var __ = "__"; /* wildcard marker */

var SOA = "__["; // start of array
var EOA = "__]"; // end of array

function die(message) {
    throw new Error(message);
}

function $Embedded(matcher) {
    this.matcher = matcher;
}

function embeddedMatcher(matcher) {
    return new $Embedded(matcher);
}

// The pattern argument defaults to wildcard, __.
function $Capture(pattern) {
    this.pattern = (typeof pattern === 'undefined' ? __ : pattern);
}

// Abbreviation: _$(x) <==> new $Capture(x)
function _$(pattern) {
    return new $Capture(pattern);
}

function isCapture(x) { return x instanceof $Capture || x === _$; }
function capturePattern(x) { return x instanceof $Capture ? x.pattern : __; }

var SOC = "__{{"; // start of capture
var EOC = "__}}"; // end of capture

function $Success(value) {
    this.value = value;
}

function $WildcardSequence(matcher) {
    this.matcher = matcher;
}

function $Dict() {
    this.length = 0;
    this.entries = {};
}

$Dict.prototype.get = function (key) {
    return this.entries[key] || emptyMatcher;
};

$Dict.prototype.set = function (key, val) {
    if (!(key in this.entries)) this.length++;
    this.entries[key] = val;
};

$Dict.prototype.clear = function (key) {
    if (key in this.entries) this.length--;
    delete this.entries[key];
};

$Dict.prototype.isEmpty = function () {
    return this.length === 0;
};

$Dict.prototype.copy = function () {
    var other = new $Dict();
    other.length = this.length;
    for (var key in this.entries) {
	if (this.entries.hasOwnProperty(key)) {
	    other.entries[key] = this.entries[key];
	}
    }
    return other;
};

$Dict.prototype.emptyGuard = function () {
    if (this.isEmpty()) return emptyMatcher;
    return this;
};

$Dict.prototype.has = function (key) {
    return key in this.entries;
};

$Dict.prototype.sortedKeys = function () {
    var ks = [];
    for (var k in this.entries) ks.push(k);
    ks.sort();
    return ks;
}

function is_emptyMatcher(m) {
    return (m === emptyMatcher);
}

///////////////////////////////////////////////////////////////////////////
// Constructors

var emptyMatcher = null;

function rsuccess(v) {
    return (v === emptyMatcher) ? emptyMatcher : new $Success(v);
}

function rseq(e, r) {
    if (r === emptyMatcher) return emptyMatcher;
    var s = new $Dict();
    s.set(e, r);
    return s;
}

function rwild(r) {
    return rseq(__, r);
}

function rwildseq(r) {
    return (r === emptyMatcher) ? emptyMatcher : new $WildcardSequence(r);
}

///////////////////////////////////////////////////////////////////////////

function compilePattern(v, p) {
    if (!p) die("compilePattern: missing pattern");
    return walk(p, rseq(EOA, rsuccess(v)));

    function walk(p, acc) {
	if (p === __) return rwild(acc);

	if (Array.isArray(p)) {
	    acc = rseq(EOA, acc);
	    for (var i = p.length - 1; i >= 0; i--) {
		acc = walk(p[i], acc);
	    }
	    return rseq(SOA, acc);
	}

	if (p instanceof $Embedded) {
	    return appendMatcher(p.matcher, function (v) { return acc; });
	} else {
	    return rseq(JSON.stringify(p), acc);
	}
    }
}

function shallowCopyArray(s) {
    return s.slice();
}

function rupdateInplace(r, key, k) {
    if (is_emptyMatcher(k)) {
	r.clear(key);
    } else {
	r.set(key, k);
    }
}

function matcherEquals(a, b) {
    if (a === null) {
	return (b === null);
    }
    if (b === null) return false;

    if (a instanceof $WildcardSequence) {
	if (!(b instanceof $WildcardSequence)) return false;
	a = a.matcher;
	b = b.matcher;
    } else if (b instanceof $WildcardSequence) return false;

    if (a instanceof $Success) {
	if (!(b instanceof $Success)) return false;
	return valuesEqual(a.value, b.value);
    }
    if (b instanceof $Success) return false;

    for (var key in a.entries) {
	if (!b.has(key)) return false;
	if (!matcherEquals(a.entries[key], b.entries[key])) return false;
    }
    return true;
}

function is_keyOpen(k) {
    return k === SOA;
}

function is_keyClose(k) {
    return k === EOA;
}

function is_keyNormal(k) {
    return !(is_keyOpen(k) || is_keyClose(k));
}

///////////////////////////////////////////////////////////////////////////
// Enough of sets to get by with

function arrayToSet(xs) {
    var s = {};
    for (var i = 0; i < xs.length; i++) {
	s[JSON.stringify(xs[i])] = xs[i];
    }
    return s;
}

function setToArray(s) {
    var r = [];
    for (var k in s) r.push(s[k]);
    return r;
}

function setUnion(s1, s2) {
    var s = {};
    setUnionInplace(s, s1);
    setUnionInplace(s, s2);
    return s;
}

function is_emptySet(s) {
    for (var k in s) {
	if (s.hasOwnProperty(k))
	    return false;
    }
    return true;
}

function setSubtract(s1, s2) {
    var s = {};
    for (var key in s1) {
	if (s1.hasOwnProperty(key) && !s2.hasOwnProperty(key)) {
	    s[key] = s1[key];
	}
    }
    return s;
}

function setIntersect(s1, s2) {
    var s = {};
    for (var key in s1) {
	if (s1.hasOwnProperty(key) && s2.hasOwnProperty(key)) {
	    s[key] = s1[key];
	}
    }
    return s;
}

function setUnionInplace(acc, s) {
    for (var key in s) {
	if (s.hasOwnProperty(key)) {
	    acc[key] = s[key];
	}
    }
}

function setEqual(s1, s2) {
    for (var key in s1) {
	if (s1.hasOwnProperty(key)) {
	    if (s1[key] !== s2[key]) return false;
	}
    }
    for (var key in s2) {
	if (s2.hasOwnProperty(key)) {
	    if (s1[key] !== s2[key]) return false;
	}
    }
    return true;
}

