diff --git a/src/schema/TODO.md b/src/schema/TODO.md
index 5c1bf19..6db1a74 100644
--- a/src/schema/TODO.md
+++ b/src/schema/TODO.md
@@ -1,5 +1,7 @@
 # nulib\schema
 
+* tenir compte de la valeur par défaut, qui *doit* être du bon type
+* type vaut soit une instance de IType, soit une tableau de types
 * dans la définition, `[type]` est remplacé par l'instance de IType lors de sa
   résolution? --> NON, sauf si c'est un type union
 * newInput dans Schema
diff --git a/src/schema/_scalar/ScalarSchema.php b/src/schema/_scalar/ScalarSchema.php
index 2aeeca7..4a0ab60 100644
--- a/src/schema/_scalar/ScalarSchema.php
+++ b/src/schema/_scalar/ScalarSchema.php
@@ -6,6 +6,7 @@ use nulib\ref\schema\ref_schema;
 use nulib\ref\schema\ref_types;
 use nur\sery\wip\schema\Schema;
 use nur\sery\wip\schema\SchemaException;
+use nur\sery\wip\schema\types;
 use nur\sery\wip\schema\types\tarray;
 use nur\sery\wip\schema\types\tbool;
 use nur\sery\wip\schema\types\tcallable;
@@ -103,7 +104,7 @@ class ScalarSchema extends Schema {
     # type
     $types = [];
     $deftype = $definition["type"];
-    $nullable = $definition["nullable"];
+    $nullable = $definition["nullable"] ?? false;
     if ($deftype === null) {
       $types[] = null;
       $nullable = true;
@@ -164,6 +165,20 @@ class ScalarSchema extends Schema {
     tarray::ensure_narray($definition["messages"]);
     tcallable::ensure_ncallable($definition["formatter_func"]);
     tbool::ensure_nbool($definition["composite"]);
+
+    # s'il n'y a qu'une seul type, l'instancier tout de suite
+    if (count($types) == 1 && $types[0] !== null) {
+      foreach ($types as $key => $name) {
+        if ($key === 0) {
+          $params = null;
+        } else {
+          $params = $name;
+          $name = $key;
+        }
+        $definition["type"] = [types::get($nullable, $name, $params, $definition)];
+      }
+    }
+
     return $definition;
   }
 
diff --git a/src/schema/_scalar/ScalarWrapper.php b/src/schema/_scalar/ScalarWrapper.php
index 13c3d9f..2427e8b 100644
--- a/src/schema/_scalar/ScalarWrapper.php
+++ b/src/schema/_scalar/ScalarWrapper.php
@@ -71,57 +71,65 @@ class ScalarWrapper extends Wrapper {
 
   /** analyser la valeur et résoudre son type */
   function _analyze(AnalyzerContext $context): int {
-    $schema = $this->schema;
-    $input = $this->input;
-    $destKey = $this->destKey;
-    $result = $this->result;
+    /** @var ScalarSchema $schema */
+    $schema = $context->schema;
+    $input = $context->input;
+    $destKey = $context->destKey;
+    /** @var ScalarResult $result */
+    $result = $context->result;
 
     if (!$input->isPresent($destKey)) return $result->setMissing($schema);
 
