X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=code%2Flambda.js;h=955254bfc21743a880bf4338e2c6913a2d81a835;hp=7dcb53d296ceacbfdab5f21a90528a1754c67005;hb=ec3beaf6933b52a2434f08d4e93829bfbaa3d043;hpb=3233e0fee04bb48a809c020b43ba23d78c95aea3

diff --git a/code/lambda.js b/code/lambda.js
index 7dcb53d2..955254bf 100644
--- a/code/lambda.js
+++ b/code/lambda.js
@@ -1,108 +1,108 @@
 /*jslint bitwise: true,
-	eqeqeq: true,
-	immed: true,
-	newcap: true,
-	nomen: true,
-	onevar: true,
-	plusplus: true,
-	regexp: true,
-	rhino: true,
-	browser: false,
-	undef: true,
-	white: true,
-
-	evil: false,
-	regexp: false,
-	sub: true,
-	laxbreak: true,
-	onevar: false,
-	debug: true */
+    eqeqeq: true,
+    immed: true,
+    newcap: true,
+    nomen: true,
+    onevar: true,
+    plusplus: true,
+    regexp: true,
+    rhino: true,
+    browser: false,
+    undef: true,
+    white: true,
+
+    evil: false,
+    regexp: false,
+    sub: true,
+    laxbreak: true,
+    onevar: false,
+    debug: true */
 
 
 // DeBruijn terms
 // substitution and translation algorithms from Chris Hankin, An Introduction to Lambda Calculi for Comptuer Scientists
 //
 function Db_free(variable) {
-	this.variable = variable;
-	this.subst = function (m, new_term) {
-		return this;
-	};
-	this.renumber = function (m, i) {
-		return this;
-	};
-	// we assume that other will have variable iff it's a Db_free
-	this.equal = function (other) {
-		return other.variable && this.variable.equal(other.variable);
-	};
-	this.contains = this.equal;
+    this.variable = variable;
+    this.subst = function (m, new_term) {
+        return this;
+    };
+    this.renumber = function (m, i) {
+        return this;
+    };
+    // we assume that other will have variable iff it's a Db_free
+    this.equal = function (other) {
+        return other.variable && this.variable.equal(other.variable);
+    };
+    this.contains = this.equal;
 }
 
 function Db_index(i) {
-	this.index = i;
-	this.subst = function (m, new_term) {
-		if (this.index < m) {
-			return this;
-		} else if (this.index > m) {
-			return new Db_index(this.index - 1);
-		} else {
-			return new_term.renumber(this.index, 1);
-		}
-	};
-	this.renumber = function (m, i) {
-		if (this.index < i) {
-			return this;
-		} else {
-			return new Db_index(this.index + m - 1);
-		}
-	};
-	// we assume that other will have index iff it's a Db_index
-	this.equal = function (other) {
-		return this.index === other.index;
-	};
-	this.contains = this.equal;
+    this.index = i;
+    this.subst = function (m, new_term) {
+        if (this.index < m) {
+            return this;
+        } else if (this.index > m) {
+            return new Db_index(this.index - 1);
+        } else {
+            return new_term.renumber(this.index, 1);
+        }
+    };
+    this.renumber = function (m, i) {
+        if (this.index < i) {
+            return this;
+        } else {
+            return new Db_index(this.index + m - 1);
+        }
+    };
+    // we assume that other will have index iff it's a Db_index
+    this.equal = function (other) {
+        return this.index === other.index;
+    };
+    this.contains = this.equal;
 }
 
 function Db_app(left, right) {
-	this.left = left;
-	this.right = right;
-	this.subst = function (m, new_term) {
-		return new Db_app(this.left.subst(m, new_term), this.right.subst(m, new_term));
-	};
-	this.renumber = function (m, i) {
-		return new Db_app(this.left.renumber(m, i), this.right.renumber(m, i));
-	};
-	// we assume that other will have left iff it's a Db_app
-	this.equal = function (other) {
-		return other.left && this.left.equal(other.left) && this.right.equal(other.right);
-	};
-	this.contains = function (other) {
-		if (other.left && this.left.equal(other.left) && this.right.equal(other.right)) {
-			return true;
-		} else {
-			return this.left.contains(other) || this.right.contains(other);
-		}
-	};
+    this.left = left;
+    this.right = right;
+    this.subst = function (m, new_term) {
+        return new Db_app(this.left.subst(m, new_term), this.right.subst(m, new_term));
+    };
+    this.renumber = function (m, i) {
+        return new Db_app(this.left.renumber(m, i), this.right.renumber(m, i));
+    };
+    // we assume that other will have left iff it's a Db_app
+    this.equal = function (other) {
+        return other.left && this.left.equal(other.left) && this.right.equal(other.right);
+    };
+    this.contains = function (other) {
+        if (other.left && this.left.equal(other.left) && this.right.equal(other.right)) {
+            return true;
+        } else {
+            return this.left.contains(other) || this.right.contains(other);
+        }
+    };
 }
 
