every [`Date`][] value except `new Date(NaN)`.
+  var ValidDate = NullaryTypeWithUrl(
+    'sanctuary-def/ValidDate',
+    Date_,
+    function(x) { return !isNaN(x.valueOf()); }
+  );
+
   //# Error :: Type
   //.
   //. Type comprising every Error value, including values of more specific
   //. constructors such as [`SyntaxError`][] and [`TypeError`][].
   var Error_ = NullaryTypeWithUrl('Error', Any, typeEq('Error'));
 
+  //  Inconsistent :: Type
+  var Inconsistent =
+  new _Type(INCONSISTENT, '', '', always2('???'), Any, K(false), [], {});
+
+  //# Null :: Type
+  //.
+  //. Type whose sole member is `null`.
+  var Null = NullaryTypeWithUrl('Null', Any, typeEq('Null'));
+
   //# Number :: Type
   //.
-  //. Type comprising every primitive Number value (including `NaN`).
+  //. Type comprising every primitive Number value
+  //. (including `NaN` and `Infinity`).
   var Number_ = NullaryTypeWithUrl('Number', Any, typeofEq('number'));
 
   //# ValidNumber :: Type
@@ -530,62 +540,31 @@
     isFinite
   );
 
-  //# Function :: Array Type -> Type
-  //.
-  //. Constructor for Function types.
-  //.
-  //. Examples:
+  //# NegativeFiniteNumber :: Type
   //.
-  //.   - `$.Function([$.Date, $.String])` represents the `Date -> String`
-  //.     type; and
-  //.   - `$.Function([a, b, a])` represents the `(a, b) -> a` type.
-  function Function_(types) {
-    function format(outer, inner) {
-      var xs = types.map(function(t, idx) {
-        return unless(t.type === RECORD || isEmpty(t.keys),
-                      stripOutermostParens,
-                      inner('$' + String(idx + 1))(String(t)));
-      });
-      var parenthesize = wrap(outer('('))(outer(')'));
-      return parenthesize(unless(types.length === 2,
-                                 parenthesize,
-                                 init(xs).join(outer(', '))) +
-                          outer(' -> ') +
-                          last(xs));
-    }
-
-    var $keys = [];
-    var $types = {};
-    types.forEach(function(t, idx) {
-      var k = '$' + String(idx + 1);
-      $keys.push(k);
-      $types[k] = {extractor: K([]), type: t};
-    });
-
-    return new _Type(FUNCTION,
-                     '',
-                     '',
-                     format,
-                     AnyFunction,
-                     K(true),
-                     $keys,
-                     $types);
-  }
+  //. Type comprising every [`FiniteNumber`][] less than zero.
+  var NegativeFiniteNumber = NullaryTypeWithUrl(
+    'sanctuary-def/NegativeFiniteNumber',
+    FiniteNumber,
+    function(x) { return x < 0; }
+  );
 
-  //# RegExp :: Type
+  //# NonZeroFiniteNumber :: Type
   //.
-  //. Type comprising every RegExp value.
-  var RegExp_ = NullaryTypeWithUrl('RegExp', Any, typeEq('RegExp'));
+  //. Type comprising every [`FiniteNumber`][] value except `0` and `-0`.
+  var NonZeroFiniteNumber = NullaryTypeWithUrl(
+    'sanctuary-def/NonZeroFiniteNumber',
+    FiniteNumber,
+    function(x) { return x !== 0; }
+  );
 
-  //# GlobalRegExp :: Type
-  //.
-  //. Type comprising every [`RegExp`][] value whose `global` flag is `true`.
+  //# PositiveFiniteNumber :: Type
   //.
-  //. See also [`NonGlobalRegExp`][].
-  var GlobalRegExp = NullaryTypeWithUrl(
-    'sanctuary-def/GlobalRegExp',
-    RegExp_,
-    function(x) { return x.global; }
+  //. Type comprising every [`FiniteNumber`][] value greater than zero.
+  var PositiveFiniteNumber = NullaryTypeWithUrl(
+    'sanctuary-def/PositiveFiniteNumber',
+    FiniteNumber,
+    function(x) { return x > 0; }
   );
 
   //# Integer :: Type
@@ -602,15 +581,6 @@
     }
   );
 
-  //# NegativeFiniteNumber :: Type
-  //.
-  //. Type comprising every [`FiniteNumber`][] value less than zero.
-  var NegativeFiniteNumber = NullaryTypeWithUrl(
-    'sanctuary-def/NegativeFiniteNumber',
-    FiniteNumber,
-    function(x) { return x < 0; }
-  );
-
   //# NegativeInteger :: Type
   //.
   //. Type comprising every [`Integer`][] value less than zero.
@@ -620,52 +590,6 @@
     function(x) { return x < 0; }
   );
 
-  //# NegativeNumber :: Type
-  //.
-  //. Type comprising every [`Number`][] value less than zero.
-  var NegativeNumber = NullaryTypeWithUrl(
-    'sanctuary-def/NegativeNumber',
-    Number_,
-    function(x) { return x < 0; }
-  );
-
-  //# NonEmpty :: Type -> Type
-  //.
-  //. Constructor for non-empty types. `$.NonEmpty($.String)`, for example, is
-  //. the type comprising every [`String`][] value except `''`.
-  //.
-  //. The given type must satisfy the [Monoid][] and [Setoid][] specifications.
-  var NonEmpty = UnaryType(
-    'sanctuary-def/NonEmpty',
-    functionUrl('NonEmpty'),
-    function(x) {
-      return Z.Monoid.test(x) &&
-             Z.Setoid.test(x) &&
-             !Z.equals(x, Z.empty(x.constructor));
-    },
-    function(monoid) { return [monoid]; }
-  );
-
-  //# NonGlobalRegExp :: Type
-  //.
-  //. Type comprising every [`RegExp`][] value whose `global` flag is `false`.
-  //.
-  //. See also [`GlobalRegExp`][].
-  var NonGlobalRegExp = NullaryTypeWithUrl(
-    'sanctuary-def/NonGlobalRegExp',
-    RegExp_,
-    function(x) { return !x.global; }
-  );
-
-  //# NonZeroFiniteNumber :: Type
-  //.
-  //. Type comprising every [`FiniteNumber`][] value except `0` and `-0`.
-  var NonZeroFiniteNumber = NullaryTypeWithUrl(
-    'sanctuary-def/NonZeroFiniteNumber',
-    FiniteNumber,
-    function(x) { return x !== 0; }
-  );
-
   //# NonZeroInteger :: Type
   //.
   //. Type comprising every [`Integer`][] value except `0` and `-0`.
@@ -675,6 +599,24 @@
     function(x) { return x !== 0; }
   );
 
+  //# PositiveInteger :: Type
+  //.
+  //. Type comprising every [`Integer`][] value greater than zero.
+  var PositiveInteger = NullaryTypeWithUrl(
+    'sanctuary-def/PositiveInteger',
+    Integer,
+    function(x) { return x > 0; }
+  );
+
+  //# NegativeNumber :: Type
+  //.
+  //. Type comprising every [`ValidNumber`][] value less than zero.
+  var NegativeNumber = NullaryTypeWithUrl(
+    'sanctuary-def/NegativeNumber',
+    ValidNumber,
+    function(x) { return x < 0; }
+  );
+
   //# NonZeroValidNumber :: Type
   //.
   //. Type comprising every [`ValidNumber`][] value except `0` and `-0`.
@@ -684,21 +626,13 @@
     function(x) { return x !== 0; }
   );
 
-  //# Null :: Type
-  //.
-  //. Type whose sole member is `null`.
-  var Null = NullaryTypeWithUrl('Null', Any, typeEq('Null'));
-
-  //# Nullable :: Type -> Type
+  //# PositiveNumber :: Type
   //.
-  //. Constructor for types which include `null` as a member.
-  var Nullable = UnaryTypeWithUrl(
-    'sanctuary-def/Nullable',
-    K(true),
-    function(nullable) {
-      // eslint-disable-next-line eqeqeq
-      return nullable === null ? [] : [nullable];
-    }
+  //. Type comprising every [`ValidNumber`][] value greater than zero.
+  var PositiveNumber = NullaryTypeWithUrl(
+    'sanctuary-def/PositiveNumber',
+    ValidNumber,
+    function(x) { return x > 0; }
   );
 
   //# Object :: Type
@@ -712,44 +646,6 @@
   //.     constructor function.
   var Object_ = NullaryTypeWithUrl('Object', Any, typeEq('Object'));
 