-    $haveType = false;
-    $types = [];
-    $type = $firstType = null;
-    $haveValue = false;
-    $value = null;
-    # d'abord chercher un type pour lequel c'est une valeur normalisée
-    $index = 0;
-    foreach ($schema->type as $key => $name) {
-      if ($key === $index) {
-        $index++;
-        $params = null;
-      } else {
-        $params = $name;
-        $name = $key;
-      }
-      $type = types::get($name, $params, $this->schema->getDefinition());
-      if ($firstType === null) $firstType = $type;
-      $types[] = $type;
-      if ($type->isAvailable($input, $destKey)) {
-        if (!$haveValue) {
-          $value = $input->get($destKey);
-          $haveValue = true;
+    $schemaTypes = $schema->type;
+    if (count($schemaTypes) == 1 && $schemaTypes[0] instanceof IType) {
+      $type = $schemaTypes[0];
+    } else {
+      # type union
+      $haveType = false;
+      $types = [];
+      $type = $firstType = null;
+      $value = null;
+      # d'abord chercher un type pour lequel c'est une valeur normalisée
+      $index = 0;
+      $haveValue = false;
+      foreach ($schemaTypes as $key => $name) {
+        if ($key === $index) {
+          $index++;
+          $params = null;
+        } else {
+          $params = $name;
+          $name = $key;
         }
-        if ($type->isValid($value, $normalized) && $normalized) {
-          $haveType = true;
-          $this->type = $type;
-          break;
+        $type = types::get($schema->nullable, $name, $params, $this->schema->getDefinition());
+        if ($firstType === null) $firstType = $type;
+        $types[] = $type;
+        if ($type->isAvailable($input, $destKey)) {
+          if (!$haveValue) {
+            $value = $input->get($destKey);
+            $haveValue = true;
+          }
+          if ($type->isValid($value, $normalized) && $normalized) {
+            $haveType = true;
+            break;
+          }
         }
       }
-    }
-    if (!$haveType) {
       # ensuite chercher un type pour lequel la valeur est valide
-      foreach ($types as $type) {
-        if ($type->isAvailable($input, $destKey) && $type->isValid($value)) {
-          $haveType = true;
-          $this->type = $type;
-          break;
+      if (!$haveType) {
+        foreach ($types as $type) {
+          if ($type->isAvailable($input, $destKey) && $type->isValid($value)) {
+            $haveType = true;
+            break;
+          }
         }
       }
+      # sinon prendre le premier type
+      if (!$haveType) {
+        $type = $firstType;
+      }
     }
+    $context->type = $this->type = $type;
 
-    # sinon prendre le premier type
-    if (!$haveType) $type = $this->type = $firstType;
-    $context->type = $type;
     if (!$type->isAvailable($input, $destKey)) return $result->setUnavailable($schema);
 
     $value = $input->get($destKey);
diff --git a/src/schema/types.php b/src/schema/types.php
index 96b703d..f02a696 100644
--- a/src/schema/types.php
+++ b/src/schema/types.php
@@ -25,16 +25,16 @@ class types {
     return self::$registry;
   }
 
-  static function get(string $name, ?array $params=null, ?array $definition=null): IType {
-    return self::registry()->get($name, $params, $definition);
+  static function get(bool $nullable, string $name, ?array $params=null, ?array $definition=null): IType {
+    return self::registry()->get($nullable, $name, $params, $definition);
   }
 
-  static function rawstring(): trawstring { return self::get("rawstring"); }
-  static function string(): tstring { return self::get("string"); }
-  static function text(): ttext { return self::get("text"); }
-  static function bool(): tbool { return self::get("bool"); }
-  static function int(): tint { return self::get("int"); }
-  static function float(): tfloat { return self::get("float"); }
-  static function array(): tarray { return self::get("array"); }
-  static function callable(): tcallable { return self::get("callable"); }
+  static function rawstring(bool $nullable=true): trawstring { return self::get($nullable, "rawstring"); }
+  static function string(bool $nullable=true): tstring { return self::get($nullable, "string"); }
+  static function text(bool $nullable=true): ttext { return self::get($nullable, "text"); }
+  static function bool(bool $nullable=true): tbool { return self::get($nullable, "bool"); }
+  static function int(bool $nullable=true): tint { return self::get($nullable, "int"); }
+  static function float(bool $nullable=true): tfloat { return self::get($nullable, "float"); }
+  static function array(bool $nullable=true): tarray { return self::get($nullable, "array"); }
+  static function callable(bool $nullable=true): tcallable { return self::get($nullable, "callable"); }
 }
diff --git a/src/schema/types/IType.php b/src/schema/types/IType.php
index f0e564f..2518248 100644
--- a/src/schema/types/IType.php
+++ b/src/schema/types/IType.php
@@ -10,6 +10,54 @@ use nur\sery\wip\schema\Schema;
  * Interface IType: un type de données
  */
 interface IType {
+  /**
+   * @return string la classe des objets gérés par ce format: le type attendu
+   * par {@link format()} et le type retourné par {@link verifix()}
+   *
+   * Les valeurs "mixed", "bool", "float", "int", "string" et "array" peuvent
+   * aussi être retournées, bien qu'elles ne soient pas à proprement parler des
+   * classes.
+   *
+   * La valeur "mixed" signifie qu'il peut s'agir de n'importe quelle classe
+   * et/ou que la valeur ne peut pas être déterminée à l'avance.
+   */
+  function getClass(): string;
+
+  /**
+   * comme {@link getClass()} mais peut être utilisé directement comme type dans
+   * une déclaration PHP. notamment, si le type est nullable et que
+   * $allowNullable==true, il y a "?" devant le nom.
+   *
+   * Par exemple:
+   * - pour un type chaine nullable, {@link getClass()} retournerait "string"
+   * alors que cette méthode retournerait "?string".
+   * - pour un type mixed, {@link getClass()} retournerait "mixed" alors que
+   * cette méthode retournerait null
+   */
+  function getPhpType(bool $allowNullable=true): ?string;
+
+  /**
+   * indiquer si c'est le type d'une valeur qui ne peut prendre que 2 états: une
+   * "vraie" et une "fausse"
+   */
+  function is2States(): bool;
+
+  /**
+   * Si {@link is2States()} est vrai, retourner les deux valeurs [faux, vrai]
+   */
+  function get2States(): array;
+
+  /**
+   * indiquer si c'est le type d'une valeur qui ne peut prendre que 3 états: une
+   * "vraie", une "fausse", et une "indéterminée"
+   */
+  function is3States(): bool;
+
+  /**
+   * Si {@link is3States()} est vrai, retourner les 3 valeurs [faux, vrai, undef]
+   */
+  function get3States(): array;
+
   /** la donnée $input($destKey) est-elle disponible? */
   function isAvailable(Input $input, $destKey): bool;
 
