WIP Add fix

Author: nicolasstucki

tests/run-macros/quote-matcher-symantics-3/quoted_1.scala

@@ -46,6 +46,11 @@ object Macros {
         '{ $sym.lam((x: R[Int]) => ${delegate for Env = envWith(x0, 'x) given env; lift(body)}).asInstanceOf[R[T]] }
       case '{ ($x0: Boolean) => $body: Any } =>
         '{ $sym.lam((x: R[Boolean]) => ${delegate for Env = envWith(x0, 'x) given env; lift(body)}).asInstanceOf[R[T]] }
+      case '{ ($x0: Int => Int) => $body: Any } =>
+        '{ $sym.lam((x: R[Int => Int]) => ${delegate for Env = envWith(x0, 'x) given env; lift(body)}).asInstanceOf[R[T]] }
+
+      case '{ Symantics.fix[$t, $u]($f) } =>
+        '{ $sym.fix[$t, $u]((x: R[$t => $u]) => $sym.app(${lift(f)}, x)).asInstanceOf[R[T]] }
 
       case Bind(FromEnv(expr)) => expr.asInstanceOf[Expr[R[T]]]
 
@@ -67,13 +72,14 @@ trait Symantics {
   def bool(x: Boolean): Repr[Boolean]
   def lam[A, B](f: Repr[A] => Repr[B]): Repr[A => B]
   def app[A, B](f: Repr[A => B], arg: Repr[A]): Repr[B]
-    def fix[A](f: Repr[A] => Repr[A]): Repr[A]
+//  def fix[A]: (Repr[A] => Repr[A]) => Repr[A]
+  def fix[A, B]: (Repr[A => B] => Repr[A => B]) => Repr[A => B]
   def add(x: Repr[Int], y: Repr[Int]): Repr[Int]
   def mult(x: Repr[Int], y: Repr[Int]): Repr[Int]
   def leq(x: Repr[Int], y: Repr[Int]): Repr[Boolean]
-  def ifThenElse[A](cond: Repr[Boolean], thenp: Repr[A], elsep: Repr[A]): Repr[A]
+  def ifThenElse[A](cond: Repr[Boolean], thenp: => Repr[A], elsep: => Repr[A]): Repr[A]
 }
 
 object Symantics {
-  def fix[A](f: A => A): A = throw new Exception("Must be used inside of `lift`")
+  def fix[A, B](f: (A => B) => (A => B)): A => B = throw new Exception("Must be used inside of `lift`")
 }

tests/run-macros/quote-matcher-symantics-3/quoted_2.scala

@@ -34,6 +34,10 @@ object Test {
 //    println(lift(new Show)(((f: Int => Int) => f(4))((x: Int) => x)))
 //    println(lift(new Eval)(((f: Int => Int) => f(4))((x: Int) => x)))
 
+    println(lift(new Show)(((x: Int) => Symantics.fix((self: Int => Int) => ((n: Int) => if (n <= 0) 1 else x * self(n + (-1)) )))(3)(25)))
+    println(lift(new Eval)(((x: Int) => Symantics.fix((self: Int => Int) => ((n: Int) => if (n <= 0) 1 else x * self(n + (-1)) )))(3)(5)))
+
+
 
   }
 
@@ -49,11 +53,11 @@ class Show extends Symantics {
     s"(arg$i => ${f(s"arg$i")})"
   }
   def app[A, B](f: Repr[A => B], arg: Repr[A]): Repr[B] = s"$f($arg)"
-  def fix[A](f: Repr[A] => Repr[A]): Repr[A] = ???
+  def fix[A, B]: (Repr[A => B] => Repr[A => B]) => Repr[A => B] = f => f("FIX")
   def add(x: Repr[Int], y: Repr[Int]): Repr[Int] = s"$x + $y"
   def mult(x: Repr[Int], y: Repr[Int]): Repr[Int] = s"($x) * ($y)"
   def leq(x: Repr[Int], y: Repr[Int]): Repr[Boolean] = s"$x <= $y"
-  def ifThenElse[A](cond: Repr[Boolean], thenp: Repr[A], elsep: Repr[A]): Repr[A] = s"if ($cond) $thenp else $elsep"
+  def ifThenElse[A](cond: Repr[Boolean], thenp: => Repr[A], elsep: => Repr[A]): Repr[A] = s"if ($cond) $thenp else $elsep"
 
   private[this] var idx: Int = 0
   private def nextIndex(): Int = {
@@ -68,9 +72,13 @@ class Eval extends Symantics {
   def bool(x: Boolean): Repr[Boolean] = x
   def lam[A, B](f: Repr[A] => Repr[B]): Repr[A => B] = f
   def app[A, B](f: Repr[A => B], arg: Repr[A]): Repr[B] = f(arg)
-  def fix[A](f: Repr[A] => Repr[A]): Repr[A] = ???
+  def fix[A, B]: (Repr[A => B] => Repr[A => B]) => Repr[A => B] = f => {
+    def self(n: A): B = f(self)(n)
+    self
+  }
   def add(x: Repr[Int], y: Repr[Int]): Repr[Int] = x + y
   def mult(x: Repr[Int], y: Repr[Int]): Repr[Int] = x * y
   def leq(x: Repr[Int], y: Repr[Int]): Repr[Boolean] = x <= y
-  def ifThenElse[A](cond: Repr[Boolean], thenp: Repr[A], elsep: Repr[A]): Repr[A] = if (cond) thenp else thenp
+  def ifThenElse[A](cond: Repr[Boolean], thenp: => Repr[A], elsep: => Repr[A]): Repr[A] = if (cond) thenp else thenp
+
 }