 function Db_lam(body) {
-	this.body = body;
-	this.subst = function (m, new_term) {
-		return new Db_lam(this.body.subst(m + 1, new_term));
-	};
-	this.renumber = function (m, i) {
-		return new Db_lam(this.body.renumber(m, i + 1));
-	};
-	// we assume that other will have body iff it's a Db_lam
-	this.equal = function (other) {
-		return other.body && this.body.equal(other.body);
-	};
-	this.contains = function (other) {
-		if (other.body && this.body.equal(other.body)) {
-			return true;
-		} else {
-			return this.body.contains(other);
-		}
-	};
+    this.body = body;
+    this.subst = function (m, new_term) {
+        return new Db_lam(this.body.subst(m + 1, new_term));
+    };
+    this.renumber = function (m, i) {
+        return new Db_lam(this.body.renumber(m, i + 1));
+    };
+    // we assume that other will have body iff it's a Db_lam
+    this.equal = function (other) {
+        return other.body && this.body.equal(other.body);
+    };
+    this.contains = function (other) {
+        if (other.body && this.body.equal(other.body)) {
+            return true;
+        } else {
+            return this.body.contains(other);
+        }
+    };
 }
 
 
@@ -111,156 +111,172 @@ function Db_lam(body) {
 // http://okmij.org/ftp/Computation/lambda-calc.html#lambda-calculator-haskell
 //
 function Variable(name, tag) {
-	this.name = name;
-	this.tag = tag || 0;
-	this.to_string = function () {
-		// append count copies of str to accum
-		function markup(accum, count) {
-			if (count === 0) {
-				return accum;
-			} else {
-				return markup(accum + "'", count - 1);
-			}
-		}
-		return markup(this.name, this.tag);
-	};
-	this.equal = function (other) {
-		return (this.tag === other.tag) && (this.name === other.name);
-	};
-	// position of this in seq
-	this.position = function (seq) {
-		for (var i = 0; i < seq.length; i += 1) {
-			if (this.equal(seq[i])) {
-				return new Db_index(i + 1);
-			}
+    this.name = name;
+    this.tag = tag || 0;
+    this.to_string = function () {
+        // append count copies of str to accum
+//         function markup(accum, count) {
+//             if (count === 0) {
+//                 return accum;
+//             } else {
+//                 return markup(accum + "'", count - 1);
+//             }
+//         }
+//         return markup(this.name, this.tag);
+		var s = this.name;
+		for (var count = 0; count < this.tag; count += 1) {
+			s += "'";
 		}
-		return new Db_free(this);
-	};
+		return s;
+    };
+    this.equal = function (other) {
+        return (this.tag === other.tag) && (this.name === other.name);
+    };
+    // position of this in seq
+    this.position = function (seq) {
+        for (var i = 0; i < seq.length; i += 1) {
+            if (this.equal(seq[i])) {
+                return new Db_index(i + 1);
+            }
+        }
+        return new Db_free(this);
+    };
 }
 
 // if v occurs free_in term, returns Some v' where v' is the highest-tagged
 // variable with the same name as v occurring (free or bound) in term
 //
 function free_in(v, term) {
-	var res = term.has_free(v);
-	return res[0] && res[1];
+    var res = term.has_free(v);
+    return res[0] && res[1];
 }
 
 function subst(v, new_term, expr) {
-	if (new_term.variable && new_term.variable.equal(v)) {
-		return expr;
-	} else {
-		return expr.subst(v, new_term);
-	}
+    if (new_term.variable && new_term.variable.equal(v)) {
+        return expr;
+    } else {
+        return expr.subst(v, new_term);
+    }
 }
 
 function equal(expr1, expr2) {
-	return expr1.debruijn([]).equal(expr2.debruijn([]));
+    return expr1.debruijn([]).equal(expr2.debruijn([]));
 }
 
 function contains(expr1, expr2) {
-	return expr1.debruijn([]).contains(expr2.debruijn([]));
+    return expr1.debruijn([]).contains(expr2.debruijn([]));
 }
 