@@ -54,4 +102,29 @@ interface IType {
    * garantie d'être du bon type
    */
   function format($value, $format=null): string;
+
+  #############################################################################
+
+  /** @return string le nom d'un getter pour une valeur de ce type */
+  function getGetterName(string $name): string;
+
+  /** @return string le nom d'un setter pour une valeur de ce type */
+  function getSetterName(string $name): string;
+
+  /** @return string le nom d'un deleter pour une valeur de ce type */
+  function getDeleterName(string $name): string;
+
+  /**
+   * @return string le nom d'une constante de classe pour une valeur de ce type
+   */
+  function getClassConstName(string $name): string;
+
+  /**
+   * @return string le nom d'une propriété d'une classe pour une valeur de ce
+   * type
+   */
+  function getObjectPropertyName(string $name): string;
+
+  /** @return string le nom d'une clé d'un tableau pour une valeur de ce type */
+  function getArrayKeyName(string $name): string;
 }
diff --git a/src/schema/types/Registry.php b/src/schema/types/Registry.php
index 2879f8b..ac64560 100644
--- a/src/schema/types/Registry.php
+++ b/src/schema/types/Registry.php
@@ -28,14 +28,15 @@ class Registry {
   /** @var IType[] */
   protected $types;
 
-  function get(string $name, ?array $params=null, ?array $definition=null): IType {
+  function get(bool $nullable, string $name, ?array $params=null, ?array $definition=null): IType {
     $class = self::TYPES[$name];
     $params = cl::merge($class::get_params_from_definition($definition), $params);
     if ($params !== null) {
-      return func::with([$class, false, $params])->invoke();
+      return func::with([$class, false, $nullable, $params])->invoke();
     }
+    if ($nullable) $name = "?$name";
     $type = cl::get($this->types, $name);
-    if ($type === null) $type = $this->types[$name] = new $class();
+    if ($type === null) $type = $this->types[$name] = new $class($nullable);
     return $type;
   }
 }
diff --git a/src/schema/types/_tsimple.php b/src/schema/types/_tsimple.php
index 91ded5d..957f0aa 100644
--- a/src/schema/types/_tsimple.php
+++ b/src/schema/types/_tsimple.php
@@ -1,19 +1,44 @@
 <?php
 namespace nur\sery\wip\schema\types;
 
+use nulib\StateException;
+use nur\prop;
 use nur\sery\wip\schema\input\Input;
+use nur\str;
 
 abstract class _tsimple implements IType {
   static function get_params_from_definition(?array $definition): ?array {
     return null;
   }
 
-  function __construct(?array $params=null) {
+  function __construct(bool $nullable, ?array $params=null) {
+    $this->nullable = $nullable;
     $this->params = $params;
   }
 
+  protected bool $nullable;
+
   protected ?array $params;
 