///////////////////////////////////////////////////////////////////////////

var unionSuccesses = function (v1, v2) {
    if (v1 === true) return v2;
    if (v2 === true) return v1;
    return setUnion(v1, v2);
};

var intersectSuccesses = function (v1, v2) {
    return v1;
};

var erasePathSuccesses = function (v1, v2) {
    var r = setSubtract(v1, v2);
    if (is_emptySet(r)) return null;
    return r;
};

var matchMatcherSuccesses = function (v1, v2, acc) {
    setUnionInplace(acc, v2);
};

var projectSuccess = function (v) {
    return v;
};

var valuesEqual = function (a, b) {
    return setEqual(a, b);
};

///////////////////////////////////////////////////////////////////////////

function expandWildseq(r) {
    return union(rwild(rwildseq(r)), rseq(EOA, r));
}

function union(o1, o2) {
    return merge(o1, o2);

    function merge(o1, o2) {
	if (is_emptyMatcher(o1)) return o2;
	if (is_emptyMatcher(o2)) return o1;
	return walk(o1, o2);
    }

    function walk(r1, r2) {
	if (r1 instanceof $WildcardSequence) {
	    if (r2 instanceof $WildcardSequence) {
		return rwildseq(walk(r1.matcher, r2.matcher));
	    }
	    r1 = expandWildseq(r1.matcher);
	} else if (r2 instanceof $WildcardSequence) {
	    r2 = expandWildseq(r2.matcher);
	}

	if (r1 instanceof $Success && r2 instanceof $Success) {
	    return rsuccess(unionSuccesses(r1.value, r2.value));
	}

	var w = merge(r1.get(__), r2.get(__));
	if (is_emptyMatcher(w)) {
	    var smaller = r1.length < r2.length ? r1 : r2;
	    var larger  = r1.length < r2.length ? r2 : r1;
	    var target = larger.copy();
	    for (var key in smaller.entries) {
		var k = merge(smaller.get(key), larger.get(key));
		rupdateInplace(target, key, k);
	    }
	    return target.emptyGuard();
	} else {
	    function examineKey(rA, key, rB) {
		if ((key !== __) && !target.has(key)) {
		    var k = merge(rA.get(key), rB.get(key));
		    if (is_keyOpen(key)) {
			rupdateInplace(target, key, merge(rwildseq(w), k));
		    } else if (is_keyClose(key)) {
			if (w instanceof $WildcardSequence) {
			    rupdateInplace(target, key, merge(w.matcher, k));
			} else {
			    rupdateInplace(target, key, k);
			}
		    } else {
			rupdateInplace(target, key, merge(w, k));
		    }
		}
	    }
	    var target = rwild(w).copy();
	    for (var key in r1.entries) { examineKey(r1, key, r2); }
	    for (var key in r2.entries) { examineKey(r2, key, r1); }
	    return target;
	}
    }
}

function unionN() {
    var acc = emptyMatcher;
    for (var i = 0; i < arguments.length; i++) {
	acc = union(acc, arguments[i]);
    }
    return acc;
}

function intersect(o1, o2) {
    if (is_emptyMatcher(o1)) return emptyMatcher;
    if (is_emptyMatcher(o2)) return emptyMatcher;
    return walk(o1, o2);

    function walkFlipped(r2, r1) { return walk(r1, r2); }

    function walk(r1, r2) {
	// INVARIANT: r1 is a part of the original o1, and
	// likewise for r2. This is so that the first arg to
	// intersectSuccesses always comes from r1, and the second
	// from r2.
	if (is_emptyMatcher(r1)) return emptyMatcher;
	if (is_emptyMatcher(r2)) return emptyMatcher;

	if (r1 instanceof $WildcardSequence) {
	    if (r2 instanceof $WildcardSequence) {
		return rwildseq(walk(r1.matcher, r2.matcher));
	    }
	    r1 = expandWildseq(r1.matcher);
	} else if (r2 instanceof $WildcardSequence) {
	    r2 = expandWildseq(r2.matcher);
	}

	if (r1 instanceof $Success && r2 instanceof $Success) {
	    return rsuccess(intersectSuccesses(r1.value, r2.value));
	}

	var w1 = r1.get(__);
	var w2 = r2.get(__);
	var w = walk(w1, w2);

	var target = new $Dict();

	function examineKey(key) {
	    if ((key !== __) && !target.has(key)) {
		var k1 = r1.get(key);
		var k2 = r2.get(key);
		if (is_emptyMatcher(k1)) {
		    if (is_emptyMatcher(k2)) {
			rupdateInplace(target, key, emptyMatcher);
		    } else {
			rupdateInplace(target, key, walkWild(walk, w1, key, k2));
		    }
		} else {
		    if (is_emptyMatcher(k2)) {
			rupdateInplace(target, key, walkWild(walkFlipped, w2, key, k1));
		    } else {
			rupdateInplace(target, key, walk(k1, k2));
		    }
		}
	    }
	}

	if (is_emptyMatcher(w1)) {
	    if (is_emptyMatcher(w2)) {
		for (var key in (r1.length < r2.length ? r1 : r2).entries) examineKey(key);
	    } else {
		for (var key in r1.entries) examineKey(key);
	    }
	} else {
	    if (is_emptyMatcher(w2)) {
		for (var key in r2.entries) examineKey(key);
	    } else {
		rupdateInplace(target, __, w);
		for (var key in r1.entries) examineKey(key);
		for (var key in r2.entries) examineKey(key);
	    }
	}
	return target.emptyGuard();
    }

    function walkWild(walker, w, key, k) {
	if (is_emptyMatcher(w)) return emptyMatcher;
	if (is_keyOpen(key)) return walker(rwildseq(w), k);
	if (is_keyClose(key)) {
	    if (w instanceof $WildcardSequence) return walker(w.matcher, k);
	    return emptyMatcher;
	}
	return walker(w, k);
    }
}