-  //# Pair :: Type -> Type -> Type
-  //.
-  //. Constructor for tuple types of length 2. Arrays are said to represent
-  //. tuples. `['foo', 42]` is a member of `Pair String Number`.
-  var Pair = BinaryTypeWithUrl(
-    'sanctuary-def/Pair',
-    function(x) { return typeEq('Array')(x) && x.length === 2; },
-    function(pair) { return [pair[0]]; },
-    function(pair) { return [pair[1]]; }
-  );
-
-  //# PositiveFiniteNumber :: Type
-  //.
-  //. Type comprising every [`FiniteNumber`][] value greater than zero.
-  var PositiveFiniteNumber = NullaryTypeWithUrl(
-    'sanctuary-def/PositiveFiniteNumber',
-    FiniteNumber,
-    function(x) { return x > 0; }
-  );
-
-  //# PositiveInteger :: Type
-  //.
-  //. Type comprising every [`Integer`][] value greater than zero.
-  var PositiveInteger = NullaryTypeWithUrl(
-    'sanctuary-def/PositiveInteger',
-    Integer,
-    function(x) { return x > 0; }
-  );
-
-  //# PositiveNumber :: Type
-  //.
-  //. Type comprising every [`Number`][] value greater than zero.
-  var PositiveNumber = NullaryTypeWithUrl(
-    'sanctuary-def/PositiveNumber',
-    Number_,
-    function(x) { return x > 0; }
-  );
-
   //# RegexFlags :: Type
   //.
   //. Type comprising the canonical RegExp flags:
@@ -767,18 +663,31 @@
     ['', 'g', 'i', 'm', 'gi', 'gm', 'im', 'gim']
   );
 
-  //# StrMap :: Type -> Type
+  //# RegExp :: Type
   //.
-  //. Constructor for homogeneous Object types.
+  //. Type comprising every RegExp value.
+  var RegExp_ = NullaryTypeWithUrl('RegExp', Any, typeEq('RegExp'));
+
+  //# GlobalRegExp :: Type
   //.
-  //. `{foo: 1, bar: 2, baz: 3}`, for example, is a member of `StrMap Number`;
-  //. `{foo: 1, bar: 2, baz: 'XXX'}` is not.
-  var StrMap = UnaryTypeWithUrl(
-    'sanctuary-def/StrMap',
-    Object_.test.bind(Object_),
-    function(strMap) {
-      return Z.reduce(function(xs, x) { return xs.concat([x]); }, [], strMap);
-    }
+  //. Type comprising every [`RegExp`][] value whose `global` flag is `true`.
+  //.
+  //. See also [`NonGlobalRegExp`][].
+  var GlobalRegExp = NullaryTypeWithUrl(
+    'sanctuary-def/GlobalRegExp',
+    RegExp_,
+    function(x) { return x.global; }
+  );
+
+  //# NonGlobalRegExp :: Type
+  //.
+  //. Type comprising every [`RegExp`][] value whose `global` flag is `false`.
+  //.
+  //. See also [`GlobalRegExp`][].
+  var NonGlobalRegExp = NullaryTypeWithUrl(
+    'sanctuary-def/NonGlobalRegExp',
+    RegExp_,
+    function(x) { return !x.global; }
   );
 
   //# String :: Type
@@ -829,13 +738,100 @@
   var Unknown =
   new _Type(UNKNOWN, '', '', always2('???'), Any, K(true), [], {});
 
-  //# ValidDate :: Type
+  //# Function :: Array Type -> Type
   //.
-  //. Type comprising every [`Date`][] value except `new Date(NaN)`.
-  var ValidDate = NullaryTypeWithUrl(
-    'sanctuary-def/ValidDate',
-    Date_,
-    function(x) { return !isNaN(x.valueOf()); }
+  //. Constructor for Function types.
+  //.
+  //. Examples:
+  //.
+  //.   - `$.Function([$.Date, $.String])` represents the `Date -> String`
+  //.     type; and
+  //.   - `$.Function([a, b, a])` represents the `(a, b) -> a` type.
+  function Function_(types) {
+    function format(outer, inner) {
+      var xs = types.map(function(t, idx) {
+        return unless(t.type === RECORD || isEmpty(t.keys),
+                      stripOutermostParens,
+                      inner('$' + String(idx + 1))(String(t)));
+      });
+      var parenthesize = wrap(outer('('))(outer(')'));
+      return parenthesize(unless(types.length === 2,
+                                 parenthesize,
+                                 init(xs).join(outer(', '))) +
+                          outer(' -> ') +
+                          last(xs));
+    }
+
+    var $keys = [];
+    var $types = {};
+    types.forEach(function(t, idx) {
+      var k = '$' + String(idx + 1);
+      $keys.push(k);
+      $types[k] = {extractor: K([]), type: t};
+    });
+
+    return new _Type(FUNCTION,
+                     '',
+                     '',
+                     format,
+                     AnyFunction,
+                     K(true),
+                     $keys,
+                     $types);
+  }
+
+  //# NonEmpty :: Type -> Type
+  //.
+  //. Constructor for non-empty types. `$.NonEmpty($.String)`, for example, is
+  //. the type comprising every [`String`][] value except `''`.
+  //.
+  //. The given type must satisfy the [Monoid][] and [Setoid][] specifications.
+  var NonEmpty = UnaryType(
+    'sanctuary-def/NonEmpty',
+    functionUrl('NonEmpty'),
+    function(x) {
+      return Z.Monoid.test(x) &&
+             Z.Setoid.test(x) &&
+             !Z.equals(x, Z.empty(x.constructor));
+    },
+    function(monoid) { return [monoid]; }
+  );
+
+  //# Nullable :: Type -> Type
+  //.
+  //. Constructor for types which include `null` as a member.
+  var Nullable = UnaryTypeWithUrl(
+    'sanctuary-def/Nullable',
+    K(true),
+    function(nullable) {
+      // eslint-disable-next-line eqeqeq
+      return nullable === null ? [] : [nullable];
+    }
+  );
+
+  //# Pair :: Type -> Type -> Type
+  //.
+  //. Constructor for tuple types of length 2. Arrays are said to represent
+  //. tuples. `['foo', 42]` is a member of `Pair String Number`.
+  var Pair = BinaryTypeWithUrl(
+    'sanctuary-def/Pair',
+    function(x) { return typeEq('Array')(x) && x.length === 2; },
+    function(pair) { return [pair[0]]; },
+    function(pair) { return [pair[1]]; }
+  );
+
+  //# StrMap :: Type -> Type
+  //.
+  //. Constructor for homogeneous Object types.
+  //.
+  //. `{foo: 1, bar: 2, baz: 3}`, for example, is a member of `StrMap Number`;
+  //. `{foo: 1, bar: 2, baz: 'XXX'}` is not.
+  var StrMap = UnaryTypeWithUrl(
+    'sanctuary-def/StrMap',
+    Object_.test.bind(Object_),
+    function(strMap) {
+      return Z.reduce(function(xs, x) { return xs.concat([x]); }, [], strMap);
+    }
   );
 
   //# env :: Array Type
@@ -2576,7 +2572,6 @@
     NonZeroFiniteNumber: NonZeroFiniteNumber,
     NonZeroInteger: NonZeroInteger,
     NonZeroValidNumber: NonZeroValidNumber,
-    None: None,
     Null: Null,
     Nullable: fromUncheckedUnaryType(Nullable),
     Number: Number_,

From c5f11304e77efd53f28bbbaae9cccd975e3517c6 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Tue, 27 Jun 2017 11:45:08 +0200
Subject: [PATCH 03/20] Add refinement support to UnaryType constructor

---
 index.js      | 37 ++++++++++++++++++++++---------------
 test/index.js |  7 ++++---
 2 files changed, 26 insertions(+), 18 deletions(-)

diff --git a/index.js b/index.js
index 50838d3..e8d55f1 100644
--- a/index.js
+++ b/index.js
@@ -441,8 +441,8 @@
 
   //  UnaryTypeWithUrl ::
   //    (String, Any -> Boolean, t a -> Array a) -> (Type -> Type)
-  function UnaryTypeWithUrl(name, test, _1) {
-    return UnaryType(name, functionUrl(name), test, _1);
+  function UnaryTypeWithUrl(name, parent, test, _1) {
+    return UnaryType(name, functionUrl(name), parent, test, _1);
   }
 
   //  BinaryTypeWithUrl ::
@@ -476,11 +476,6 @@
   //. Type comprising every [`arguments`][arguments] object.
   var Arguments = NullaryTypeWithUrl('Arguments', Any, typeEq('Arguments'));
 
-  //# Array :: Type -> Type
-  //.
-  //. Constructor for homogeneous Array types.
-  var Array_ = UnaryTypeWithUrl('Array', typeEq('Array'), id);
-
   //# Boolean :: Type
   //.
   //. Type comprising `true` and `false`.
@@ -738,6 +733,11 @@
   var Unknown =
   new _Type(UNKNOWN, '', '', always2('???'), Any, K(true), [], {});
 
