structural ⍢, (f⍤g)A

src/APL/Indexer.java

@@ -37,6 +37,10 @@ public Indexer(int[] sh, int IO) {
     }
   }
 
+  public int pos() {
+    return ci-1;
+  }
+
   public boolean hasNext() {
     return ci < ia;
   }
@@ -110,7 +114,7 @@ public static double[][] inds(Obj ov) { // ⎕VI←1 indexes to double[][]
   }
   private static final int[] i1 = new int[1];
   private static final int[] i0 = new int[0];
-  public static final int[] indsh(Obj ov) { // must be called after inds(ov)
+  public static int[] indsh(Obj ov) { // must be called after inds(ov)
     Value v = (Value) ov;
     if (v instanceof Primitive) return i1;
     if (v.ia == 0) return i0;
@@ -119,7 +123,6 @@ public static final int[] indsh(Obj ov) { // must be called after inds(ov)
     return fst.shape;
   }
 
-  @SuppressWarnings("NullableProblems") // not using @NotNull for non-intelliJ compilers
   public Iterator<int[]> iterator() {
     return this;
   }

src/APL/types/Fun.java

@@ -34,6 +34,12 @@ public Obj callInvA(Value a, Value w) {
     throw new DomainError(this+" doesn't support dyadic inverting of ⍺", this, w);
   }
 
+  public boolean strInv() { return false; } // can assume that this Fun has been called before of what's to be inverted
+  public boolean strInvW() { return false; }
+
+  public Value strInv(Value w, Value origW) { throw new IllegalStateException("calling unsupported strInv(w, origW)"); }
+  public Value strInvW(Value a, Value w, Value origW) { throw new IllegalStateException("calling unsupported strInvW(a, w, origW)"); }
+
   public interface NumMV {
     Value call(Num w);
     default boolean retNum() {

src/APL/types/Num.java

@@ -220,7 +220,7 @@ public Value safePrototype() {
   }
 
   @Override
-  public Value[] values() {
+  public Value[] valuesCopy() {
     return new Value[]{this};
   }
 

src/APL/types/Value.java

@@ -24,7 +24,7 @@ public abstract class Value extends Obj implements Iterable<Value> {
     this.rank = rank;
   }
   public int[] asIntVec() { // succeeds on rank ≤ 1
-    RankError.must(rank<=1, "using rank "+rank+" array as vector");
+    RankError.must(rank<=1, "using rank "+rank+" array as an integer vector");
     return asIntArr();
   }
   public abstract int[] asIntArr();
@@ -118,6 +118,9 @@ public String oneliner() {
 
 
   public Value[] values() {
+    return valuesCopy();
+  }
+  public Value[] valuesCopy() {
     Value[] vs = new Value[ia];
     for (int i = 0; i < ia; i++) vs[i] = get(i);
     return vs;

src/APL/types/arrs/DoubleArr.java

@@ -128,7 +128,7 @@ public Value squeeze() {
   }
 
   @Override
-  public Value[] values() {
+  public Value[] valuesCopy() {
     Value[] vs = new Value[ia];
     for (int i = 0; i < ia; i++) vs[i] = new Num(arr[i]);
     return vs;

src/APL/types/arrs/EmptyArr.java

@@ -52,8 +52,8 @@ public Value ofShape(int[] sh) {
 
   private static final Value[] NO_VALUES = new Value[0];
   @Override
-  public Value[] values() {
-    return NO_VALUES;
+  public Value[] valuesCopy() {
+    return NO_VALUES; // safe, copy or not - doesn't matter
   }
 
   @Override

src/APL/types/arrs/HArr.java

@@ -70,10 +70,12 @@ public Value safePrototype() {
     if (ia == 0) return null;
     return arr[0].safePrototype();
   }
-  @Override
   public Value[] values() {
     return arr;
   }
+  public Value[] valuesCopy() {
+    return arr.clone();
+  }
   public Value ofShape(int[] sh) {
     assert ia == Arr.prod(sh);
     return new HArr(arr, sh);

src/APL/types/arrs/Rank0Arr.java

@@ -48,7 +48,7 @@ public Value ofShape(int[] sh) {
   }
 
   @Override
-  public Value[] values() {
+  public Value[] valuesCopy() {
     return new Value[]{item};
   }
 }