 
 function Lambda_var(variable) {
-	this.variable = variable;
-	this.debruijn = function (seq) {
-		return this.variable.position(seq);
-	};
-	this.to_string = function (as_atom) {
-		return this.variable.to_string();
-	};
-	this.has_free = function (v) {
-		if (v.name !== this.variable.name) {
-			return [false, v];
-		} else if (v.tag === this.variable.tag) {
-			return [true, v];
-		} else {
-			return [false, this.variable];
-		}
-	};
-	this.subst = function (v, new_term) {
-		if (this.variable.equal(v)) {
-			return new_term;
-		} else {
-			return this;
-		}
-	};
-	this.check_eta = function () {
-		return this;
-	};
-	this.eval_loop = function (stack, eta) {
-		function unwind(left, stack) {
-			if (stack.length === 0) {
-				return left;
-			} else {
-				var x = stack[0];
-				var xs = stack.slice(1);
-				return unwind(new Lambda_app(left, x.eval_loop([], eta)), xs);
+    this.variable = variable;
+    this.debruijn = function (seq) {
+        return this.variable.position(seq);
+    };
+    this.to_string = function (as_atom) {
+        return this.variable.to_string();
+    };
+    this.has_free = function (v) {
+        if (v.name !== this.variable.name) {
+            return [false, v];
+        } else if (v.tag === this.variable.tag) {
+            return [true, v];
+        } else {
+            return [false, this.variable];
+        }
+    };
+    this.subst = function (v, new_term) {
+        if (this.variable.equal(v)) {
+            return new_term;
+        } else {
+            return this;
+        }
+    };
+    this.check_eta = function () {
+        return this;
+    };
+    this.eval_loop = function (stack, eta) {
+        function unwind(left, stack) {
+//             if (stack.length === 0) {
+//                 return left;
+//             } else {
+//                 var x = stack[0];
+//                 var xs = stack.slice(1);
+//                 return unwind(new Lambda_app(left, x.eval_loop([], eta)), xs);
+//             }
+			var res = left, x;
+			while (stack.length) {
+				x = stack.shift();
+				// res = new Lambda_app(res, x.eval_loop([], eta));
+				res = new Lambda_app(res, reduce(x, eta, false));
 			}
-		}
-		return unwind(this, stack);
-	};
-	this.eval_cbv = function (aggressive) {
-		return this;
-	};
+			return res;
+        }
+        // return unwind(this, stack);
+		// trampoline to, args
+		return [null, unwind(this, stack)];
+    };
+    this.eval_cbv = function (aggressive) {
+        return this;
+    };
 }
 
 function Lambda_app(left, right) {
-	this.left = left;
-	this.right = right;
-	this.debruijn = function (seq) {
-		return new Db_app(this.left.debruijn(seq), this.right.debruijn(seq));
-	};
-	this.to_string = function (as_atom) {
-		var base;
-		if (this.left.left) {
-			base = this.left.to_string() + " " + this.right.to_string(true);
-		} else {
-			base = this.left.to_string(true) + " " + this.right.to_string(true);
-		}
-		if (as_atom) {
-			return "(" + base + ")";
-		} else {
-			return base;
-		}
-	};
-	this.has_free = function (v) {
-		var left_res = this.left.has_free(v);
-		var right_res = this.right.has_free(v);
-		var left_bool = left_res[0];
-		var right_bool = right_res[0];
-		var left_tag = left_res[1].tag;
-		var right_tag = right_res[1].tag;
-		var res;
-		if (left_tag > right_tag) {
-			res = left_res[1];
-		} else {
-			res = right_res[1];
-		}
-		return [left_bool || right_bool, res];
-	};
-	this.subst = function (v, new_term) {
-		return new Lambda_app(subst(v, new_term, this.left), subst(v, new_term, this.right));
-	};
-	this.check_eta = function () {
-		return this;
-	};
-	this.eval_loop = function (stack, eta) {
-		var new_stack = stack.slice(0);
-		new_stack.unshift(this.right);
-		return this.left.eval_loop(new_stack, eta);
-	};
-	this.eval_cbv = function (aggressive) {
-		var left = this.left.eval_cbv(aggressive);
-		var right = this.right.eval_cbv(aggressive);
-		if (left.body) {
-			return subst(left.bound, right, left.body).eval_cbv(aggressive);
-		} else {
-			return new Lambda_app(left, right);
-		}
-	};
+    this.left = left;
+    this.right = right;
+    this.debruijn = function (seq) {
+        return new Db_app(this.left.debruijn(seq), this.right.debruijn(seq));
+    };
+    this.to_string = function (as_atom) {
+        var base;
+        if (this.left.left) {
+            base = this.left.to_string() + " " + this.right.to_string(true);
+        } else {
+            base = this.left.to_string(true) + " " + this.right.to_string(true);
+        }
+        if (as_atom) {
+            return "(" + base + ")";
+        } else {
+            return base;
+        }
+    };
+    this.has_free = function (v) {
+        var left_res = this.left.has_free(v);
+        var right_res = this.right.has_free(v);
+        var left_bool = left_res[0];
+        var right_bool = right_res[0];
+        var left_tag = left_res[1].tag;
+        var right_tag = right_res[1].tag;
+        var res;
+        if (left_tag > right_tag) {
+            res = left_res[1];
+        } else {
+            res = right_res[1];
+        }
+        return [left_bool || right_bool, res];
+    };
+    this.subst = function (v, new_term) {
+        return new Lambda_app(subst(v, new_term, this.left), subst(v, new_term, this.right));
+    };
+    this.check_eta = function () {
+        return this;
+    };
+    this.eval_loop = function (stack, eta) {
+        var new_stack = stack.slice(0);
+        new_stack.unshift(this.right);
+        // return this.left.eval_loop(new_stack, eta);
+		// trampoline to, args
+		return [this.left, new_stack, eta];
+    };
+    this.eval_cbv = function (aggressive) {
+        var left = this.left.eval_cbv(aggressive);
+        var right = this.right.eval_cbv(aggressive);
+        if (left.body) {
+            return subst(left.bound, right, left.body).eval_cbv(aggressive);
+        } else {
+            return new Lambda_app(left, right);
+        }
+    };
 }
 