// Removes r2's mappings from r1. Assumes r2 has previously been
// union'd into r1. The erasePathSuccesses function should return
// null to signal "no remaining success values".
function erasePath(o1, o2) {
    return walk(o1, o2);

    function walk(r1, r2) {
	if (is_emptyMatcher(r1)) {
	    return emptyMatcher;
	} else {
	    if (is_emptyMatcher(r2)) {
		return r1;
	    }
	}

	if (r1 instanceof $WildcardSequence) {
	    if (r2 instanceof $WildcardSequence) {
		return rwildseq(walk(r1.matcher, r2.matcher));
	    }
	    r1 = expandWildseq(r1.matcher);
	} else if (r2 instanceof $WildcardSequence) {
	    r2 = expandWildseq(r2.matcher);
	}

	if (r1 instanceof $Success && r2 instanceof $Success) {
	    return rsuccess(erasePathSuccesses(r1.value, r2.value));
	}

	var w1 = r1.get(__);
	var w2 = r2.get(__);
	var w = walk(w1, w2);
	var target;

	function examineKey(key) {
	    if (key !== __) {
		var k1 = r1.get(key);
		var k2 = r2.get(key);
		var updatedK;
		if (is_emptyMatcher(k2)) {
		    updatedK = walkWild(key, k1, w2);
		} else {
		    updatedK = walk(k1, k2);
		}
		// Here we ensure a "minimal" remainder in cases
		// where after an erasure, a particular key's
		// continuation is the same as the wildcard's
		// continuation. TODO: the matcherEquals check may
		// be expensive. If so, how can it be made
		// cheaper?
		if (is_keyOpen(key)) {
		    rupdateInplace(target, key,
				   ((updatedK instanceof $WildcardSequence) &&
				    matcherEquals(updatedK.matcher, w))
				   ? emptyMatcher
				   : updatedK);
		} else if (is_keyClose(key)) {
		    // We take care of this case later, after the
		    // target is fully constructed/rebuilt.
		    rupdateInplace(target, key, updatedK);
		} else {
		    rupdateInplace(target, key,
				   (matcherEquals(updatedK, w) ? emptyMatcher : updatedK));
		}
	    }
	}

	if (is_emptyMatcher(w2)) {
	    target = r1.copy();
	    for (var key in r2.entries) examineKey(key);
	} else {
	    target = new $Dict();
	    rupdateInplace(target, __, w);
	    for (var key in r1.entries) examineKey(key);
	    for (var key in r2.entries) examineKey(key);
	}

	// Here, the target is complete. If it has only two keys,
	// one wild and one is_keyClose, and wild's continuation
	// is a $WildcardSequence and the other continuation is
	// identical to the sequence's continuation, then replace
	// the whole thing with a nested $WildcardSequence.
	// (We know w === target.get(__) from before.)
	//
	// TODO: I suspect actually this applies even if there are
	// more than two keys, so long as all their continuations
	// are identical and there's at least one is_keyClose
	// alongside a wild.
	if (target.length === 2) {
	    var finalW = target.get(__);
	    if (finalW instanceof $WildcardSequence) {
		for (var key in target.entries) {
		    if ((key !== __) && is_keyClose(key)) {
			var k = target.get(key);
			if (matcherEquals(k, finalW.matcher)) {
			    return finalW;
			}
		    }
		}
	    }
	}

	return target.emptyGuard();
    }

    function walkWild(key, k, w) {
	if (is_emptyMatcher(w)) return k;
	if (is_keyOpen(key)) return walk(k, rwildseq(w));
	if (is_keyClose(key)) {
	    if (w instanceof $WildcardSequence) return walk(k, w.matcher);
	    return k;
	}
	return walk(k, w);
    }
}

// Returns null on failed match, otherwise the appropriate success
// value contained in the matcher r.
function matchValue(r, v) {
    var failureResult = null;

    var vs = [v];
    var stack = [[]];

    while (!is_emptyMatcher(r)) {
	if (r instanceof $WildcardSequence) {
	    if (stack.length === 0) return failureResult;
	    vs = stack.pop();
	    r = r.matcher;
	    continue;
	}

	if (r instanceof $Success) {
	    if (vs.length === 0 && stack.length === 0) return r.value;
	    return failureResult;
	}

	if (vs.length === 0) {
	    if (stack.length === 0) return failureResult;
	    vs = stack.pop();
	    r = r.get(EOA);
	    continue;
	}

	var v = vs.shift();

	if (typeof v === 'string' && v.substring(0, 2) === '__') {
	    die("Cannot match special string starting with __");
	}

	if (Array.isArray(v)) {
	    if (SOA in r.entries) {
		r = r.get(SOA);
		stack.push(vs);
		vs = shallowCopyArray(v);
	    } else {
		r = r.get(__);
	    }
	} else {
	    var key;
	    try {
		key = JSON.stringify(v);
	    } catch (exn) {
		// For example, v might be cyclic, as in DOM events.
		key = null;
	    }
	    if (key in r.entries) {
		r = r.get(key);
	    } else {
		r = r.get(__);
	    }
	}
    }

    return failureResult;
}

// TODO: better name for this
function matchMatcher(o1, o2, seed) {
    var acc = typeof seed === 'undefined' ? {} : seed; // will be modified in place
    walk(o1, o2);
    return acc;