+  //# Array :: Type -> Type
+  //.
+  //. Constructor for homogeneous Array types.
+  var Array_ = UnaryTypeWithUrl('Array', Any, typeEq('Array'), id);
+
   //# Function :: Array Type -> Type
   //.
   //. Constructor for Function types.
@@ -789,6 +789,7 @@
   var NonEmpty = UnaryType(
     'sanctuary-def/NonEmpty',
     functionUrl('NonEmpty'),
+    Any,
     function(x) {
       return Z.Monoid.test(x) &&
              Z.Setoid.test(x) &&
@@ -802,6 +803,7 @@
   //. Constructor for types which include `null` as a member.
   var Nullable = UnaryTypeWithUrl(
     'sanctuary-def/Nullable',
+    Any,
     K(true),
     function(nullable) {
       // eslint-disable-next-line eqeqeq
@@ -828,7 +830,8 @@
   //. `{foo: 1, bar: 2, baz: 'XXX'}` is not.
   var StrMap = UnaryTypeWithUrl(
     'sanctuary-def/StrMap',
-    Object_.test.bind(Object_),
+    Object_,
+    K(true),
     function(strMap) {
       return Z.reduce(function(xs, x) { return xs.concat([x]); }, [], strMap);
     }
@@ -1393,7 +1396,7 @@
       [String_, String_, Type, Function_([Any, Boolean_]), Type],
       NullaryType);
 
-  //# UnaryType :: String -> String -> (Any -> Boolean) -> (t a -> Array a) -> (Type -> Type)
+  //# UnaryType :: String -> String -> Type -> (Any -> Boolean) -> ((t a -> Array a) -> (Type -> Type))
   //.
   //. Type constructor for types with one type variable (such as [`Array`][]).
   //.
@@ -1403,6 +1406,8 @@
   //.
   //.   - the documentation URL of `t` (exposed as `t.url`);
   //.
+  //.   - the parent of `t` (exposed as `t.parent`);
+  //.
   //.   - a predicate which accepts any JavaScript value and returns `true`
   //.     if (and only if) the value is a member of `t x` for some type `x`;
   //.
@@ -1424,6 +1429,7 @@
   //. const Maybe = $.UnaryType(
   //.   maybeTypeIdent,
   //.   'http://example.com/my-package#Maybe',
+  //.   $.Any,
   //.   x => type(x) === maybeTypeIdent,
   //.   maybe => maybe.isJust ? [maybe.value] : []
   //. );
@@ -1471,14 +1477,14 @@
   //. //
   //. //   Since there is no type of which all the above values are members, the type-variable constraint has been violated.
   //. ```
-  function UnaryType(name, url, test, _1) {
+  function UnaryType(name, url, parent, test, _1) {
     return function($1) {
       function format(outer, inner) {
         return outer('(' + stripNamespace(name) + ' ') +
                inner('$1')(String($1)) + outer(')');
       }
       var types = {$1: {extractor: _1, type: $1}};
-      return new _Type(UNARY, name, url, format, Any, test, ['$1'], types);
+      return new _Type(UNARY, name, url, format, parent, test, ['$1'], types);
     };
   }
 
@@ -1487,19 +1493,20 @@
       {},
       [String_,
        String_,
+       Type,
        Function_([Any, Boolean_]),
        Function_([Unchecked('t a'), Array_(Unchecked('a'))]),
        AnyFunction],
-      function(name, url, test, _1) {
+      function(name, url, parent, test, _1) {
         return def(stripNamespace(name),
                    {},
                    [Type, Type],
-                   UnaryType(name, url, test, _1));
+                   UnaryType(name, url, parent, test, _1));
       });
 
   //  fromUnaryType :: Type -> (Type -> Type)
   function fromUnaryType(t) {
-    return UnaryType(t.name, t.url, t.test.bind(t), t.types.$1.extractor);
+    return UnaryType(t.name, t.url, t.parent, t._test, t.types.$1.extractor);
   }
 
   //# BinaryType :: String -> String -> (Any -> Boolean) -> (t a b -> Array a) -> (t a b -> Array b) -> (Type -> Type -> Type)
@@ -2539,7 +2546,7 @@
   function fromUncheckedUnaryType(typeConstructor) {
     var t = typeConstructor(Unknown);
     var _1 = t.types.$1.extractor;
-    return CheckedUnaryType(t.name, t.url, t.test.bind(t), _1);
+    return CheckedUnaryType(t.name, t.url, t.parent, t._test, _1);
   }
 
   //  fromUncheckedBinaryType :: ((Type, Type) -> Type) ->
diff --git a/test/index.js b/test/index.js
index be3b194..271eb3d 100644
--- a/test/index.js
+++ b/test/index.js
@@ -131,6 +131,7 @@ function Just(x) { return new _Maybe('Just', x); }
 var Maybe = $.UnaryType(
   'my-package/Maybe',
   'http://example.com/my-package#Maybe',
+  $.Any,
   function(x) { return type(x) === 'my-package/Maybe'; },
   function(maybe) { return maybe.isJust ? [maybe.value] : []; }
 );
@@ -3109,10 +3110,10 @@ describe('NullaryType', function() {
 
 describe('UnaryType', function() {
 
-  it('is a quaternary function', function() {
+  it('is a quinary function', function() {
     eq(typeof $.UnaryType, 'function');
-    eq($.UnaryType.length, 4);
-    eq($.UnaryType.toString(), 'UnaryType :: String -> String -> (Any -> Boolean) -> (t a -> Array a) -> Function');
+    eq($.UnaryType.length, 5);
+    eq($.UnaryType.toString(), 'UnaryType :: String -> String -> Type -> (Any -> Boolean) -> (t a -> Array a) -> Function');
   });
 
   it('returns a type constructor which type checks its arguments', function() {

From 90b7aa3bcc4af2623e238bc15e7e748cab1c6ac3 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Thu, 29 Jun 2017 13:34:30 +0200
Subject: [PATCH 04/20] Add refinement support to BinaryType constructor

---
 index.js      | 30 ++++++++++++++++--------------
 test/index.js | 11 +++++++----
 2 files changed, 23 insertions(+), 18 deletions(-)

diff --git a/index.js b/index.js
index e8d55f1..9e59b22 100644
--- a/index.js
+++ b/index.js
@@ -370,10 +370,6 @@
 
   _Type['@@type'] = 'sanctuary-def/Type';
 
-  _Type.prototype.test = function(x) {
-    return this.parent.test(x) && this._test(x);
-  };
-
   _Type.prototype.validate = function(x) {
     var self = this;
     return Z.chain(function(x) {
@@ -448,8 +444,8 @@
   //  BinaryTypeWithUrl ::
   //    (String, Any -> Boolean, t a b -> Array a, t a b -> Array b) ->
   //      ((Type, Type) -> Type)
-  function BinaryTypeWithUrl(name, test, _1, _2) {
-    return BinaryType(name, functionUrl(name), test, _1, _2);
+  function BinaryTypeWithUrl(name, parent, test, _1, _2) {
+    return BinaryType(name, functionUrl(name), parent, test, _1, _2);
   }
 
   //. ### Types
@@ -817,7 +813,8 @@
   //. tuples. `['foo', 42]` is a member of `Pair String Number`.
   var Pair = BinaryTypeWithUrl(
     'sanctuary-def/Pair',
-    function(x) { return typeEq('Array')(x) && x.length === 2; },
+    Array_(Any),
+    function(x) { return x.length === 2; },
     function(pair) { return [pair[0]]; },
     function(pair) { return [pair[1]]; }
   );
@@ -1509,7 +1506,7 @@
     return UnaryType(t.name, t.url, t.parent, t._test, t.types.$1.extractor);
   }
 
-  //# BinaryType :: String -> String -> (Any -> Boolean) -> (t a b -> Array a) -> (t a b -> Array b) -> (Type -> Type -> Type)
+  //# BinaryType :: String -> String -> Type -> (Any -> Boolean) -> (t a b -> Array a) -> (t a b -> Array b) -> (Type -> Type -> Type)
   //.
   //. Type constructor for types with two type variables (such as [`Pair`][]).
   //.
@@ -1519,6 +1516,8 @@
   //.
   //.   - the documentation URL of `t` (exposed as `t.url`);
   //.
+  //.   - the parent of `t` (exposed as `t.parent`);
+  //.
   //.   - a predicate which accepts any JavaScript value and returns `true`
   //.     if (and only if) the value is a member of `t x y` for some types
   //.     `x` and `y`;
@@ -1547,6 +1546,7 @@
   //. const $Pair = $.BinaryType(
   //.   pairTypeIdent,
   //.   'http://example.com/my-package#Pair',
+  //.   Any,
   //.   x => type(x) === pairTypeIdent,
   //.   pair => [pair[0]],
   //.   pair => [pair[1]]
@@ -1601,7 +1601,7 @@
   //. //
   //. //   The value at position 1 is not a member of ‘Rank’.
   //. ```
-  function BinaryType(name, url, test, _1, _2) {
+  function BinaryType(name, url, parent, test, _1, _2) {
     return function($1, $2) {
       function format(outer, inner) {
         return outer('(' + stripNamespace(name) + ' ') +
@@ -1614,7 +1614,7 @@
                        name,
                        url,
                        format,
-                       Any,
+                       parent,
                        test,
                        ['$1', '$2'],
                        types);
@@ -1626,22 +1626,24 @@
       {},
       [String_,
        String_,
+       Type,
        Function_([Any, Boolean_]),
        Function_([Unchecked('t a b'), Array_(Unchecked('a'))]),
        Function_([Unchecked('t a b'), Array_(Unchecked('b'))]),
        AnyFunction],
-      function(name, url, test, _1, _2) {
+      function(name, url, parent, test, _1, _2) {
         return def(stripNamespace(name),
                    {},
                    [Type, Type, Type],
-                   BinaryType(name, url, test, _1, _2));
+                   BinaryType(name, url, parent, test, _1, _2));
       });
 