 
@@ -269,112 +285,130 @@ function Lambda_app(left, right) {
 
 
 function Lambda_lam(variable, body) {
-	this.bound = variable;
-	this.body = body;
-	this.debruijn = function (seq) {
-		var new_seq = seq.slice(0);
-		new_seq.unshift(this.bound);
-		return new Db_lam(this.body.debruijn(new_seq));
-	};
-	this.to_string = function (as_atom) {
-		var base = "\\" + this.to_string_funct();
-		if (as_atom) {
-			return "(" + base + ")";
-		} else {
-			return base;
-		}
-	};
-	this.to_string_funct = function () {
-		if (this.body.to_string_funct) {
-			return this.bound.to_string() + " " + this.body.to_string_funct();
-		} else {
-			return this.bound.to_string() + ". " + this.body.to_string();
-		}
-	};
-	this.has_free = function (v) {
-		if (this.bound.equal(v)) {
-			return [false, v];
-		} else {
-			return this.body.has_free(v);
-		}
-	};
-	this.subst = function (v, new_term) {
-		function bump_tag(v1, v2) {
-			var max;
-			if (v1.tag > v2.tag) {
-				max = v1.tag;
-			} else {
-				max = v2.tag;
-			}
-			return new Variable(v1.name, max + 1);
-		}
-		function bump_tag2(v1, v2) {
-			if (v1.name !== v2.name) {
-				return v1;
-			} else {
-				return bump_tag(v1, v2);
-			}
-		}
-		if (this.bound.equal(v)) {
-			return this;
-		} else {
-			var res = free_in(this.bound, new_term);
+    this.bound = variable;
+    this.body = body;
+    this.debruijn = function (seq) {
+        var new_seq = seq.slice(0);
+        new_seq.unshift(this.bound);
+        return new Db_lam(this.body.debruijn(new_seq));
+    };
+    this.to_string = function (as_atom) {
+        var base = "\\" + this.to_dotted();
+        if (as_atom) {
+            return "(" + base + ")";
+        } else {
+            return base;
+        }
+    };
+    this.to_dotted = function () {
+        if (this.body.to_dotted) {
+            return this.bound.to_string() + " " + this.body.to_dotted();
+        } else {
+            return this.bound.to_string() + ". " + this.body.to_string();
+        }
+    };
+    this.has_free = function (v) {
+        if (this.bound.equal(v)) {
+            return [false, v];
+        } else {
+            return this.body.has_free(v);
+        }
+    };
+    this.subst = function (v, new_term) {
+        function bump_tag(v1, v2) {
+            var max;
+            if (v1.tag > v2.tag) {
+                max = v1.tag;
+            } else {
+                max = v2.tag;
+            }
+            return new Variable(v1.name, max + 1);
+        }
+        function bump_tag2(v1, v2) {
+            if (v1.name !== v2.name) {
+                return v1;
+            } else {
+                return bump_tag(v1, v2);
+            }
+        }
+        if (this.bound.equal(v)) {
+            return this;
+        } else {
+            var res = free_in(this.bound, new_term);
             // if x is free in the inserted term new_term, a capture is possible
-			if (res) {
-				// this.bound is free in new_term, need to alpha-convert
-				var uniq_x = bump_tag2(bump_tag(this.bound, res), v);
-				var res2 = free_in(uniq_x, this.body);
-				if (res2) {
-					uniq_x = bump_tag(uniq_x, res2);
-				}
-				var body2 = subst(this.bound, new Lambda_var(uniq_x), this.body);
-				return new Lambda_lam(uniq_x, subst(v, new_term, body2));
-			} else {
-				// this.bound not free in new_term, can substitute new_term for v without any captures
-				return new Lambda_lam(this.bound, subst(v, new_term, this.body));
-			}
-		}
-	};
-	this.check_eta = function () {
-		if (this.body.right && this.body.right.variable && this.bound.equal(this.body.right.variable) && !free_in(this.bound, this.body.left)) {
-			return this.body.left;
-		} else {
-			return this;
-		}
-	};
-	this.eval_loop = function (stack, eta) {
-		if (stack.length === 0) {
-			var term = new Lambda_lam(this.bound, this.body.eval_loop([], eta));
+            if (res) {