    function walkFlipped(r2, r1) { return walk(r1, r2); }

    function walk(r1, r2) {
	if (is_emptyMatcher(r1) || is_emptyMatcher(r2)) return;

	if (r1 instanceof $WildcardSequence) {
	    if (r2 instanceof $WildcardSequence) {
		walk(r1.matcher, r2.matcher);
		return;
	    }
	    r1 = expandWildseq(r1.matcher);
	} else if (r2 instanceof $WildcardSequence) {
	    r2 = expandWildseq(r2.matcher);
	}

	if (r1 instanceof $Success && r2 instanceof $Success) {
	    matchMatcherSuccesses(r1.value, r2.value, acc);
	    return;
	}

	var w1 = r1.get(__);
	var w2 = r2.get(__);
	walk(w1, w2);

	function examineKey(key) {
	    if (key !== __) {
		var k1 = r1.get(key);
		var k2 = r2.get(key);
		if (is_emptyMatcher(k1)) {
		    if (is_emptyMatcher(k2)) {
			return;
		    } else {
			walkWild(walk, w1, key, k2);
		    }
		} else {
		    if (is_emptyMatcher(k2)) {
			walkWild(walkFlipped, w2, key, k1);
		    } else {
			walk(k1, k2);
		    }
		}
	    }
	}

	// Optimize similarly to intersect().
	if (is_emptyMatcher(w1)) {
	    if (is_emptyMatcher(w2)) {
		for (var key in (r1.length < r2.length ? r1 : r2).entries) examineKey(key);
	    } else {
		for (var key in r1.entries) examineKey(key);
	    }
	} else {
	    if (is_emptyMatcher(w2)) {
		for (var key in r2.entries) examineKey(key);
	    } else {
		for (var key in r1.entries) examineKey(key);
		for (var key in r2.entries) examineKey(key);
	    }
	}
    }

    function walkWild(walker, w, key, k) {
	if (is_emptyMatcher(w)) return;
	if (is_keyOpen(key)) {
	    walker(rwildseq(w), k);
	    return;
	}
	if (is_keyClose(key)) {
	    if (w instanceof $WildcardSequence) walker(w.matcher, k);
	    return;
	}
	walker(w, k);
    }
}

function appendMatcher(m, mTailFn) {
    return walk(m);

    function walk(m) {
	if (is_emptyMatcher(m)) return emptyMatcher;
	if (m instanceof $WildcardSequence) return rwildseq(walk(m.matcher));
	if (m instanceof $Success) die("Ill-formed matcher");

	var target = new $Dict();
	for (var key in m.entries) {
	    var k = m.get(key);
	    if (is_keyClose(key) && (k instanceof $Success)) {
		target = union(target, mTailFn(k.value));
	    } else {
		rupdateInplace(target, key, walk(k));
	    }
	}
	return target.emptyGuard();
    }
}

function relabel(m, f) {
    return walk(m);

    function walk(m) {
	if (is_emptyMatcher(m)) return emptyMatcher;
	if (m instanceof $WildcardSequence) return rwildseq(walk(m.matcher));
	if (m instanceof $Success) return rsuccess(f(m.value));

	var target = new $Dict();
	for (var key in m.entries) {
	    rupdateInplace(target, key, walk(m.get(key)));
	}
	return target.emptyGuard();
    }
}

function compileProjection(/* projection, projection, ... */) {
    var acc = [];
    for (var i = 0; i < arguments.length; i++) {
	walk(arguments[i]);
    }
    acc.push(EOA);
    return acc;

    function walk(p) {
	if (isCapture(p)) {
	    acc.push(SOC);
	    walk(capturePattern(p));
	    acc.push(EOC);
	    return;
	}

	if (Array.isArray(p)) {
	    acc.push(SOA);
	    for (var i = 0; i < p.length; i++) {
		walk(p[i]);
	    }
	    acc.push(EOA);
	    return;
	}

	if (p instanceof $Embedded) {
	    die("Cannot embed matcher in projection");
	} else {
	    if (p === __) {
		acc.push(p);
	    } else {
		acc.push(JSON.stringify(p));
	    }
	}
    }
}

function projectionToPattern(p) {
    return walk(p);

    function walk(p) {
	if (isCapture(p)) return walk(capturePattern(p));

	if (Array.isArray(p)) {
	    var result = [];
	    for (var i = 0; i < p.length; i++) {
		result.push(walk(p[i]));
	    }
	    return result;
	}

	if (p instanceof $Embedded) {
	    return p.matcher;
	} else {
	    return p;
	}
    }
}

function project(m, spec) {
    return walk(false, m, 0);

    function walk(isCapturing, m, specIndex) {
	if (specIndex >= spec.length) {
	    if (isCapturing) die("Bad specification: unclosed capture");
	    if (m instanceof $Success) {
		return rseq(EOA, rsuccess(projectSuccess(m.value)));
	    } else {
		return emptyMatcher;
	    }
	}

	if (is_emptyMatcher(m)) return emptyMatcher;

	var item = spec[specIndex];
	var nextIndex = specIndex + 1;

	if (item === EOC) {
	    if (!isCapturing) die("Bad specification: unepxected EOC");
	    return walk(false, m, nextIndex);
	}

	if (item === SOC) {
	    if (isCapturing) die("Bad specification: nested capture");
	    return walk(true, m, nextIndex);
	}

	if (item === __) {
	    if (m instanceof $WildcardSequence) {
		if (isCapturing) {
		    return rwild(walk(isCapturing, m, nextIndex));
		} else {
		    return walk(isCapturing, m, nextIndex);
		}
	    }