src/APL/types/arrs/Shape1Arr.java

@@ -48,7 +48,7 @@ public Value ofShape(int[] sh) {
   }
 
   @Override
-  public Value[] values() {
+  public Value[] valuesCopy() {
     return new Value[]{item};
   }
 

src/APL/types/arrs/SingleItemArr.java

@@ -58,7 +58,7 @@ public Value ofShape(int[] sh) {
   public boolean quickDoubleArr() {
     return item instanceof Num;
   }
-  public Value[] values() {
+  public Value[] valuesCopy() {
     Value[] vs = new Value[ia];
     for (int i = 0; i < ia; i++) vs[i] = item;
     return vs;

src/APL/types/functions/DerivedDop.java

@@ -32,4 +32,10 @@ public Obj call(Value a, Value w) {
     if (!(ww instanceof Arr) && wws.length() != 1) wws = "("+wws+")";
     return aa.toString()+op.repr()+wws;
   }
+
+  public boolean strInv() { return op.strInv(aa, ww); }
+  public boolean strInvW() { return op.strInvW(aa, ww); }
+
+  public Value strInv(Value w, Value origW) { return op.strInv(aa, ww, w, origW); }
+  public Value strInvW(Value a, Value w, Value origW) { return op.strInvW(aa, ww, a, w, origW); }
 }

src/APL/types/functions/DerivedMop.java

@@ -30,4 +30,10 @@ public Obj call(Value a, Value w) {
   @Override public String repr() {
     return aa.toString()+op.repr();
   }
+
+  public boolean strInv() { return op.strInv(aa); }
+  public boolean strInvW() { return op.strInvW(aa); }
+
+  public Value strInv(Value w, Value origW) { return op.strInv(aa, w, origW); }
+  public Value strInvW(Value a, Value w, Value origW) { return op.strInvW(aa, a, w, origW); }
 }

src/APL/types/functions/Dop.java

@@ -37,6 +37,10 @@ public Obj callInvW(Obj aa, Obj ww, Value a, Value w) {
   public Obj callInvA(Obj aa, Obj ww, Value a, Value w) {
     throw new DomainError(this+" doesn't support dyadic inverting of ⍺", this, w);
   }
+  public boolean strInv(Obj aa, Obj ww) { return false; }
+  public boolean strInvW(Obj aa, Obj ww) { return false; }
+  public Value strInv(Obj aa, Obj ww, Value w, Value origW) { throw new IllegalStateException("calling unsupported dop.strInv(w, origW)"); }
+  public Value strInvW(Obj aa, Obj ww, Value a, Value w, Value origW) { throw new IllegalStateException("calling unsupported dop.strInvW(a, w, origW)"); }
 
   public String toString() {
     return repr();

src/APL/types/functions/Mop.java

@@ -37,6 +37,10 @@ public Obj callInvW(Obj f, Value a, Value w) {
   public Obj callInvA(Obj f, Value a, Value w) {
     throw new DomainError(this+" doesn't support dyadic inverting of ⍺", this, w);
   }
+  public boolean strInv(Obj f) { return false; }
+  public boolean strInvW(Obj f) { return false; }
+  public Value strInv(Obj f, Value w, Value origW) { throw new IllegalStateException("calling unsupported mop.strInv(w, origW)"); }
+  public Value strInvW(Obj f, Value a, Value w, Value origW) { throw new IllegalStateException("calling unsupported mop.strInvW(a, w, origW)"); }
 
   public String toString() {
     return repr();

src/APL/types/functions/builtins/dops/AtBuiltin.java

@@ -14,8 +14,12 @@ public class AtBuiltin extends Dop {
   public AtBuiltin(Scope sc) {
     super(sc);
   }
-  public Obj call(Obj aa, Obj ww, Value w, DerivedDop derv) {
-    int IO = sc.IO;
+
+  public Obj at(Obj aa, Obj ww, Value w, DerivedDop derv) {
+    return at(aa, ww, w, sc.IO);
+  }
+
+  public static Value at(Obj aa, Obj ww, Value w, int IO) {
     int ia = w.ia;
     if (ww instanceof Fun) {
       Value vba = (Value) ((Fun) ww).call(w);
@@ -74,7 +78,7 @@ public Obj call(Obj aa, Obj ww, Value w, DerivedDop derv) {
           for (int i = 0; i < matchingCount; i++) {
             ra[indexes[i]] = replacement[i];
           }
-          return Arr.create(ra, w.shape);
+          return Arr.createL(ra, w.shape);
         } else {
           for (int i = 0; i < matchingCount; i++) {
             indexes[i] = Indexer.ind(w.shape, wwd, i, IO);

src/APL/types/functions/builtins/dops/DualBuiltin.java

@@ -1,5 +1,6 @@
 package APL.types.functions.builtins.dops;
 