   //  xprod :: (Type, Array Type, Array Type) -> Array Type
   function xprod(t, $1s, $2s) {
     var specialize = BinaryType(t.name,
                                 t.url,
-                                t.test.bind(t),
+                                t.parent,
+                                t._test,
                                 t.types.$1.extractor,
                                 t.types.$2.extractor);
     var $types = [];
@@ -2555,7 +2557,7 @@
     var t = typeConstructor(Unknown, Unknown);
     var _1 = t.types.$1.extractor;
     var _2 = t.types.$2.extractor;
-    return CheckedBinaryType(t.name, t.url, t.test.bind(t), _1, _2);
+    return CheckedBinaryType(t.name, t.url, t.parent, t._test, _1, _2);
   }
 
   return {
diff --git a/test/index.js b/test/index.js
index 271eb3d..6fe8de2 100644
--- a/test/index.js
+++ b/test/index.js
@@ -182,6 +182,7 @@ function Right(x) { return new _Either('Right', x); }
 var Either = $.BinaryType(
   'my-package/Either',
   'http://example.com/my-package#Either',
+  $.Any,
   function(x) { return type(x) === 'my-package/Either'; },
   function(either) { return either.isLeft ? [either.value] : []; },
   function(either) { return either.isRight ? [either.value] : []; }
@@ -220,6 +221,7 @@ Pair.prototype.toString = function() {
 var $Pair = $.BinaryType(
   'my-package/Pair',
   'http://example.com/my-package#Pair',
+  $.Any,
   function(x) { return type(x) === 'my-package/Pair'; },
   function(pair) { return [pair[0]]; },
   function(pair) { return [pair[1]]; }
@@ -2477,7 +2479,8 @@ describe('def', function() {
     var Pair = $.BinaryType(
       'my-package/Pair',
       'http://example.com/my-package#Pair',
-      function(x) { return Object.prototype.toString.call(x) === '[object Array]' && x.length === 2; },
+      $.Array($.Any),
+      function(x) { return x.length === 2; },
       function(pair) { return [pair[0]]; },
       function(pair) { return [pair[1]]; }
     );
@@ -3136,10 +3139,10 @@ describe('UnaryType', function() {
 
 describe('BinaryType', function() {
 
-  it('is a quinary function', function() {
+  it('is a sexternary function', function() {
     eq(typeof $.BinaryType, 'function');
-    eq($.BinaryType.length, 5);
-    eq($.BinaryType.toString(), 'BinaryType :: String -> String -> (Any -> Boolean) -> (t a b -> Array a) -> (t a b -> Array b) -> Function');
+    eq($.BinaryType.length, 6);
+    eq($.BinaryType.toString(), 'BinaryType :: String -> String -> Type -> (Any -> Boolean) -> (t a b -> Array a) -> (t a b -> Array b) -> Function');
   });
 
   it('returns a type constructor which type checks its arguments', function() {

From fa55a1046d62aff3bb6aa2693c4dae2ceeaeddb2 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Thu, 29 Jun 2017 13:58:27 +0200
Subject: [PATCH 05/20] Remove no longer necessary null-check

---
 index.js | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/index.js b/index.js
index 9e59b22..213c3b2 100644
--- a/index.js
+++ b/index.js
@@ -1747,8 +1747,7 @@
     }
 
     function test(x) {
-      return x != null &&
-             keys.every(function(k) { return hasOwnProperty.call(x, k); });
+      return keys.every(function(k) { return hasOwnProperty.call(x, k); });
     }
 
     var $types = {};

From 75a55dd76920dde634d8e10d67d0fb41eb39d401 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Thu, 29 Jun 2017 18:12:08 +0200
Subject: [PATCH 06/20] Incorporate PR feedback

---
 index.js      | 44 +++++++++++++++++++++++++-------------------
 test/index.js |  2 +-
 2 files changed, 26 insertions(+), 20 deletions(-)

diff --git a/index.js b/index.js
index 213c3b2..2ee0405 100644
--- a/index.js
+++ b/index.js
@@ -435,16 +435,24 @@
     return EnumType(name, functionUrl(name), members);
   }
 
-  //  UnaryTypeWithUrl ::
-  //    (String, Any -> Boolean, t a -> Array a) -> (Type -> Type)
-  function UnaryTypeWithUrl(name, parent, test, _1) {
+  //  UnaryTypeWithUrl :: ... -> (Type -> Type)
+  function UnaryTypeWithUrl(
+    name,           // :: String
+    parent,         // :: Type
+    test,           // :: Any -> Boolean
+    _1              // :: t a -> Array a
+  ) {
     return UnaryType(name, functionUrl(name), parent, test, _1);
   }
 
-  //  BinaryTypeWithUrl ::
-  //    (String, Any -> Boolean, t a b -> Array a, t a b -> Array b) ->
-  //      ((Type, Type) -> Type)
-  function BinaryTypeWithUrl(name, parent, test, _1, _2) {
+  //  BinaryTypeWithUrl :: ... -> ((Type, Type) -> Type)
+  function BinaryTypeWithUrl(
+    name,           // :: String
+    parent,         // :: Type
+    test,           // :: Any -> Boolean
+    _1,             // :: t a b -> Array a
+    _2              // :: t a b -> Array b
+  ) {
     return BinaryType(name, functionUrl(name), parent, test, _1, _2);
   }
 
@@ -1303,9 +1311,9 @@
   //. The environment is only significant if the type contains
   //. [type variables][].
   //.
-  //. Using types as predicates is powerful. One could, for example,
-  //. define a [record type][] for each endpoint of a REST API and
-  //. validate the bodies of incoming POST requests against these types.
+  //. Using types as predicates is powerful. One could, for example, define a
+  //. [record type][] for each endpoint of a REST API and validate the bodies
+  //. of incoming POST requests against these types.
   function test(env, t, x) {
     var typeInfo = {name: 'name', constraints: {}, types: [t]};
     return satisfactoryTypes(env, typeInfo, {}, t, 0, [], [x]).isRight;
@@ -1325,7 +1333,7 @@
   //.
   //.   - the documentation URL of `t` (exposed as `t.url`); and
   //.
-  //.   - the parent of `t` (exposed as `t.parent`);
+  //.   - the parent type of `t` (exposed as `t.parent`);
   //.
   //.   - a predicate which accepts any JavaScript value and returns `true` if
   //.     (and only if) the value is a member of `t`.
@@ -1393,7 +1401,7 @@
       [String_, String_, Type, Function_([Any, Boolean_]), Type],
       NullaryType);
 
-  //# UnaryType :: String -> String -> Type -> (Any -> Boolean) -> ((t a -> Array a) -> (Type -> Type))
+  //# UnaryType :: String -> String -> Type -> (Any -> Boolean) -> (t a -> Array a) -> (Type -> Type)
   //.
   //. Type constructor for types with one type variable (such as [`Array`][]).
   //.
@@ -1403,7 +1411,7 @@
   //.
   //.   - the documentation URL of `t` (exposed as `t.url`);
   //.
-  //.   - the parent of `t` (exposed as `t.parent`);
+  //.   - the parent type of `t` (exposed as `t.parent`);
   //.
   //.   - a predicate which accepts any JavaScript value and returns `true`
   //.     if (and only if) the value is a member of `t x` for some type `x`;
@@ -1516,7 +1524,7 @@
   //.
   //.   - the documentation URL of `t` (exposed as `t.url`);
   //.
-  //.   - the parent of `t` (exposed as `t.parent`);
+  //.   - the parent type of `t` (exposed as `t.parent`);
   //.
   //.   - a predicate which accepts any JavaScript value and returns `true`
   //.     if (and only if) the value is a member of `t x y` for some types
@@ -1608,8 +1616,6 @@
                inner('$1')(String($1)) + outer(' ') +
                inner('$2')(String($2)) + outer(')');
       }
-      var types = {$1: {extractor: _1, type: $1},
-                   $2: {extractor: _2, type: $2}};
       return new _Type(BINARY,
                        name,
                        url,
@@ -1617,7 +1623,8 @@
                        parent,
                        test,
                        ['$1', '$2'],
-                       types);
+                       {$1: {extractor: _1, type: $1},
+                        $2: {extractor: _2, type: $2}});
     };
   }
 