	    if (m instanceof $Success) {
		return emptyMatcher;
	    }

	    var target;
	    if (isCapturing) {
		target = new $Dict();
		rupdateInplace(target, __, walk(isCapturing, m.get(__), nextIndex));
		for (var key in m.entries) {
		    if (key !== __) {
			var mk = m.get(key);
			if (is_keyOpen(key)) {
			    function cont(mk2) { return walk(isCapturing, mk2, nextIndex); }
			    rupdateInplace(target, key, captureNested(mk, cont));
			} else if (is_keyClose(key)) {
			    // do nothing
			} else {
			    rupdateInplace(target, key, walk(isCapturing, mk, nextIndex));
			}
		    }
		}
	    } else {
		target = walk(isCapturing, m.get(__), nextIndex);
		for (var key in m.entries) {
		    if (key !== __) {
			var mk = m.get(key);
			if (is_keyOpen(key)) {
			    function cont(mk2) { return walk(isCapturing, mk2, nextIndex); }
			    target = union(target, skipNested(mk, cont));
			} else if (is_keyClose(key)) {
			    // do nothing
			} else {
			    target = union(target, walk(isCapturing, mk, nextIndex));
			}
		    }
		}
	    }
	    return target;
	}

	var result;
	if (m instanceof $WildcardSequence) {
	    if (is_keyOpen(item)) {
		result = walk(isCapturing, rwildseq(m), nextIndex);
	    } else if (is_keyClose(item)) {
		result = walk(isCapturing, m.matcher, nextIndex);
	    } else {
		result = walk(isCapturing, m, nextIndex);
	    }
	} else if (m instanceof $Success) {
	    result = emptyMatcher;
	} else {
	    if (is_keyOpen(item)) {
		result = walk(isCapturing, rwildseq(m.get(__)), nextIndex);
	    } else if (is_keyClose(item)) {
		result = emptyMatcher;
	    } else {
		result = walk(isCapturing, m.get(__), nextIndex);
	    }
	    result = union(result, walk(isCapturing, m.get(item), nextIndex));
	}
	if (isCapturing) {
	    result = rseq(item, result);
	}
	return result;
    }

    function captureNested(m, cont) {
	if (m instanceof $WildcardSequence) {
	    return rwildseq(cont(m.matcher));
	}

	if (is_emptyMatcher(m) || (m instanceof $Success)) {
	    return emptyMatcher;
	}

	var target = new $Dict();
	rupdateInplace(target, __, captureNested(m.get(__), cont));
	for (var key in m.entries) {
	    if (key !== __) {
		var mk = m.get(key);
		if (is_keyOpen(key)) {
		    function cont2(mk2) { return captureNested(mk2, cont); }
		    rupdateInplace(target, key, captureNested(mk, cont2));
		} else if (is_keyClose(key)) {
		    rupdateInplace(target, key, cont(mk));
		} else {
		    rupdateInplace(target, key, captureNested(mk, cont));
		}
	    }
	}
	return target.emptyGuard();
    }

    function skipNested(m, cont) {
	if (m instanceof $WildcardSequence) {
	    return cont(m.matcher);
	}

	if (is_emptyMatcher(m) || (m instanceof $Success)) {
	    return emptyMatcher;
	}

	var target = skipNested(m.get(__), cont);
	for (var key in m.entries) {
	    if (key !== __) {
		var mk = m.get(key);
		if (is_keyOpen(key)) {
		    function cont2(mk2) { return skipNested(mk2, cont); }
		    target = union(target, skipNested(mk, cont2));
		} else if (is_keyClose(key)) {
		    target = union(target, cont(mk));
		} else {
		    target = union(target, skipNested(mk, cont));
		}
	    }
	}
	return target;
    }
}

function matcherKeys(m) {
    if (is_emptyMatcher(m)) return [];
    return walkSeq(m, function (vss, vsk) { return vss; });

    function walk(m, k) {
	if (m instanceof $WildcardSequence) return null;
	if (m instanceof $Success) return [];
	if (m.has(__)) return null;
	var acc = [];
	for (var key in m.entries) {
	    var mk = m.get(key);
	    var piece;
	    if (is_keyOpen(key)) {
		function seqK(vss, vsk) {
		    var acc = [];
		    for (var i = 0; i < vss.length; i++) {
			var vs = vss[i];
			acc = acc.concat(k(transformSeqs(vs, key), vsk));
		    }
		    return acc;
		}
		piece = walkSeq(mk, seqK);
	    } else if (is_keyClose(key)) {
		die("matcherKeys: internal error: unexpected key-close");
	    } else {
		piece = k(JSON.parse(key), mk);
	    }
	    if (piece == null) return null;
	    acc = acc.concat(piece);
	}
	return acc;
    }

    function walkSeq(m, k) {
	if (m instanceof $WildcardSequence) return null;
	if (m instanceof $Success) return k([], emptyMatcher); // TODO: ??
	if (m.has(__)) return null;
	var acc = [];
	for (var key in m.entries) {
	    var mk = m.get(key);
	    var piece;
	    if (is_keyClose(key)) {
		piece = k([[]], mk);
	    } else {
		function outerK(v, vk) {
		    return walkSeq(vk, innerK);
		    function innerK(vss, vsk) {
			var acc = [];
			for (var i = 0; i < vss.length; i++) {
			    var vs = shallowCopyArray(vss[i]);
			    vs.unshift(v);
			    acc.push(vs);
			}
			return k(acc, vsk);
		    }
		}
		piece = walk(rseq(key, mk), outerK);
	    }
	    if (piece == null) return null;
	    acc = acc.concat(piece);
	}
	return acc;
    }

    function transformSeqs(vs, opener) {
	if (opener === SOA) return vs;
	die("Internal error: unknown opener " + opener);
    }
}