+import APL.errors.SyntaxError;
 import APL.types.*;
 import APL.types.functions.*;
 
@@ -11,14 +12,30 @@ public class DualBuiltin extends Dop {
 
 
   public Obj call(Obj aa, Obj ww, Value w, DerivedDop derv) {
-    isFn(aa, '⍶'); isFn(ww, '⍹');
+    isFn(ww, '⍹');
     Fun under = (Fun) ww;
-    return under.callInv( (Value) ((Fun)aa).call((Value) under.call(w)));
+    Value sub = (Value) under.call(w);
+    if (under.strInv()) {
+      Value obj = aa instanceof Value? (Value) aa : (Value) ((Fun) aa).call(sub);
+      return under.strInv(obj, w);
+    }
+
+    if (!(aa instanceof Fun)) throw new SyntaxError("⍶ of computational ⍢ must be a function");
+    Value obj = (Value) ((Fun) aa).call(sub);
+    return under.callInv(obj);
   }
   public Obj callInv(Obj aa, Obj ww, Value w) {
-    isFn(aa, '⍶'); isFn(ww, '⍹');
+    isFn(ww, '⍹');
     Fun under = (Fun) ww;
-    return under.callInv( (Value) ((Fun)aa).callInv((Value) under.call(w)));
+    Value sub = (Value) under.call(w);
+    if (under.strInv()) {
+      Value obj = aa instanceof Value? (Value) aa : (Value) ((Fun) aa).callInv(sub);
+      return under.strInv(obj, w);
+    }
+
+    if (!(aa instanceof Fun)) throw new SyntaxError("⍶ of computational ⍢ must be a function");
+    Value obj = (Value) ((Fun) aa).callInv(sub);
+    return under.callInv(obj);
   }
 
   public Obj call(Obj aa, Obj ww, Value a, Value w, DerivedDop derv) {

src/APL/types/functions/builtins/dops/JotBuiltin.java

@@ -43,4 +43,19 @@ public Obj call(Obj aa, Obj ww, Value a, Value w, DerivedDop derv) {
     }
     return ((Fun)aa).call(a, (Value)((Fun)ww).call(w));
   }
+  public boolean strInv(Obj aa, Obj ww) {
+    if (!(ww instanceof Fun)) return false;
+    Fun wwf = (Fun) ww;
+    return aa instanceof Fun? ((Fun) aa).strInv() && wwf.strInv() : wwf.strInvW();
+  }
+  public Value strInv(Obj aa, Obj ww, Value w, Value origW) {
+    Fun wwf = (Fun) ww;
+    if (aa instanceof Fun) {
+      Fun aaf = (Fun) aa;
+      Value gI = aaf.strInv(w, (Value) wwf.call(origW));
+      return wwf.strInv(gI, origW);
+    } else {
+      return wwf.strInvW((Value) aa, w, origW);
+    }
+  }
 }

src/APL/types/functions/builtins/dops/JotDiaeresisBuiltin.java

@@ -1,5 +1,6 @@
 package APL.types.functions.builtins.dops;
 
+import APL.errors.SyntaxError;
 import APL.types.*;
 import APL.types.functions.*;
 