@@ -1872,7 +1879,6 @@
       function format(outer, inner) {
         return outer('(' + name + ' ') + inner('$1')(String($1)) + outer(')');
       }
-      var types = {$1: {extractor: K([]), type: $1}};
       return new _Type(VARIABLE,
                        name,
                        '',
@@ -1880,7 +1886,7 @@
                        Any,
                        K(true),
                        ['$1'],
-                       types);
+                       {$1: {extractor: K([]), type: $1}});
     };
   }
 
diff --git a/test/index.js b/test/index.js
index 6fe8de2..ecd6e5a 100644
--- a/test/index.js
+++ b/test/index.js
@@ -3139,7 +3139,7 @@ describe('UnaryType', function() {
 
 describe('BinaryType', function() {
 
-  it('is a sexternary function', function() {
+  it('is a senary function', function() {
     eq(typeof $.BinaryType, 'function');
     eq($.BinaryType.length, 6);
     eq($.BinaryType.toString(), 'BinaryType :: String -> String -> Type -> (Any -> Boolean) -> (t a b -> Array a) -> (t a b -> Array b) -> Function');

From aada3db81c41c2ce07a43e0095d2a90e45eb5109 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Fri, 30 Jun 2017 11:27:30 +0200
Subject: [PATCH 07/20] Add refinement support to RecordType constructor

Fixes #141
---
 index.js      | 26 +++++++++++++++-----------
 test/index.js | 18 +++++++++---------
 2 files changed, 24 insertions(+), 20 deletions(-)

diff --git a/index.js b/index.js
index 2ee0405..4ba6d10 100644
--- a/index.js
+++ b/index.js
@@ -1691,20 +1691,25 @@
   var CheckedEnumType =
   def('EnumType', {}, [String_, String_, Array_(Any), Type], EnumType);
 
-  //# RecordType :: StrMap Type -> Type
+  //# RecordType :: Type -> StrMap Type -> Type
   //.
   //. `RecordType` is used to construct record types. The type definition
   //. specifies the name and type of each required field.
   //.
   //. To define a record type one must provide:
   //.
+  //.   - the parent type of `t` (exposed as `t.parent`);
+  //.
   //.   - an object mapping field name to type.
   //.
   //. For example:
   //.
   //. ```javascript
   //. //    Point :: Type
-  //. const Point = $.RecordType({x: $.FiniteNumber, y: $.FiniteNumber});
+  //. const Point = $.RecordType($.Any, {
+  //.   x: $.FiniteNumber,
+  //.   y: $.FiniteNumber
+  //. });
   //.
   //. //    dist :: Point -> Point -> FiniteNumber
   //. const dist =
@@ -1740,7 +1745,7 @@
   //. //
   //. //   The value at position 1 is not a member of ‘{ x :: FiniteNumber, y :: FiniteNumber }’.
   //. ```
-  function RecordType(fields) {
+  function RecordType(parent, fields) {
     var keys = Object.keys(fields).sort();
 
     function format(outer, inner) {
@@ -1754,7 +1759,9 @@
     }
 
     function test(x) {
-      return keys.every(function(k) { return hasOwnProperty.call(x, k); });
+      if (x == null) return false;
+      var o = Object(x);
+      return keys.every(function(k) { return k in o; });
     }
 
     var $types = {};
@@ -1762,11 +1769,11 @@
       $types[k] = {extractor: function(x) { return [x[k]]; }, type: fields[k]};
     });
 
-    return new _Type(RECORD, '', '', format, Object_, test, keys, $types);
+    return new _Type(RECORD, '', '', format, parent, test, keys, $types);
   }
 
   var CheckedRecordType =
-  def('RecordType', {}, [StrMap(Type), Type], RecordType);
+  def('RecordType', {}, [Type, StrMap(Type), Type], RecordType);
 
   //# TypeVariable :: String -> Type
   //.
@@ -2543,11 +2550,8 @@
                def);
   }
 
-  var create =
-  def('create',
-      {},
-      [RecordType({checkTypes: Boolean_, env: Array_(Any)}), AnyFunction],
-      _create);
+  var Options = RecordType(Object_, {checkTypes: Boolean_, env: Array_(Any)});
+  var create = def('create', {}, [Options, AnyFunction], _create);
 
   //  fromUncheckedUnaryType :: (Type -> Type) -> (Type -> Type)
   function fromUncheckedUnaryType(typeConstructor) {
diff --git a/test/index.js b/test/index.js
index ecd6e5a..a7ea0c8 100644
--- a/test/index.js
+++ b/test/index.js
@@ -1204,14 +1204,14 @@ describe('def', function() {
 
   it('supports record types', function() {
     eq(typeof $.RecordType, 'function');
-    eq($.RecordType.length, 1);
-    eq($.RecordType.toString(), 'RecordType :: StrMap Type -> Type');
+    eq($.RecordType.length, 2);
+    eq($.RecordType.toString(), 'RecordType :: Type -> StrMap Type -> Type');
 
     //  Point :: Type
-    var Point = $.RecordType({x: $.Number, y: $.Number});
+    var Point = $.RecordType($.Any, {x: $.Number, y: $.Number});
 
     //  Line :: Type
-    var Line = $.RecordType({start: Point, end: Point});
+    var Line = $.RecordType($.Any, {start: Point, end: Point});
 
     //  dist :: Point -> Point -> Number
     var dist = def('dist', {}, [Point, Point, $.Number], function(p, q) {
@@ -1312,13 +1312,13 @@ describe('def', function() {
 
     eq(id([{x: 0, y: 0}, {x: 1, y: 1}]), [{x: 0, y: 0}, {x: 1, y: 1}]);
 
-    throws(function() { $.RecordType({x: /XXX/, y: /XXX/, z: $.Any}); },
+    throws(function() { $.RecordType($.Any, {x: /XXX/, y: /XXX/, z: $.Any}); },
            TypeError,
            'Invalid value\n' +
            '\n' +
-           'RecordType :: StrMap Type -> Type\n' +
-           '                     ^^^^\n' +
-           '                      1\n' +
+           'RecordType :: Type -> StrMap Type -> Type\n' +
+           '                             ^^^^\n' +
+           '                              1\n' +
            '\n' +
            '1)  /XXX/ :: RegExp\n' +
            '\n' +
@@ -1327,7 +1327,7 @@ describe('def', function() {
            'See https://github.com/sanctuary-js/sanctuary-def/tree/v' + version + '#Type for information about the Type type.\n');
 
     //  Foo :: Type
-    var Foo = $.RecordType({x: a, y: a});
+    var Foo = $.RecordType($.Any, {x: a, y: a});
 
     //  foo :: Foo -> Foo
     var foo = def('foo', {}, [Foo, Foo], identity);

From 96d562c8839fe072ac9853bfd10c94193f49e68a Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Fri, 30 Jun 2017 12:18:01 +0200
Subject: [PATCH 08/20] Document how to use record type refinement

---
 index.js | 54 +++++++++++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 51 insertions(+), 3 deletions(-)

diff --git a/index.js b/index.js
index 4ba6d10..7fbfa15 100644
--- a/index.js
+++ b/index.js
@@ -1720,9 +1720,6 @@
   //. dist({x: 0, y: 0}, {x: 3, y: 4});
   //. // => 5
   //.
-  //. dist({x: 0, y: 0}, {x: 3, y: 4, color: 'red'});
-  //. // => 5
-  //.
   //. dist({x: 0, y: 0}, {x: NaN, y: NaN});
   //. // ! TypeError: Invalid value
   //. //
@@ -1745,6 +1742,57 @@
   //. //
   //. //   The value at position 1 is not a member of ‘{ x :: FiniteNumber, y :: FiniteNumber }’.
   //. ```
+  //.
+  //. ##### Extending record types
+  //.
+  //. By using the `parent` argument of the RecordType constructor, we can
+  //. define record types which must contain all the same properties of
+  //. another. For example, we could define `Poinst3D` as a refinement of our
+  //. `Point` from the previous example:
+  //.
+  //. ```js
+  //. //    Point3D :: Type
+  //. const Point3D = $.RecordType(Point, {z: $.FiniteNumber});
+  //.
+  //. //    a :: Point
+  //. const a = {x: 0, y: 0};
+  //.
+  //. //    b :: Point, Point3D
+  //. const b = {x: 3, y: 4, z: 5};
+  //.
+  //. Point.validate(a)   // => Right(a)
+  //. Point3D.validate(a) // => Left({propPath: ['z'], value: undefined})
+  //.
+  //. Point.validate(b)   // => Right(b)
+  //. Point3D.validate(b) // => Right(b)
+  //.
+  //. dist(a, b);
+  //. // => 5
+  //. ```
+  //.
+  //. We can see that `b` is a member of `Point3D` as well as `Point`, allowing
+  //. us to call `dist` on it. By default record types allow additional
+  //. properties, allowing for this "extension". If you wish for a record type
+  //. to allow no additional properties, we can refine it as such:
+  //.
+  //. ```js
+  //. //    strict :: Type -> Type
+  //. const strict = t => $.NullaryType(
+  //.   'Strict' + t.name,
+  //.   '',
+  //.   t,
+  //.   x => Object.keys(x).length === t.keys.length
+  //. );
+  //.
+  //. //    StrictPoint3D :: Type
+  //. const StrictPoint3D = strict(Point3D)
+  //.
+  //. //    a :: Point, Point3D
+  //. const a = {x: 1, y: 2, z: 3, color: 'red'}
+  //.
+  //. Point3D.validate(a)       // => Right(a)
+  //. StrictPoint3D.validate(a) // => Left({propPath: [], value: a})
+  //. ```
   function RecordType(parent, fields) {
     var keys = Object.keys(fields).sort();
 