+  function getPhpType(bool $allowNullable=true): ?string {
+    $phpType = $this->getClass();
+    if ($phpType === "mixed") return null;
+    if ($this->nullable && $allowNullable) $phpType = "?$phpType";
+    return $phpType;
+  }
+
+  function get2States(): array {
+    throw StateException::not_implemented();
+  }
+
+  function is3States(): bool {
+    return false;
+  }
+
+  function get3States(): array {
+    throw StateException::not_implemented();
+  }
+
   function isAvailable(Input $input, $destKey): bool {
     return $input->isAvailable($destKey) && $input->get($destKey) !== false;
   }
@@ -25,4 +50,34 @@ abstract class _tsimple implements IType {
   function extract(string $value): string {
     return $value;
   }
+
+  function is2States(): bool {
+    return false;
+  }
+
+  #############################################################################
+
+  function getGetterName(string $name): string {
+    return prop::get_getter_name($name);
+  }
+
+  function getSetterName(string $name): string {
+    return prop::get_setter_name($name);
+  }
+
+  function getDeleterName(string $name): string {
+    return prop::get_deletter_name($name);
+  }
+
+  function getClassConstName(string $name): string {
+    return strtoupper($name);
+  }
+
+  function getObjectPropertyName(string $name): string {
+    return str::us2camel($name);
+  }
+
+  function getArrayKeyName(string $name): string {
+    return $name;
+  }
 }
diff --git a/src/schema/types/_tunion.php b/src/schema/types/_tunion.php
new file mode 100644
index 0000000..113e02d
--- /dev/null
+++ b/src/schema/types/_tunion.php
@@ -0,0 +1,10 @@
+<?php
+namespace nur\sery\wip\schema\types;
+
+abstract class _tunion extends _tsimple {
+  function getPhpType(bool $allowNullable=true): ?string {
+    # assumer mixed pour le moment
+    #XXX à terme, lister les types de l'union
+    return null;
+  }
+}
diff --git a/src/schema/types/tarray.php b/src/schema/types/tarray.php
index 6c39d5b..abf7092 100644
--- a/src/schema/types/tarray.php
+++ b/src/schema/types/tarray.php
@@ -29,6 +29,10 @@ class tarray extends _tstring {
     if ($array !== null) self::ensure_array($array);
   }
 
+  function getClass(): string {
+    return "array";
+  }
+
   function isValid($value, ?bool &$normalized=null): bool {
     $normalized = is_array($value);
     return is_scalar($value) || is_array($value);
diff --git a/src/schema/types/tbool.php b/src/schema/types/tbool.php
index 8e85a01..891fe21 100644
--- a/src/schema/types/tbool.php
+++ b/src/schema/types/tbool.php
@@ -3,6 +3,7 @@ namespace nur\sery\wip\schema\types;
 
 use nulib\cl;
 use nulib\ValueException;
+use nur\prop;
 use nur\sery\wip\schema\_scalar\ScalarResult;
 use nur\sery\wip\schema\_scalar\ScalarSchema;
 use nur\sery\wip\schema\input\Input;
@@ -51,6 +52,26 @@ class tbool extends _tformatable {
     if ($bool !== null) self::ensure_bool($bool);
   }
 
+  function getClass(): string {
+    return "bool";
+  }
+
+  function is2States(): bool {
+    return !$this->nullable;
+  }
+
+  function get2States(): array {
+    return [false, true];
+  }
+
+  function is3States(): bool {
+    return $this->nullable;
+  }
+
+  function get3States(): array {
+    return [false, true, null];
+  }
+
   function isAvailable(Input $input, $destKey): bool {
     return $input->isAvailable($destKey);
   }
@@ -124,4 +145,8 @@ class tbool extends _tformatable {
     }
     return $value? $format[0]: $format[1];
   }
+
+  function getGetterName(string $name): string {
+    return prop::get_getter_name($name, !$this->nullable);
+  }
 }
diff --git a/src/schema/types/tcallable.php b/src/schema/types/tcallable.php
index f5ec37c..a36032c 100644
--- a/src/schema/types/tcallable.php
+++ b/src/schema/types/tcallable.php
@@ -18,6 +18,10 @@ class tcallable extends _tsimple {
     if ($callable !== null) self::ensure_callable($callable);
   }
 
+  function getClass(): string {
+    return func::class;
+  }
+
   function isValid($value, ?bool &$normalized=null): bool {
     $normalized = is_callable($value);
     return func::check($value);
diff --git a/src/schema/types/tcontent.php b/src/schema/types/tcontent.php
index 0a950ca..aff7d17 100644
--- a/src/schema/types/tcontent.php
+++ b/src/schema/types/tcontent.php
@@ -7,7 +7,7 @@ use nur\sery\wip\schema\_scalar\ScalarSchema;
 use nur\sery\wip\schema\Result;
 use nur\sery\wip\schema\Schema;
 