function prettyMatcher(m, initialIndent) {
    var acc = [];
    walk(initialIndent || 0, m);
    return acc.join('');

    function walk(i, m) {
	if (is_emptyMatcher(m)) {
	    acc.push("::: no further matches possible");
	    return;
	}
	if (m instanceof $WildcardSequence) {
	    acc.push("...>");
	    walk(i + 4, m.matcher);
	    return;
	}
	if (m instanceof $Success) {
	    var vs = JSON.stringify(typeof m.value === 'object'
				    ? setToArray(m.value)
				    : m.value);
	    acc.push("{" + vs + "}");
	    return;
	}

	if (m.length === 0) {
	    acc.push(" ::: empty hash!");
	    return;
	}

	var needSep = false;
	var keys = m.sortedKeys();
	for (var keyi = 0; keyi < keys.length; keyi++) {
	    var key = keys[keyi];
	    var k = m.entries[key];
	    if (needSep) {
		acc.push("\n");
		acc.push(indentStr(i));
	    } else {
		needSep = true;
	    }
	    acc.push(" ");
	    if (key === __) key = '★';
	    if (key === SOA) key = '<';
	    if (key === EOA) key = '>';
	    acc.push(key);
	    walk(i + key.length + 1, k);
	}
    }

    function indentStr(i) {
	return new Array(i + 1).join(' '); // eww
    }
}

function serializeMatcher(m, serializeSuccess) {
    return walk(m);
    function walk(m) {
	if (is_emptyMatcher(m)) return [];
	if (m instanceof $WildcardSequence) {
	    return ["...)", walk(m.matcher)];
	}
	if (m instanceof $Success) {
	    return ["", serializeSuccess(m.value)];
	}
	var acc = [];
	for (var key in m.entries) {
	    var k = m.entries[key];
	    if (key === __) key = ["__"];
	    else if (key === SOA) key = ["("];
	    else if (key === EOA) key = [")"];
	    else key = JSON.parse(key);
	    acc.push([key, walk(k)]);
	}
	return acc;
    }
}

function deserializeMatcher(r, deserializeSuccess) {
    return walk(r);
    function walk(r) {
	if (r.length === 0) return emptyMatcher;
	if (r[0] === "...)") return rwildseq(walk(r[1]));
	if (r[0] === "") return rsuccess(deserializeSuccess(r[1]));
	var acc = new $Dict();
	for (var i = 0; i < r.length; i++) {
	    var rkey = r[i][0];
	    var rk = r[i][1];
	    var key;
	    if (Array.isArray(rkey)) {
		switch (rkey[0]) {
		case "__": key = __; break;
		case "(": key = SOA; break;
		case ")": key = EOA; break;
		default: die("Invalid serialized special key: " + rkey[0]);
		}
	    } else {
		key = JSON.stringify(rkey);
	    }
	    rupdateInplace(acc, key, walk(rk));
	}
	return acc;
    }
}

///////////////////////////////////////////////////////////////////////////
// Gestalts.
// TODO: support Infinity as a level number

function GestaltLevel(subs, advs) {
    this.subscriptions = subs;
    this.advertisements = advs;
}

GestaltLevel.prototype.isEmpty = function () {
    return is_emptyMatcher(this.subscriptions) && is_emptyMatcher(this.advertisements);
};

GestaltLevel.prototype.equals = function (other) {
    return matcherEquals(this.subscriptions, other.subscriptions)
	&& matcherEquals(this.advertisements, other.advertisements);
};

GestaltLevel.prototype.pretty = function () {
    var acc = [];
    if (!is_emptyMatcher(this.subscriptions)) {
	acc.push("  - subs:");
	acc.push(prettyMatcher(this.subscriptions, 9));
	acc.push("\n");
    }
    if (!is_emptyMatcher(this.advertisements)) {
	acc.push("  - advs:");
	acc.push(prettyMatcher(this.advertisements, 9));
	acc.push("\n");
    }
    return acc.join('');
};

function straightGestaltLevelOp(op) {
    return function (p1, p2) {
	return new GestaltLevel(op(p1.subscriptions, p2.subscriptions),
				op(p1.advertisements, p2.advertisements));
    };
};

var emptyLevel = new GestaltLevel(emptyMatcher, emptyMatcher);
var emptyMetaLevel = [];

function Gestalt(metaLevels) {
    this.metaLevels = metaLevels;
}

Gestalt.prototype.getMetaLevel = function (n) {
    return this.metaLevels[n] || emptyMetaLevel;
};

Gestalt.prototype.getLevel = function (metaLevel, level) {
    return this.getMetaLevel(metaLevel)[level] || emptyLevel;
};

Gestalt.prototype.metaLevelCount = function () { return this.metaLevels.length; };
Gestalt.prototype.levelCount = function (n) { return this.getMetaLevel(n).length; };

Gestalt.prototype.matchValue = function (body, metaLevel, isFeedback) {
    var levels = this.getMetaLevel(metaLevel);
    var pids = {};
    for (var i = 0; i < levels.length; i++) {
	var matcher = (isFeedback ? levels[i].advertisements : levels[i].subscriptions);
	setUnionInplace(pids, matchValue(matcher, body));
    }
    return setToArray(pids);
};

Gestalt.prototype.project = function (spec, getAdvertisements, metaLevel, level) {
    var l = this.getLevel(metaLevel | 0, level | 0);
    var matcher = (getAdvertisements ? l.advertisements : l.subscriptions);
    return project(matcher, spec);
};

Gestalt.prototype.drop = function () {
    var mls = shallowCopyArray(this.metaLevels);
    mls.shift();
    return new Gestalt(mls);
};

Gestalt.prototype.lift = function () {
    var mls = shallowCopyArray(this.metaLevels);
    mls.unshift(emptyMetaLevel);
    return new Gestalt(mls);
};