+                // this.bound is free in new_term, need to alpha-convert
+                var uniq_x = bump_tag2(bump_tag(this.bound, res), v);
+                var res2 = free_in(uniq_x, this.body);
+                if (res2) {
+                    uniq_x = bump_tag(uniq_x, res2);
+                }
+                var body2 = subst(this.bound, new Lambda_var(uniq_x), this.body);
+                return new Lambda_lam(uniq_x, subst(v, new_term, body2));
+            } else {
+                // this.bound not free in new_term, can substitute new_term for v without any captures
+                return new Lambda_lam(this.bound, subst(v, new_term, this.body));
+            }
+        }
+    };
+    this.check_eta = function () {
+        if (this.body.right && this.body.right.variable && this.bound.equal(this.body.right.variable) && !free_in(this.bound, this.body.left)) {
+            return this.body.left;
+        } else {
+            return this;
+        }
+    };
+    this.eval_loop = function (stack, eta) {
+        if (stack.length === 0) {
+			// var term = new Lambda_lam(this.bound, this.body.eval_loop([], eta));
+			var term = new Lambda_lam(this.bound, reduce(this.body, eta, false));
 			if (eta) {
-				return term.check_eta();
+				return [null, term.check_eta()];
 			} else {
-				return term;
+				return [null, term];
+			}
+        } else {
+            var x = stack[0];
+            var xs = stack.slice(1);
+            // return subst(this.bound, x, this.body).eval_loop(xs, eta);
+			// trampoline to, args
+			return [subst(this.bound, x, this.body), xs, eta];
+        }
+    };
+    this.eval_cbv = function (aggressive) {
+        if (aggressive) {
+            return new Lambda_lam(this.bound, this.body.eval_cbv(aggressive));
+        } else {
+            return this;
+        }
+    };
+    this.to_int = function (sofar) {
+//         if (this.body.body && this.body.body.variable && this.body.bound.equal(this.body.body.variable)) {
+//             return 0 + sofar;
+//         } else if (this.body.variable && this.bound.equal(this.body.variable)) {
+//             return 1 + sofar;
+//         } else if (this.body.body && this.body.body.left && this.body.body.left.variable && this.bound.equal(this.body.body.left.variable)) {
+//             var new_int = new Lambda_lam(this.bound, new Lambda_lam(this.body.bound, this.body.body.right));
+//             return new_int.to_int(1 + sofar);
+//         } else {
+//             return "not a church numeral";
+//         }
+		var res = 0, s = this.bound, z, cursor;
+		if (this.body.variable && s.equal(this.body.variable)) {
+			return 1;
+		} else if (this.body.bound) {
+			z = this.body.bound;
+			cursor = this.body.body;
+			while (cursor.left && cursor.left.variable && s.equal(cursor.left.variable)) {
+				res += 1;
+				cursor = cursor.right;
+			}
+			if (cursor.variable && z.equal(cursor.variable)) {
+				return res;
 			}
-		} else {
-			var x = stack[0];
-			var xs = stack.slice(1);
-			return subst(this.bound, x, this.body).eval_loop(xs, eta);
-		}
-	};
-	this.eval_cbv = function (aggressive) {
-		if (aggressive) {
-			return new Lambda_lam(this.bound, this.body.eval_cbv(aggressive));
-		} else {
-			return this;
-		}
-	};
-	this.to_int = function (sofar) {
-		if (this.body.body && this.body.body.variable && this.body.bound.equal(this.body.body.variable)) {
-			return 0 + sofar;
-		} else if (this.body.variable && this.bound.equal(this.body.variable)) {
-			return 1 + sofar;
-		} else if (this.body.body && this.body.body.left && this.body.body.left.variable && this.bound.equal(this.body.body.left.variable)) {
-			var new_int = new Lambda_lam(this.bound, new Lambda_lam(this.body.bound, this.body.body.right));
-			return new_int.to_int(1 + sofar);
-		} else {
-			return "not a church numeral";
 		}
-	};
+		return "not a church numeral";
+    };
 }
 
