marked.wppl

var people = {
  "heights": [2, 6, 10, 14, 18, 22, 26, 30],
  "probabilities": [1, 2, 3, 4, 4, 3, 2, 1]
};

// generate a state of the form [john's height, bill's height]
var statePrior = function() {
  return [categorical(people.probabilities, people.heights),categorical(people.probabilities, people.heights)];
};

var thetaPrior = function() {
  return uniformDraw(people.heights);
};

var utterances = ["asTall", "asShort", "tall", "short", ""];
var cost = {
  "asTall": 1,
  "asShort": 2,
  "tall" : 1,
  "short" : 2,
  "": 0
};
var utterancePrior = function() {
  return uniformDraw(utterances);
};

var meaning = function(utterance, state, thetaTall, thetaShort) {
  utterance == "" ? true : 
  utterance == "tall" ? state[0] >= thetaTall :
  utterance == "short" ? state[0] <= thetaShort :
  state[0] == state[1] // you don't have the height in mind
//     state[0] == 18 // you have the height in mind
};

var QUDs = ["tall?","short?","height?"]
var QUDprior = function(){
  return uniformDraw(QUDs)
}
var QUDfns = {
  "tall?" : function(state,thetaTall,thetaShort){return state[0]>=thetaTall},
  "short?" : function(state,thetaTall,thetaShort){return state[0]<=thetaShort},
  "height?" : function(state,thetaTall,thetaShort){return state[0]}
}

var literalListener = cache(function(utterance,thetaTall,thetaShort, QUD) {
  return Infer({method: "enumerate"}, function() {
    var state = statePrior();
    var QUDfn = QUDfns[QUD]
    condition(meaning(utterance, state, thetaTall,thetaShort))
    return QUDfn(state,thetaTall,thetaShort);
  });
});

var speaker = cache(function(state,thetaTall,thetaShort, QUD, alpha) {
  return Infer({method: "enumerate"}, function() {
    var utterance = utterancePrior();
    var QUDfn = QUDfns[QUD]
    factor( alpha * (literalListener(utterance,thetaTall,thetaShort, QUD).score(QUDfn(state,thetaTall,thetaShort)) 
                     - cost[utterance]));
    return utterance;
  });
});

var pragmaticListener = function(utterance, alpha) {
  return Infer({method: "enumerate"}, function() {
    var state = statePrior();
    var thetaTall = thetaPrior();
    var thetaShort = thetaPrior();
    var QUD = QUDprior();
    factor(speaker(state,thetaTall,thetaShort, QUD, alpha).score(utterance));
    return { state: state[0] , qud: QUD};
  });
};

var diff = function(i) {
  var t = expectation(marginalize(pragmaticListener("asTall", i), "state"));
  var s = expectation(marginalize(pragmaticListener("asShort", i), "state"));
  return t - s;
}
map(function(i) {display("alpha = " + i); display(diff(i))}, [1,2,3,4,5,6,7,8,9,10])

// alpha = 1
// 3.552713678800501e-15
// alpha = 2
// 5.329070518200751e-15
// alpha = 3
// 1.7763568394002505e-15
// alpha = 4
// 1.7763568394002505e-15
// alpha = 5
// -1.0658141036401503e-14
// alpha = 6
// -8.881784197001252e-15
// alpha = 7
// 1.2434497875801753e-14
// alpha = 8
// -1.7763568394002505e-14
// alpha = 9
// -2.3092638912203256e-14
// alpha = 10
// 3.907985046680551e-14