From 7b0ac2c92ad3af121d5e79ac2b44418f89237fb8 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Fri, 30 Jun 2017 12:26:40 +0200
Subject: [PATCH 09/20] Incorporate PR feedback

---
 index.js | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/index.js b/index.js
index 7fbfa15..b441515 100644
--- a/index.js
+++ b/index.js
@@ -1554,7 +1554,7 @@
   //. const $Pair = $.BinaryType(
   //.   pairTypeIdent,
   //.   'http://example.com/my-package#Pair',
-  //.   Any,
+  //.   $.Any,
   //.   x => type(x) === pairTypeIdent,
   //.   pair => [pair[0]],
   //.   pair => [pair[1]]
@@ -1708,7 +1708,7 @@
   //. //    Point :: Type
   //. const Point = $.RecordType($.Any, {
   //.   x: $.FiniteNumber,
-  //.   y: $.FiniteNumber
+  //.   y: $.FiniteNumber,
   //. });
   //.
   //. //    dist :: Point -> Point -> FiniteNumber

From 6d6960bbf04dabb2131f58554b01896cb288455e Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Fri, 30 Jun 2017 12:27:07 +0200
Subject: [PATCH 10/20] :warning: Change env from Array Any to Array Type

---
 index.js      | 2 +-
 test/index.js | 6 +++---
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/index.js b/index.js
index b441515..db69250 100644
--- a/index.js
+++ b/index.js
@@ -2598,7 +2598,7 @@
                def);
   }
 
-  var Options = RecordType(Object_, {checkTypes: Boolean_, env: Array_(Any)});
+  var Options = RecordType(Object_, {checkTypes: Boolean_, env: Array_(Type)});
   var create = def('create', {}, [Options, AnyFunction], _create);
 
   //  fromUncheckedUnaryType :: (Type -> Type) -> (Type -> Type)
diff --git a/test/index.js b/test/index.js
index a7ea0c8..1efea50 100644
--- a/test/index.js
+++ b/test/index.js
@@ -240,13 +240,13 @@ describe('create', function() {
            TypeError,
            'Invalid value\n' +
            '\n' +
-           'create :: { checkTypes :: Boolean, env :: Array Any } -> Function\n' +
-           '          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n' +
+           'create :: { checkTypes :: Boolean, env :: Array Type } -> Function\n' +
+           '          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n' +
            '                               1\n' +
            '\n' +
            '1)  true :: Boolean\n' +
            '\n' +
-           'The value at position 1 is not a member of ‘{ checkTypes :: Boolean, env :: Array Any }’.\n');
+           'The value at position 1 is not a member of ‘{ checkTypes :: Boolean, env :: Array Type }’.\n');
   });
 
 });

From 02ea18c0e3ce256cf14d637c24be485b84ce2af0 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Fri, 30 Jun 2017 12:33:34 +0200
Subject: [PATCH 11/20] Rephrase the documentation using "one" over "we"

---
 index.js | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/index.js b/index.js
index db69250..8d1bcdb 100644
--- a/index.js
+++ b/index.js
@@ -1745,9 +1745,9 @@
   //.
   //. ##### Extending record types
   //.
-  //. By using the `parent` argument of the RecordType constructor, we can
+  //. By using the `parent` argument of the RecordType constructor, one can
   //. define record types which must contain all the same properties of
-  //. another. For example, we could define `Poinst3D` as a refinement of our
+  //. another. For example, one could define `Poinst3D` as a refinement of
   //. `Point` from the previous example:
   //.
   //. ```js
@@ -1770,10 +1770,10 @@
   //. // => 5
   //. ```
   //.
-  //. We can see that `b` is a member of `Point3D` as well as `Point`, allowing
-  //. us to call `dist` on it. By default record types allow additional
-  //. properties, allowing for this "extension". If you wish for a record type
-  //. to allow no additional properties, we can refine it as such:
+  //. The `b` value is a member of `Point3D` as well as `Point`, allowing one
+  //. to call `dist` on it. By default record types allow additional
+  //. properties, permitting record "extension". If one wishes for a record
+  //. type to allow for no additional properties, it can be refined as such:
   //.
   //. ```js
   //. //    strict :: Type -> Type

From 017a37660a07a1e106d1897e63e649750bd2ec0f Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Fri, 30 Jun 2017 13:00:53 +0200
Subject: [PATCH 12/20] Add assertions for record extension

---
 test/index.js | 14 +++++++++++---
 1 file changed, 11 insertions(+), 3 deletions(-)

diff --git a/test/index.js b/test/index.js
index 1efea50..e359aa0 100644
--- a/test/index.js
+++ b/test/index.js
@@ -1210,6 +1210,9 @@ describe('def', function() {
     //  Point :: Type
     var Point = $.RecordType($.Any, {x: $.Number, y: $.Number});
 
+    //  Point3D :: Type
+    var Point3D = $.RecordType(Point, {z: $.Number});
+
     //  Line :: Type
     var Line = $.RecordType($.Any, {start: Point, end: Point});
 
@@ -1224,12 +1227,17 @@ describe('def', function() {
     });
 
     eq(dist({x: 0, y: 0}, {x: 0, y: 0}), 0);
-    eq(dist({x: 0, y: 0}, {x: 0, y: 0, color: 'red'}), 0);
+    eq(dist({x: 0, y: 0}, {x: 0, y: 0, z: 0}), 0);
     eq(dist({x: 1, y: 1}, {x: 4, y: 5}), 5);
-    eq(dist({x: 1, y: 1}, {x: 4, y: 5, color: 'red'}), 5);
+    eq(dist({x: 1, y: 1}, {x: 4, y: 5, z: 6}), 5);
 
     eq(length({start: {x: 1, y: 1}, end: {x: 4, y: 5}}), 5);
-    eq(length({start: {x: 1, y: 1}, end: {x: 4, y: 5, color: 'red'}}), 5);
+    eq(length({start: {x: 1, y: 1}, end: {x: 4, y: 5, z: 6}}), 5);
+
+    eq($.test([], Point3D, {x: 0, y: 0}), false);
+    eq($.test([], Point3D, {x: 0, z: 0}), false);
+    eq($.test([], Point3D, {y: 0, z: 0}), false);
+    eq($.test([], Point3D, {x: 0, y: 0, z: 0}), true);
 
     throws(function() { dist(null); },
            TypeError,

From 1ae62f47053b4141ed34ca5fa05292296913079e Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Wed, 5 Jul 2017 11:34:20 +0200
Subject: [PATCH 13/20] Aleviate minor complaints about documentation