 
@@ -385,205 +419,216 @@ function Lambda_lam(variable, body) {
 // cbv is 1: use call-by-value, don't descend inside lambda
 // cbv is 2: applicative order
 function reduce(expr, eta, cbv) {
-	if (cbv) {
-		return expr.eval_cbv(cbv > 1);
-	} else {
-		return expr.eval_loop([], eta);
-	}
+    if (cbv) {
+        return expr.eval_cbv(cbv > 1);
+    } else {
+        // return expr.eval_loop([], eta);
+		// using trampoline to reduce call stack overflows
+		var to_eval = expr, res = [[], eta];
+		while (to_eval !== null) {
+			res = to_eval.eval_loop.apply(to_eval, res);
+			to_eval = res.shift();
+		}
+		return res[0];
+    }
 }
 
 function make_var(name) {
-	return new Variable(name);
+    return new Variable(name);
 }
 function make_app(aa, bb) {
-	return new Lambda_app(aa, bb);
+    return new Lambda_app(aa, bb);
 }
 function make_lam(a, aa) {
-	return new Lambda_lam(a, aa);
+    return new Lambda_lam(a, aa);
 }
 
 try {
-	if (console && console.debug) {
-		function print() {
-			console.debug.apply(this, arguments);
-		}
-	}
+    if (console && console.debug) {
+        function print() {
+            console.debug.apply(this, arguments);
+        }
+    }
 } catch (e) {}
 