Gestalt.prototype.equals = function (other) {
    if (this.metaLevels.length !== other.metaLevels.length) return false;
    for (var i = 0; i < this.metaLevels.length; i++) {
	var ls1 = this.metaLevels[i];
	var ls2 = other.metaLevels[i];
	if (ls1.length !== ls2.length) return false;
	for (var j = 0; j < ls1.length; j++) {
	    var p1 = ls1[j];
	    var p2 = ls2[j];
	    if (!p1.equals(p2)) return false;
	}
    }
    return true;
};

function simpleGestalt(isAdv, pat, metaLevel, level) {
    metaLevel = metaLevel || 0;
    level = level || 0;
    var matcher = compilePattern(true, pat);
    var l = new GestaltLevel(isAdv ? emptyMatcher : matcher,
			     isAdv ? matcher : emptyMatcher);
    var levels = [l];
    while (level--) { levels.unshift(emptyLevel); }
    var metaLevels = [levels];
    while (metaLevel--) { metaLevels.unshift(emptyMetaLevel); }
    return new Gestalt(metaLevels);
}

var emptyGestalt = new Gestalt([]);

// Not quite what it says on the tin - the true fullGestalt
// wouldn't be parameterized on the number of levels and
// metalevels, but instead would be full at *all* levels and
// metalevels. Our representation leaks through into the interface
// here :-/
function fullGestalt(nMetalevels, nLevels) {
    var matcher = compilePattern(true, __);
    var l = new GestaltLevel(matcher, matcher);
    var levels = [];
    while (nLevels--) { levels.push(l); }
    var metaLevels = [];
    while (nMetalevels--) { metaLevels.push(levels); }
    return new Gestalt(metaLevels);
}

Gestalt.prototype.isEmpty = function () {
    for (var i = 0; i < this.metaLevels.length; i++) {
	var levels = this.metaLevels[i];
	for (var j = 0; j < levels.length; j++) {
	    if (!levels[j].isEmpty()) return false;
	}
    }
    return true;
};

function maybePushLevel(levels, i, level) {
    if (!level.isEmpty()) {
	while (levels.length < i) levels.push(emptyLevel);
	levels.push(level);
    }
}

function maybePushMetaLevel(metaLevels, i, metaLevel) {
    if (metaLevel.length > 0) {
	while (metaLevels.length < i) metaLevels.push(emptyMetaLevel);
	metaLevels.push(metaLevel);
    }
}

Gestalt.prototype.mapZip = function (other, lengthCombiner, f) {
    var metaLevels = [];
    var mls1 = this.metaLevels;
    var mls2 = other.metaLevels;
    var nm = lengthCombiner(mls1.length, mls2.length);
    for (var i = 0; i < nm; i++) {
	var levels = [];
	var ls1 = mls1[i] || emptyMetaLevel;
	var ls2 = mls2[i] || emptyMetaLevel;
	var nl = lengthCombiner(ls1.length, ls2.length);
	for (var j = 0; j < nl; j++) {
	    var p1 = ls1[j] || emptyLevel;
	    var p2 = ls2[j] || emptyLevel;
	    var p = f(p1, p2);
	    maybePushLevel(levels, j, p);
	}
	maybePushMetaLevel(metaLevels, i, levels);
    }
    return new Gestalt(metaLevels);
};

Gestalt.prototype.union1 = function (other) {
    return this.mapZip(other, Math.max, straightGestaltLevelOp(union));
};

function gestaltUnion(gs) {
    if (gs.length === 0) return emptyGestalt;
    var acc = gs[0];
    for (var i = 1; i < gs.length; i++) {
	acc = acc.union1(gs[i]);
    }
    return acc;
}

Gestalt.prototype.union = function () {
    return arguments.length > 0 ? this.union1(gestaltUnion(arguments)) : this;
};

// Accumulates matchers from higher-numbered levels into
// lower-numbered levels.
function telescopeLevels(levels) {
    var result = shallowCopyArray(levels);
    for (var i = result.length - 2; i >= 0; i--) {
	result[i] =
	    new GestaltLevel(union(result[i].subscriptions, result[i+1].subscriptions),
			     union(result[i].advertisements, result[i+1].advertisements));
    }
    return result;
};

Gestalt.prototype.telescoped = function () {
    var mls = [];
    for (var i = 0; i < this.metaLevels.length; i++) {
	mls.push(telescopeLevels(this.metaLevels[i]));
    }
    return new Gestalt(mls);
};

Gestalt.prototype.filter = function (perspective) {
    var metaLevels = [];
    var mls1 = this.metaLevels;
    var mls2 = perspective.metaLevels;
    var nm = Math.min(mls1.length, mls2.length);
    for (var i = 0; i < nm; i++) {
	var levels = [];
	var ls1 = mls1[i] || emptyMetaLevel;
	var ls2 = mls2[i] || emptyMetaLevel;
	var nl = Math.min(ls1.length, ls2.length - 1);
	for (var j = 0; j < nl; j++) {
	    var p1 = ls1[j] || emptyLevel;
	    var subs = emptyMatcher;
	    var advs = emptyMatcher;
	    for (var k = j + 1; k < ls2.length; k++) {
		var p2 = ls2[k] || emptyLevel;
		subs = union(subs, intersect(p1.subscriptions, p2.advertisements));
		advs = union(advs, intersect(p1.advertisements, p2.subscriptions));
	    }
	    maybePushLevel(levels, j, new GestaltLevel(subs, advs));
	}
	maybePushMetaLevel(metaLevels, i, levels);
    }
    return new Gestalt(metaLevels);
};