---
 index.js | 48 ++++++++++++++++++++++++++----------------------
 1 file changed, 26 insertions(+), 22 deletions(-)

diff --git a/index.js b/index.js
index 8d1bcdb..b15f227 100644
--- a/index.js
+++ b/index.js
@@ -1745,37 +1745,38 @@
   //.
   //. ##### Extending record types
   //.
-  //. By using the `parent` argument of the RecordType constructor, one can
+  //. By using the `parent` argument of the `RecordType` constructor, one can
   //. define record types which must contain all the same properties of
-  //. another. For example, one could define `Poinst3D` as a refinement of
+  //. another. For example, one could define `Point3D` as a refinement of
   //. `Point` from the previous example:
   //.
-  //. ```js
+  //. ```javascript
   //. //    Point3D :: Type
   //. const Point3D = $.RecordType(Point, {z: $.FiniteNumber});
   //.
-  //. //    a :: Point
-  //. const a = {x: 0, y: 0};
+  //. //    p1 :: Point
+  //. const p1 = {x: 0, y: 0};
   //.
-  //. //    b :: Point, Point3D
-  //. const b = {x: 3, y: 4, z: 5};
+  //. //    p2 :: Point, Point3D
+  //. const p2 = {x: 3, y: 4, z: 5};
   //.
-  //. Point.validate(a)   // => Right(a)
-  //. Point3D.validate(a) // => Left({propPath: ['z'], value: undefined})
+  //. Point.validate(p1);    // => Right({x: 0, y: 0})
+  //. Point3D.validate(p1);  // => Left({propPath: ['z'], value: undefined})
   //.
-  //. Point.validate(b)   // => Right(b)
-  //. Point3D.validate(b) // => Right(b)
+  //. Point.validate(p2);    // => Right({x: 3, y: 4, z: 5})
+  //. Point3D.validate(p2);  // => Right({x: 3, y: 4, z: 5})
   //.
-  //. dist(a, b);
+  //. dist(p1, p2);
   //. // => 5
   //. ```
   //.
-  //. The `b` value is a member of `Point3D` as well as `Point`, allowing one
-  //. to call `dist` on it. By default record types allow additional
-  //. properties, permitting record "extension". If one wishes for a record
-  //. type to allow for no additional properties, it can be refined as such:
+  //. The `p2` value is a member of `Point3D` as well as `Point`, making it a
+  //. valid argument to `dist`. By default record types allow additional
+  //. properties (which is what allowed `p2` to be a member of `Point`). If one
+  //. wishes for a record type to allow for no additional properties, it can be
+  //. refined as such:
   //.
-  //. ```js
+  //. ```javascript
   //. //    strict :: Type -> Type
   //. const strict = t => $.NullaryType(
   //.   'Strict' + t.name,
@@ -1785,13 +1786,16 @@
   //. );
   //.
   //. //    StrictPoint3D :: Type
-  //. const StrictPoint3D = strict(Point3D)
+  //. const StrictPoint3D = strict(Point3D);
+  //.
+  //. //    p :: Point, Point3D
+  //. const p = {x: 1, y: 2, z: 3, color: 'red'};
   //.
-  //. //    a :: Point, Point3D
-  //. const a = {x: 1, y: 2, z: 3, color: 'red'}
+  //. Point3D.validate(p);
+  //. // => Right({x: 1, y: 2, z: 3, color: 'red'})
   //.
-  //. Point3D.validate(a)       // => Right(a)
-  //. StrictPoint3D.validate(a) // => Left({propPath: [], value: a})
+  //. StrictPoint3D.validate(p);
+  //. // => Left({propPath: [], value: {x: 1, y: 2, z: 3, color: 'red'}})
   //. ```
   function RecordType(parent, fields) {
     var keys = Object.keys(fields).sort();

From 4b906681eac53ca9af97e7b15c102e6c32385cb0 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Wed, 5 Jul 2017 13:05:02 +0200
Subject: [PATCH 14/20] In-line Options record definition with create
 definition

---
 index.js | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

diff --git a/index.js b/index.js
index b15f227..1eb03d9 100644
--- a/index.js
+++ b/index.js
@@ -2602,8 +2602,12 @@
                def);
   }
 
-  var Options = RecordType(Object_, {checkTypes: Boolean_, env: Array_(Type)});
-  var create = def('create', {}, [Options, AnyFunction], _create);
+  var create =
+  def('create',
+      {},
+      [RecordType(Object_, {checkTypes: Boolean_, env: Array_(Type)}),
+       AnyFunction],
+      _create);
 
   //  fromUncheckedUnaryType :: (Type -> Type) -> (Type -> Type)
   function fromUncheckedUnaryType(typeConstructor) {

From 9708db1800a0bc2c04b72b67ab1356489d124948 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Wed, 5 Jul 2017 16:37:03 +0200
Subject: [PATCH 15/20] Add Strict type constructor

---
 index.js      | 42 ++++++++++++++++++++++++++++--------------
 test/index.js | 16 ++++++++++++++++
 2 files changed, 44 insertions(+), 14 deletions(-)

diff --git a/index.js b/index.js
index 1eb03d9..924277f 100644
--- a/index.js
+++ b/index.js
@@ -827,6 +827,23 @@
     function(pair) { return [pair[1]]; }
   );
 
+  //# Strict :: Type -> Type
+  //.
+  //. Constructor for strict record types. For example:
+  //. `$.Strict($.Record($.Any, {name: $.String}))`, is the type comprising
+  //. every object with a `name :: String` property, without any other
+  //. properties.
+  function Strict(t) {
+    function test(x) {
+      return Object.keys(x).length === t.keys.length;
+    }
+
+    return NullaryType('sanctuary-def/Strict',
+                       functionUrl('Strict'),
+                       t,
+                       test);
+  }
+
   //# StrMap :: Type -> Type
   //.
   //. Constructor for homogeneous Object types.
@@ -1774,27 +1791,22 @@
   //. valid argument to `dist`. By default record types allow additional
   //. properties (which is what allowed `p2` to be a member of `Point`). If one
   //. wishes for a record type to allow for no additional properties, it can be
-  //. refined as such:
+  //. refined using the [`Strict`][] constructor:
   //.
   //. ```javascript
-  //. //    strict :: Type -> Type
-  //. const strict = t => $.NullaryType(
-  //.   'Strict' + t.name,
-  //.   '',
-  //.   t,
-  //.   x => Object.keys(x).length === t.keys.length
-  //. );
-  //.
   //. //    StrictPoint3D :: Type
-  //. const StrictPoint3D = strict(Point3D);
+  //. const StrictPoint3D = Strict(Point3D);
   //.
-  //. //    p :: Point, Point3D
-  //. const p = {x: 1, y: 2, z: 3, color: 'red'};
+  //. //    p3 :: Point, Point3D
+  //. const p3 = {x: 1, y: 2, z: 3, color: 'red'};
   //.
-  //. Point3D.validate(p);
+  //. Point3D.validate(p3);
   //. // => Right({x: 1, y: 2, z: 3, color: 'red'})
   //.
-  //. StrictPoint3D.validate(p);
+  //. StrictPoint3D.validate(p2);
+  //. // => Right({x: 3, y: 4, z: 5})
+  //.
+  //. StrictPoint3D.validate(p3);
   //. // => Left({propPath: [], value: {x: 1, y: 2, z: 3, color: 'red'}})
   //. ```
   function RecordType(parent, fields) {
@@ -2657,6 +2669,7 @@
     RegExp: RegExp_,
     RegexFlags: RegexFlags,
     StrMap: fromUncheckedUnaryType(StrMap),
+    Strict: Strict,
     String: String_,
     Symbol: Symbol_,
     Type: Type,
@@ -2695,6 +2708,7 @@
 //. [`Pair`]:               #Pair
 //. [`RegExp`]:             #RegExp
 //. [`RegexFlags`]:         #RegexFlags
+//. [`Strict`]:             #Strict
 //. [`String`]:             #String
 //. [`SyntaxError`]:        https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/SyntaxError
 //. [`TypeClass`]:          https://github.com/sanctuary-js/sanctuary-type-classes#TypeClass
diff --git a/test/index.js b/test/index.js
index e359aa0..18ed6d5 100644
--- a/test/index.js
+++ b/test/index.js
@@ -1357,6 +1357,22 @@ describe('def', function() {
            'Since there is no type of which all the above values are members, the type-variable constraint has been violated.\n');
   });
 
+  it('supports "strict" record types', function() {
+
+    //  Point :: Type
+    var Point = $.RecordType($.Any, {x: $.Number, y: $.Number});
+
+    //  StrictPoint :: Type
+    var StrictPoint = $.Strict(Point);
+
+    //  p :: Point
+    var p = {x: 1, y: 2, z: 3};
+
+    eq($.test([], Point, p), true);
+    eq($.test([], StrictPoint, p), false);
+
+  });
+
   it('supports "nullable" types', function() {
     eq(typeof $.Nullable, 'function');
     eq($.Nullable.length, 1);

From cc92cd2f3aed66dcea628d0a03a50d88b1b80aed Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Wed, 5 Jul 2017 16:50:15 +0200
Subject: [PATCH 16/20] Rephrase documentation on additional record fields

---
 index.js | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/index.js b/index.js
index 924277f..b92be9e 100644
--- a/index.js
+++ b/index.js
@@ -1788,10 +1788,12 @@
   //. ```
   //.
   //. The `p2` value is a member of `Point3D` as well as `Point`, making it a
-  //. valid argument to `dist`. By default record types allow additional
-  //. properties (which is what allowed `p2` to be a member of `Point`). If one
-  //. wishes for a record type to allow for no additional properties, it can be
-  //. refined using the [`Strict`][] constructor:
+  //. valid argument to `dist`. By default, record types permit the presence
+  //. of additional fields. As a result, p2 is a member of Point as well as
+  //. Point3D.
+  //.
+  //. One could use the [`Strict`][] constructor to define record types which
+  //. do not permit additional fields:
   //.
   //. ```javascript
   //. //    StrictPoint3D :: Type