 
 
 
+/* Chris's original
+
+// Basic data structure, essentially a LISP/Scheme-like cons
+// pre-terminal nodes are expected to be of the form new cons(null, "string")
+function cons(car, cdr) {
+  this.car = car;
+  this.cdr = cdr;
+}
+
+// takes a stack of symbols, returns a pair: a tree and the remaining symbols
+function parse(split) {
+  if (split == null) return (new cons (null, null));
+  if (split.length == 0) return (new cons (null, null));
+  var token = split.shift();
+  if (token == ")") return (new cons (null, split));
+  var next = parse(split);
+  if (token == "(") {
+	var nextnext = parse(next.cdr);
+	return (new cons ((new cons (next.car, nextnext.car)),
+					  nextnext.cdr));
+  }
+  return (new cons ((new cons ((new cons (null, token)),
+							   next.car)),
+					next.cdr))
+}
+
+// substitute arg in for v in tree
+function sub(tree, v, arg) {
+  if (tree == null) return (null);
+  if (tree.car == null) if (tree.cdr == v) return (arg);
+  if (tree.car == null) return (tree);
+
+  // perform alpha reduction to prevent variable collision
+  if (isBindingForm(tree))
+	return (new cons (tree.car,
+					  sub(sub(tree.cdr,         // inner sub = alpha reduc.
+							  tree.cdr.car.cdr,
+							  fresh(tree.cdr.car.cdr)),
+						  v,
+						  arg)));
+
+  return (new cons ((sub (tree.car, v, arg)),
+					(sub (tree.cdr, v, arg))))
+}
+
+// Guaranteed unique for each call as long as string is not empty.
+var i = 0;
+function fresh(string) {
+  i = i+1;
+  if (typeof(string) != "string") return (string);
+  return (new cons (null,
+					string.substring(0,1) + (i).toString()));
+}
+
+// Keep reducing until there is no more change
+function fixedPoint (tree) {
+  var t2 = reduce(tree);
+  if (treeToString(tree) == treeToString(t2)) return (tree);
+  return (fixedPoint (t2));
+}
+
+// Reduce all the arguments, then try to do beta conversion on the whole
+function reduce(tree) {
+  if (tree == null) return (tree);
+  if (typeof(tree) == "string") return (tree);
+  return (convert (new cons (reduce (tree.car), mapReduce (tree.cdr))));
+}
+
+// Reduce all the arguments in a list
+function mapReduce(tree) {
+  if (tree == null) return (tree);
+  if (tree.car == null) return (tree);
+  return (new cons (reduce (tree.car), mapReduce(tree.cdr )));
+}
+
+// If the list is of the form ((lambda var body) arg), do beta reduc.
+function convert(tree) {
+	if (isLet(tree)) {
+	  return (sub(tree.cdr.car, tree.car.cdr.car.cdr, tree.car.cdr.cdr.car));}
+	else
+	  if (isConvertable(tree)) {
+		return (sub(tree.car.cdr.cdr.car, tree.car.cdr.car.cdr, tree.cdr.car));}
+	  else return(tree);
+}
+
+// Is of form ((let var arg) body)?
+function isLet(tree) {
+  if (tree == null) return (false);
+  if (!(isBindingForm(tree.car))) return (false);
+  if (tree.car.car.cdr != "let") return (false);
+  if (tree.cdr == null) return (false);
+  if (tree.cdr.car == null) return (false);
+  return(true);
+}
+
+// Is of form ((lambda var body) arg)?
+function isConvertable(tree) {
+  if (tree == null) return (false);
+  if (!(isBindingForm(tree.car))) return (false);
+  if (tree.car.car.cdr != "lambda") return (false);
+  if (tree.cdr == null) return (false);
+  if (tree.cdr.car == null) return (false);
+  return(true);
+}
+
+// Is of form (lambda var body)?
+function isBindingForm(tree) {
+  if (tree == null) return (false);
+  if (tree.car == null) return (false);
+  if (tree.car.car != null) return (false);
+  if ((tree.car.cdr != "lambda")
+	  && (tree.car.cdr != "let")
+	  && (tree.car.cdr != "exists")
+	  && (tree.car.cdr != "forall")
+	  && (tree.car.cdr != "\u03BB")
+	  && (tree.car.cdr != "\u2200")
+	  && (tree.car.cdr != "\u2203")
+	 )
+	return (false);
+  if (tree.car.cdr == null) return (false);
+  if (tree.cdr.car == null) return (false);
+  if (tree.cdr.car.car != null) return (false);
+  if (tree.cdr.cdr == null) return (false);
+  return (true);
+}
+
+function treeToString(tree) {
+  if (tree == null) return ("")
+  if (tree.car == null) return (tree.cdr)
+  if ((tree.car).car == null)
+	return (treeToString(tree.car) + " " + treeToString(tree.cdr))
+  return ("(" + treeToString(tree.car) + ")" + treeToString(tree.cdr))
+}
+
+// use this instead of treeToString if you want to see the full structure
+function treeToStringRaw(tree) {
+  if (tree == null) return ("@")
+  if (typeof(tree) == "string") return (tree);
+  return ("(" + treeToStringRaw(tree.car) + "." +
+				treeToStringRaw(tree.cdr) + ")")
+}
+
+// Make sure each paren will count as a separate token
+function stringToTree(input) {
+  input = input.replace(/let/g, " ( ( let ");
+  input = input.replace(/=/g, " ");
+  input = input.replace(/in/g, " ) ");
+  input = input.replace(/\(/g, " ( ");
+  input = input.replace(/\)/g, " ) ");
+  input = input.replace(/;.*\n/g," ");
+  input = input.replace(/\^/g, " ^ ");
+  input = input.replace(/[\\]/g, " lambda ");
+  input = input.replace(/\u03BB/g, " lambda ");
+  return ((parse(input.split(/[ \f\n\r\t\v]+/))).car)
+}
+
+// Adjust spaces to print pretty
+function formatTree(tree) {
+  output = treeToStringRaw (tree);
+  output = output.replace(/^[ \f\n\r\t\v]+/, "");
+  output = output.replace(/[ \f\n\r\t\v]+$/, "");
+  output = output.replace(/[ \f\n\r\t\v]+\)/g, ")");
+  output = output.replace(/\)([^)(])/g, ") $1");
+  output = output.replace(/lambda/g, "\\");
+//  output = output.replace(/lambda/g, "\u03BB");
+//  output = output.replace(/exists/g, "\u2203");
+//  output = output.replace(/forall/g, "\u2200");
+  return (output)
+}
+
+function mytry(form) {
+  i = 0;
+  form.result.value = formatTree((stringToTree(form.input.value)));
+  // form.result.value = formatTree(fixedPoint(stringToTree(form.input.value)));
+}
+
+*/
 