-abstract class tcontent extends _tsimple {
+abstract class tcontent extends _tunion {
   static function ensure_content(&$content): void {
     if ($content === null || $content === false) $content = [];
     elseif (!is_string($content) && !is_array($content)) $content = strval($content);
@@ -17,6 +17,10 @@ abstract class tcontent extends _tsimple {
     if ($content !== null) self::ensure_content($content);
   }
 
+  function getClass(): string {
+    return "string|array";
+  }
+
   function isValid($value, ?bool &$normalized=null): bool {
     $normalized = is_string($value) || is_array($value);
     return is_scalar($value) || is_array($value);
diff --git a/src/schema/types/tfloat.php b/src/schema/types/tfloat.php
index 47f3956..486187e 100644
--- a/src/schema/types/tfloat.php
+++ b/src/schema/types/tfloat.php
@@ -16,6 +16,10 @@ class tfloat extends _tformatable {
     if ($float !== null) self::ensure_float($float);
   }
 
+  function getClass(): string {
+    return "float";
+  }
+
   function isValid($value, ?bool &$normalized=null): bool {
     $normalized = is_float($value);
     return is_scalar($value);
diff --git a/src/schema/types/tint.php b/src/schema/types/tint.php
index 51dbeec..33ae3ac 100644
--- a/src/schema/types/tint.php
+++ b/src/schema/types/tint.php
@@ -17,7 +17,11 @@ class tint extends _tformatable {
   }
 
   //const INT_PATTERN = '/^[-+]?[0-9]+(?:\.[0-9]*)?$/';
-  
+
+  function getClass(): string {
+    return "int";
+  }
+
   function isValid($value, ?bool &$normalized=null): bool {
     $normalized = is_int($value);
     return is_scalar($value);
diff --git a/src/schema/types/tkey.php b/src/schema/types/tkey.php
index ff10afb..102beee 100644
--- a/src/schema/types/tkey.php
+++ b/src/schema/types/tkey.php
@@ -6,7 +6,7 @@ use nur\sery\wip\schema\_scalar\ScalarSchema;
 use nur\sery\wip\schema\Result;
 use nur\sery\wip\schema\Schema;
 
-class tkey extends _tsimple {
+class tkey extends _tunion {
   static function ensure_key(&$key): void {
     if ($key === null) $key = "";
     elseif ($key === false) $key = 0;
@@ -17,6 +17,10 @@ class tkey extends _tsimple {
     if ($key !== null) self::ensure_key($key);
   }
 
+  function getClass(): string {
+    return "string|int";
+  }
+
   function isValid($value, ?bool &$normalized=null): bool {
     $normalized = is_string($value) || is_int($value);
     return is_scalar($value);
diff --git a/src/schema/types/tpkey.php b/src/schema/types/tpkey.php
index 3766b04..1606087 100644
--- a/src/schema/types/tpkey.php
+++ b/src/schema/types/tpkey.php
@@ -6,7 +6,7 @@ use nur\sery\wip\schema\_scalar\ScalarSchema;
 use nur\sery\wip\schema\Result;
 use nur\sery\wip\schema\Schema;
 
-class tpkey extends _tsimple {
+class tpkey extends _tunion {
   static function ensure_pkey(&$pkey): void {
     if ($pkey === null) $pkey = "";
     elseif ($pkey === false) $pkey = 0;
@@ -22,6 +22,10 @@ class tpkey extends _tsimple {
     if ($pkey !== null) self::ensure_pkey($pkey);
   }
 
+  function getClass(): string {
+    return "string|int|array";
+  }
+
   function isValid($value, ?bool &$normalized=null): bool {
     $normalized = is_string($value) || is_int($value) || is_array($value);
     return is_scalar($value) || is_array($value);
diff --git a/src/schema/types/trawstring.php b/src/schema/types/trawstring.php
index f36bdd1..2b60bc0 100644
--- a/src/schema/types/trawstring.php
+++ b/src/schema/types/trawstring.php
@@ -18,6 +18,10 @@ class trawstring extends _tstring {
     if ($string !== null) self::ensure_string($string);
   }
 
+  function getClass(): string {
+    return "string";
+  }
+
   function isNull($value): bool {
     return $value === null;
   }