From 2fce7d96f78306eaa85fbf8b35f4052bf8022330 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Wed, 5 Jul 2017 17:00:25 +0200
Subject: [PATCH 17/20] Incorporate PR feedback

---
 index.js | 13 ++++++-------
 1 file changed, 6 insertions(+), 7 deletions(-)

diff --git a/index.js b/index.js
index b92be9e..37397cc 100644
--- a/index.js
+++ b/index.js
@@ -829,10 +829,9 @@
 
   //# Strict :: Type -> Type
   //.
-  //. Constructor for strict record types. For example:
-  //. `$.Strict($.Record($.Any, {name: $.String}))`, is the type comprising
-  //. every object with a `name :: String` property, without any other
-  //. properties.
+  //. Constructor for strict record types.
+  //. `$.Strict($.Record($.Any, {name: $.String}))`, for example, is the type
+  //. comprising every object with exactly one field, `name`, of type `String`.
   function Strict(t) {
     function test(x) {
       return Object.keys(x).length === t.keys.length;
@@ -1788,9 +1787,9 @@
   //. ```
   //.
   //. The `p2` value is a member of `Point3D` as well as `Point`, making it a
-  //. valid argument to `dist`. By default, record types permit the presence
-  //. of additional fields. As a result, p2 is a member of Point as well as
-  //. Point3D.
+  //. valid argument to `dist`. By default, record types permit the presence of
+  //. additional fields. As a result, `p2` is a member of `Point` as well as
+  //. `Point3D`.
   //.
   //. One could use the [`Strict`][] constructor to define record types which
   //. do not permit additional fields:

From f1da1c4b640dc4782984a3825de080a1d06a23d1 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Wed, 5 Jul 2017 17:51:22 +0200
Subject: [PATCH 18/20] Take all enumerable properties into account for strict
 record types

---
 index.js | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/index.js b/index.js
index 37397cc..8a9bf45 100644
--- a/index.js
+++ b/index.js
@@ -834,7 +834,9 @@
   //. comprising every object with exactly one field, `name`, of type `String`.
   function Strict(t) {
     function test(x) {
-      return Object.keys(x).length === t.keys.length;
+      var len = 0, o = Object(x);
+      for (var k in o) len += 1; // eslint-disable-line no-unused-vars
+      return t.keys.length === len;
     }
 
     return NullaryType('sanctuary-def/Strict',

From e08290ca12b53ca0631b6961f45ac32cc7e09831 Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Mon, 10 Jul 2017 10:51:20 +0200
Subject: [PATCH 19/20] Let record and strict types acknowledge all enumerable
 properties

---
 index.js      | 30 ++++++++++++++++--------------
 test/index.js | 14 ++++++++++----
 2 files changed, 26 insertions(+), 18 deletions(-)

diff --git a/index.js b/index.js
index 8a9bf45..694a8c6 100644
--- a/index.js
+++ b/index.js
@@ -260,6 +260,13 @@
     };
   }
 
+  //  keys :: Any -> Array
+  function keys(x) {
+    var props = [], o = Object(x);
+    for (var prop in o) props.push(prop);
+    return props;
+  }
+
   //  last :: Array a -> a
   function last(xs) { return xs[xs.length - 1]; }
 
@@ -833,16 +840,12 @@
   //. `$.Strict($.Record($.Any, {name: $.String}))`, for example, is the type
   //. comprising every object with exactly one field, `name`, of type `String`.
   function Strict(t) {
-    function test(x) {
-      var len = 0, o = Object(x);
-      for (var k in o) len += 1; // eslint-disable-line no-unused-vars
-      return t.keys.length === len;
-    }
-
     return NullaryType('sanctuary-def/Strict',
                        functionUrl('Strict'),
                        t,
-                       test);
+                       function test(x) {
+                         return t.keys.length === keys(x).length;
+                       });
   }
 
   //# StrMap :: Type -> Type
@@ -1813,7 +1816,7 @@
   //. // => Left({propPath: [], value: {x: 1, y: 2, z: 3, color: 'red'}})
   //. ```
   function RecordType(parent, fields) {
-    var keys = Object.keys(fields).sort();
+    var props = keys(fields).sort();
 
     function format(outer, inner) {
       return wrap(outer('{'))(outer(' }'))(Z.map(function(k) {
@@ -1822,21 +1825,20 @@
                unless(t.type === RECORD || isEmpty(t.keys),
                       stripOutermostParens,
                       inner(k)(String(t)));
-      }, keys).join(outer(',')));
+      }, props).join(outer(',')));
     }
 
     function test(x) {
-      if (x == null) return false;
-      var o = Object(x);
-      return keys.every(function(k) { return k in o; });
+      var actualProps = keys(x);
+      return props.every(function(k) { return actualProps.indexOf(k) >= 0; });
     }
 
     var $types = {};
-    keys.forEach(function(k) {
+    props.forEach(function(k) {
       $types[k] = {extractor: function(x) { return [x[k]]; }, type: fields[k]};
     });
 
-    return new _Type(RECORD, '', '', format, parent, test, keys, $types);
+    return new _Type(RECORD, '', '', format, parent, test, props, $types);
   }
 
   var CheckedRecordType =
diff --git a/test/index.js b/test/index.js
index 18ed6d5..8f0d3bb 100644
--- a/test/index.js
+++ b/test/index.js
@@ -1230,6 +1230,7 @@ describe('def', function() {
     eq(dist({x: 0, y: 0}, {x: 0, y: 0, z: 0}), 0);
     eq(dist({x: 1, y: 1}, {x: 4, y: 5}), 5);
     eq(dist({x: 1, y: 1}, {x: 4, y: 5, z: 6}), 5);
+    eq(dist(Object.assign(Object.create({x: 1}), {y: 1}), {x: 4, y: 5}), 5);
 
     eq(length({start: {x: 1, y: 1}, end: {x: 4, y: 5}}), 5);
     eq(length({start: {x: 1, y: 1}, end: {x: 4, y: 5, z: 6}}), 5);
@@ -1365,11 +1366,16 @@ describe('def', function() {
     //  StrictPoint :: Type
     var StrictPoint = $.Strict(Point);
 
-    //  p :: Point
-    var p = {x: 1, y: 2, z: 3};
+    //  p1 :: Point
+    var p1 = {x: 1, y: 2, z: 3};
 
-    eq($.test([], Point, p), true);
-    eq($.test([], StrictPoint, p), false);
+    //  p2 :: Point, StrictPoint
+    var p2 = Object.assign(Object.create({x: 1}), {y: 2});
+
+    eq($.test([], Point, p1), true);
+    eq($.test([], StrictPoint, p1), false);
+    eq($.test([], Point, p2), true);
+    eq($.test([], StrictPoint, p2), true);
 
   });
 

From 7b57bc0a2bb974763b81833a1bce2554c0da2cfd Mon Sep 17 00:00:00 2001
From: Aldwin Vlasblom <aldwin.vlasblom@gmail.com>
Date: Mon, 10 Jul 2017 13:02:01 +0200
Subject: [PATCH 20/20] WIP: Level Strict and NonEmpty in terms of approach

---
 index.js | 27 ++++++++++++---------------
 1 file changed, 12 insertions(+), 15 deletions(-)

diff --git a/index.js b/index.js
index 694a8c6..d97e49e 100644
--- a/index.js
+++ b/index.js
@@ -797,17 +797,16 @@
   //. the type comprising every [`String`][] value except `''`.
   //.
   //. The given type must satisfy the [Monoid][] and [Setoid][] specifications.
-  var NonEmpty = UnaryType(
-    'sanctuary-def/NonEmpty',
-    functionUrl('NonEmpty'),
-    Any,
-    function(x) {
+  function NonEmpty(parent) {
+    function test(x) {
       return Z.Monoid.test(x) &&
              Z.Setoid.test(x) &&
              !Z.equals(x, Z.empty(x.constructor));
-    },
-    function(monoid) { return [monoid]; }
-  );
+    }
+    function extract(monoid) { return [monoid]; }
+    var t = UnaryTypeWithUrl('sanctuary-def/NonEmpty', parent, test, extract);
+    return t(parent);
+  }
 
   //# Nullable :: Type -> Type
   //.
@@ -839,13 +838,11 @@
   //. Constructor for strict record types.
   //. `$.Strict($.Record($.Any, {name: $.String}))`, for example, is the type
   //. comprising every object with exactly one field, `name`, of type `String`.
-  function Strict(t) {
-    return NullaryType('sanctuary-def/Strict',
-                       functionUrl('Strict'),
-                       t,
-                       function test(x) {
-                         return t.keys.length === keys(x).length;
-                       });
+  function Strict(parent) {
+    function test(x) { return parent.keys.length === keys(x).length; }
+    function extract(record) { return [record]; }
+    var t = UnaryTypeWithUrl('sanctuary-def/Strict', parent, test, extract);
+    return t(parent);
   }
 
   //# StrMap :: Type -> Type