-// // Basic data structure, essentially a LISP/Scheme-like cons
-// // pre-terminal nodes are expected to be of the form new cons(null, "string")
-// function cons(car, cdr) {
-//   this.car = car;
-//   this.cdr = cdr;
-// }
-
-// // takes a stack of symbols, returns a pair: a tree and the remaining symbols
-// function parse(split) {
-//   if (split == null) return (new cons (null, null));
-//   if (split.length == 0) return (new cons (null, null));
-//   var token = split.shift();
-//   if (token == ")") return (new cons (null, split));
-//   var next = parse(split);
-//   if (token == "(") {
-//     var nextnext = parse(next.cdr);
-//     return (new cons ((new cons (next.car, nextnext.car)),
-//                       nextnext.cdr));
-//   }
-//   return (new cons ((new cons ((new cons (null, token)),
-//                                next.car)),
-//                     next.cdr))
-// }
-
-// // substitute arg in for v in tree
-// function sub(tree, v, arg) {
-//   if (tree == null) return (null);
-//   if (tree.car == null) if (tree.cdr == v) return (arg);
-//   if (tree.car == null) return (tree);
-
-//   // perform alpha reduction to prevent variable collision
-//   if (isBindingForm(tree)) 
-//     return (new cons (tree.car, 
-//                       sub(sub(tree.cdr,         // inner sub = alpha reduc.
-//                               tree.cdr.car.cdr, 
-//                               fresh(tree.cdr.car.cdr)),
-//                           v,
-//                           arg)));
-
-//   return (new cons ((sub (tree.car, v, arg)),
-//                     (sub (tree.cdr, v, arg))))
-// }
-
-// // Guaranteed unique for each call as long as string is not empty.
-// var i = 0;
-// function fresh(string) {
-//   i = i+1;
-//   if (typeof(string) != "string") return (string);
-//   return (new cons (null,  
-//                     string.substring(0,1) + (i).toString()));
-// }
-
-// // Keep reducing until there is no more change
-// function fixedPoint (tree) {
-//   var t2 = reduce(tree);
-//   if (treeToString(tree) == treeToString(t2)) return (tree);
-//   return (fixedPoint (t2));
-// }
-
-// // Reduce all the arguments, then try to do beta conversion on the whole
-// function reduce(tree) {
-//   if (tree == null) return (tree);
-//   if (typeof(tree) == "string") return (tree);
-//   return (convert (new cons (reduce (tree.car), mapReduce (tree.cdr))));
-// }
-
-// // Reduce all the arguments in a list
-// function mapReduce(tree) {
-//   if (tree == null) return (tree);
-//   if (tree.car == null) return (tree);
-//   return (new cons (reduce (tree.car), mapReduce(tree.cdr )));
-// }
-
-// // If the list is of the form ((lambda var body) arg), do beta reduc.
-// function convert(tree) {
-//     if (isLet(tree)) {
-//       return (sub(tree.cdr.car, tree.car.cdr.car.cdr, tree.car.cdr.cdr.car));}
-//     else 
-//       if (isConvertable(tree)) {
-//         return (sub(tree.car.cdr.cdr.car, tree.car.cdr.car.cdr, tree.cdr.car));}
-//       else return(tree);
-// } 
-
-// // Is of form ((let var arg) body)?
-// function isLet(tree) {
-//   if (tree == null) return (false);
-//   if (!(isBindingForm(tree.car))) return (false);
-//   if (tree.car.car.cdr != "let") return (false);
-//   if (tree.cdr == null) return (false);
-//   if (tree.cdr.car == null) return (false);
-//   return(true);
-// }  
-
-// // Is of form ((lambda var body) arg)?
-// function isConvertable(tree) {
-//   if (tree == null) return (false);
-//   if (!(isBindingForm(tree.car))) return (false);
-//   if (tree.car.car.cdr != "lambda") return (false);
-//   if (tree.cdr == null) return (false);
-//   if (tree.cdr.car == null) return (false);
-//   return(true);
-// }  
-
-// // Is of form (lambda var body)?
-// function isBindingForm(tree) {
-//   if (tree == null) return (false);
-//   if (tree.car == null) return (false);
-//   if (tree.car.car != null) return (false);
-//   if ((tree.car.cdr != "lambda") 
-//       && (tree.car.cdr != "let")
-//       && (tree.car.cdr != "exists")
-//       && (tree.car.cdr != "forall")
-//       && (tree.car.cdr != "\u03BB")
-//       && (tree.car.cdr != "\u2200")
-//       && (tree.car.cdr != "\u2203")
-//      )
-//     return (false);
-//   if (tree.car.cdr == null) return (false);
-//   if (tree.cdr.car == null) return (false);
-//   if (tree.cdr.car.car != null) return (false);
-//   if (tree.cdr.cdr == null) return (false);
-//   return (true);
-// }
-
-// function treeToString(tree) {
-//   if (tree == null) return ("")
-//   if (tree.car == null) return (tree.cdr)
-//   if ((tree.car).car == null) 
-//     return (treeToString(tree.car) + " " + treeToString(tree.cdr))
-//   return ("(" + treeToString(tree.car) + ")" + treeToString(tree.cdr))
-// }
-
-// // use this instead of treeToString if you want to see the full structure
-// function treeToStringRaw(tree) {
-//   if (tree == null) return ("@")
-//   if (typeof(tree) == "string") return (tree);
-//   return ("(" + treeToStringRaw(tree.car) + "." + 
-//                 treeToStringRaw(tree.cdr) + ")")
-// }
-
-// // Make sure each paren will count as a separate token
-// function stringToTree(input) {
-//   input = input.replace(/let/g, " ( ( let ");
-//   input = input.replace(/=/g, " ");
-//   input = input.replace(/in/g, " ) ");
-//   input = input.replace(/\(/g, " ( ");
-//   input = input.replace(/\)/g, " ) ");
-//   input = input.replace(/;.*\n/g," ");
-//   input = input.replace(/\^/g, " ^ ");
-//   input = input.replace(/[\\]/g, " lambda ");
-//   input = input.replace(/\u03BB/g, " lambda ");
-//   return ((parse(input.split(/[ \f\n\r\t\v]+/))).car)
-// }
-
-// // Adjust spaces to print pretty
-// function formatTree(tree) {
-//   output = treeToStringRaw (tree);
-//   output = output.replace(/^[ \f\n\r\t\v]+/, "");
-//   output = output.replace(/[ \f\n\r\t\v]+$/, "");
-//   output = output.replace(/[ \f\n\r\t\v]+\)/g, ")");
-//   output = output.replace(/\)([^)(])/g, ") $1");
-//   output = output.replace(/lambda/g, "\\");
-// //  output = output.replace(/lambda/g, "\u03BB");
-// //  output = output.replace(/exists/g, "\u2203");
-// //  output = output.replace(/forall/g, "\u2200");
-//   return (output)
-// }
-
-// function mytry(form) { 
-//   i = 0;
-//   form.result.value = formatTree((stringToTree(form.input.value)));
-//   // form.result.value = formatTree(fixedPoint(stringToTree(form.input.value)));
-// }