Gestalt.prototype.match = function (perspective) {
    var pids = {};
    var nm = Math.min(this.metaLevels.length, perspective.metaLevels.length);
    for (var i = 0; i < nm; i++) {
	var ls1 = this.metaLevels[i] || emptyMetaLevel;
	var ls2 = perspective.metaLevels[i] || emptyMetaLevel;
	var nl = Math.min(ls1.length, ls2.length - 1);
	for (var j = 0; j < nl; j++) {
	    var p1 = ls1[j] || emptyLevel;
	    for (var k = j + 1; k < ls2.length; k++) {
		var p2 = ls2[k] || emptyLevel;
		matchMatcher(p1.subscriptions, p2.advertisements, pids);
		matchMatcher(p1.advertisements, p2.subscriptions, pids);
	    }
	}
    }
    return setToArray(pids);
};

Gestalt.prototype.erasePath = function (path) {
    return this.mapZip(path, Math.max, straightGestaltLevelOp(erasePath));
};

function mapLevels(inputMetaLevels, f, emptyCheck, inputEmptyLevel, outputEmptyLevel) {
    var outputMetaLevels = [];
    for (var i = 0; i < inputMetaLevels.length; i++) {
	var ls = inputMetaLevels[i];
	var levels = [];
	for (var j = 0; j < ls.length; j++) {
	    var p = f(ls[j] || inputEmptyLevel, i, j);
	    if (!emptyCheck(p, i, j)) {
		while (levels.length < j) levels.push(outputEmptyLevel);
		levels.push(p);
	    }
	}
	if (levels.length > 0) {
	    while (outputMetaLevels.length < i) outputMetaLevels.push(emptyMetaLevel);
	    outputMetaLevels.push(levels);
	}
    }
    return outputMetaLevels;
};

Gestalt.prototype.transform = function (f) {
    return new Gestalt(mapLevels(this.metaLevels, function (p, ml, l) {
	return new GestaltLevel(f(p.subscriptions, ml, l, false),
				f(p.advertisements, ml, l, true));
    }, function (p) {
	return p.isEmpty();
    }, emptyLevel, emptyLevel));
};

Gestalt.prototype.stripLabel = function () {
    return this.transform(function (m) { return relabel(m, function (v) { return true; }); });
};

Gestalt.prototype.label = function (pid) {
    var pids = arrayToSet([pid]);
    return this.transform(function (m) { return relabel(m, function (v) { return pids; }); });
};

Gestalt.prototype.pretty = function () {
    var acc = [];
    if (this.isEmpty()) {
	acc.push("EMPTY GESTALT\n");
    } else {
	for (var i = 0; i < this.metaLevels.length; i++) {
	    var ls = this.metaLevels[i];
	    for (var j = 0; j < ls.length; j++) {
		var p = ls[j];
		if (!p.isEmpty()) {
		    acc.push("GESTALT metalevel " + i + " level " + j + ":\n");
		    acc.push(p.pretty());
		}
	    }
	}
    }
    return acc.join('');
};

Gestalt.prototype.serialize = function (serializeSuccess) {
    if (typeof serializeSuccess === 'undefined') {
	serializeSuccess = function (v) { return v === true ? true : setToArray(v); };
    }
    return ["gestalt", mapLevels(this.metaLevels, function (p) {
	return [serializeMatcher(p.subscriptions, serializeSuccess),
		serializeMatcher(p.advertisements, serializeSuccess)];
    }, function (pr) {
	return pr.length === 2 && pr[0].length === 0 && pr[1].length === 0;
    }, emptyLevel, [[],[]])];
};

function deserializeGestalt(r, deserializeSuccess) {
    if (typeof deserializeSuccess === 'undefined') {
	deserializeSuccess = function (v) { return v === true ? true : arrayToSet(v); };
    }
    if (r[0] !== "gestalt") die("Invalid gestalt serialization: " + r);
    return new Gestalt(mapLevels(r[1], function (pr) {
	return new GestaltLevel(deserializeMatcher(pr[0], deserializeSuccess),
				deserializeMatcher(pr[1], deserializeSuccess));
    }, function (p) {
	return p.isEmpty();
    }, [[],[]], emptyLevel));
}

///////////////////////////////////////////////////////////////////////////

module.exports.__ = __;
module.exports.arrayToSet = arrayToSet;
module.exports.setToArray = setToArray;
module.exports.setUnion = setUnion;
module.exports.setSubtract = setSubtract;
module.exports.setIntersect = setIntersect;
module.exports.setEqual = setEqual;
module.exports.is_emptySet = is_emptySet;
module.exports.$Capture = $Capture;
module.exports._$ = _$;
module.exports.is_emptyMatcher = is_emptyMatcher;
module.exports.emptyMatcher = emptyMatcher;
module.exports.embeddedMatcher = embeddedMatcher;
module.exports.compilePattern = compilePattern;
module.exports.union = unionN;
module.exports.intersect = intersect;
module.exports.erasePath = erasePath;
module.exports.matchValue = matchValue;
module.exports.matchMatcher = matchMatcher;
module.exports.appendMatcher = appendMatcher;
module.exports.relabel = relabel;
module.exports.compileProjection = compileProjection;
module.exports.projectionToPattern = projectionToPattern;
module.exports.project = project;
module.exports.matcherKeys = matcherKeys;
module.exports.matcherEquals = matcherEquals;
module.exports.prettyMatcher = prettyMatcher;
module.exports.serializeMatcher = serializeMatcher;
module.exports.deserializeMatcher = deserializeMatcher;

module.exports.GestaltLevel = GestaltLevel;
module.exports.Gestalt = Gestalt;
module.exports.simpleGestalt = simpleGestalt;
module.exports.emptyGestalt = emptyGestalt;
module.exports.fullGestalt = fullGestalt;
module.exports.gestaltUnion = gestaltUnion;
module.exports.deserializeGestalt = deserializeGestalt;