@@ -15,4 +16,14 @@ public Obj call(Obj aa, Obj ww, Value a, Value w, DerivedDop derv) {
     isFn(aa, '⍶'); isFn(ww, '⍹');
     return ((Fun) aa).call((Value) ((Fun) ww).call(a, w));
   }
-}
+
+  public Obj call(Obj aa, Obj ww, Value w, DerivedDop derv) {
+    isFn(aa, '⍶'); isFn(ww, '⍹');
+    return ((Fun) aa).call((Value) ((Fun) ww).call(w));
+  }
+
+  public Obj callInv(Obj aa, Obj ww, Value w) {
+    isFn(aa, '⍶'); isFn(ww, '⍹');
+    return ((Fun) aa).call((Value) ((Fun) ww).call(w));
+  }
+}

src/APL/types/functions/builtins/dops/RepeatBuiltin.java

@@ -102,4 +102,22 @@ public Obj callInvA(Obj aa, Obj ww, Value a, Value w) {
 
     throw new DomainError("inverting ⍺ of f⍣C is only possible when C∊¯1 1");
   }
+
+  public boolean strInv(Obj aa, Obj ww) {
+    return aa instanceof Fun && ((Fun) aa).strInv() && ww instanceof Num;
+  }
+  public Value strInv(Obj aa, Obj ww, Value w, Value origW) {
+    int n = ((Num) ww).asInt();
+    Value[] origs = new Value[n];
+    Value corig = origW;
+    for (int i = 0; i < n; i++) {
+      origs[i] = corig;
+      corig = (Value) ((Fun) aa).call(corig);
+    }
+    Value c = w;
+    for (int i = n-1; i >= 0; i--) {
+      c = ((Fun) aa).strInv(c, origs[i]);
+    }
+    return c;
+  }
 }

src/APL/types/functions/builtins/fns/CatBuiltin.java

@@ -100,4 +100,11 @@ private static void copyChunksD(boolean scalar, double[] av, double[] rv, int of
     }
   }
 
+
+
+  public boolean strInv() { return true; }
+  public Value strInv(Value w, Value origW) {
+    if (w.ia != origW.ia) throw new DomainError("⍢, expected equal amount of output & output items", this);
+    return w.ofShape(origW.shape);
+  }
 }

src/APL/types/functions/builtins/fns/DownArrowBuiltin.java

@@ -50,7 +50,7 @@ public Obj call(Value w) {
     return new HArr(res, nsh);
   }
 
-  public Obj call(Value a, Value w) { // FIXME ⍴⍴⍺ < ⍴⍴⍵
+  public Obj call(Value a, Value w) { // TODO ⍴⍺ < ⍴⍴⍵
     int IO = sc.IO;
     int[] shape = a.asIntVec();
     if (shape.length == 0) return w;
@@ -76,4 +76,14 @@ public Obj call(Value a, Value w) { // FIXME ⍴⍴⍺ < ⍴⍴⍵
     }
     return Arr.create(arr, shape);
   }
+
+  public boolean strInvW() { return true; }
+  public Value strInvW(Value a, Value w, Value origW) {
+    int[] ls = a.asIntVec();
+    int[] sh = origW.shape;
+    for (int i = 0; i < ls.length; i++) {
+      ls[i] = ls[i]>0? ls[i]-sh[i] : ls[i]+sh[i];
+    }
+    return UpArrowBuiltin.strInv(ls, w, origW);
+  }
 }

src/APL/types/functions/builtins/fns/EpsilonBuiltin.java

@@ -1,5 +1,7 @@
 package APL.types.functions.builtins.fns;
 
+import APL.Main;
+import APL.errors.DomainError;
 import APL.types.*;
 import APL.types.functions.Builtin;
 
@@ -51,4 +53,27 @@ public Obj call(Value a, Value w) {
     }
     return Arr.create(res, a.shape);
   }
+
+
+  public boolean strInv() { return true; }
+  public Value strInv(Value w, Value origW) {
+    Value[] vs = w.values();
+    Value[] res = new Value[origW.ia];
+    int e = copyIn(res, vs, origW, 0);
+    if (e != w.ia) throw new DomainError("⍢∊ expected equal amount of output & output items", this);
+    return Arr.create(res, origW.shape);
+  }
+  private int copyIn(Value[] res, Value[] vs, Value orig, int s) {
+    for (int i = 0; i < orig.ia; i++) {
+      Value origN = orig.get(i);
+      if (origN instanceof Primitive) {
+        res[i] = vs[s++];
+      } else {
+        Value[] resN = new Value[origN.ia];
+        s = copyIn(resN, vs, origN, s);
+        res[i] = Arr.create(resN, origN.shape);
+      }
+    }
+    return s;
+  }
 }