Hyperbole

// Define list of kettle prices under consideration (possible price states)
var states = [50, 51, 500, 501, 1000, 1001, 5000, 5001, 10000, 10001];

// Prior probability of kettle prices (taken from human experiments)
var statePrior = function() {
  return categorical({
    ps: [0.4205, 0.3865, 0.0533, 0.0538, 0.0223, 0.0211, 0.0112, 0.0111, 0.0083, 0.0120],
    vs: states})
};

// Probability that given a price state, the speaker thinks it's too
// expensive (taken from human experiments)
var valencePriors = {
  50: 0.3173,
  51: 0.3173,
  500: 0.7920,
  501: 0.7920,
  1000: 0.8933,
  1001: 0.8933,
  5000: 0.9524,
  5001: 0.9524,
  10000: 0.9864,
  10001: 0.9864
};
var valencePrior = function(state) {
  return bernoulli(valencePriors[state]) //todo: convert to 1,0?
}


// Prior over QUDs (de-reference through qud name since mem 
// doesn't play nice with function values)
var qudPrior = function() {
  return categorical({
    ps:[0.17, 0.32, 0.17, 0.17, 0.17],
    vs:['s',  'v',  'sv', 'as', 'asv'] })
};

var qudFns = {
  s: function(state, valence){return state},
  v: function(state, valence){return valence},
  sv: function(state, valence){return [state, valence]},
  as: function(state, valence){return approx(state, 10)},
  asv: function(state, valence){return [approx(state, 10), valence]}
};


// Round x to nearest multiple of b (used for approximate interpretation):
var approx = function(x,b) {
  return b * Math.round(x / b)
};

// Define list of possible utterances (same as price states)
var utterances = states;

// Sharp numbers are costlier
var utterancePrior = function() {
  return categorical({
    vs: utterances,
    ps: [0.18, 0.1, 0.18, 0.1, 0.18, 0.1, 0.18, 0.1, 0.18, 0.1]})
};

// Literal interpretation "meaning" function, just check if uttered number
// reflects price state
var literalInterpretation = function(utterance, state) {
  return utterance == state;
}

// Literal listener, infers the qud value assuming the utterance is 
// true of the state
var litListener = cache(function(utterance, qud) {
  return Infer({method: 'enumerate'},
   function() {
    var state = statePrior()
    var valence = valencePrior(state)
    var qudfn = qudFns[qud]
    condition(literalInterpretation(utterance, state))
    return qudfn(state, valence)
  })
});

// Speaker, chooses an utterance to convey a particular value of the qud
var speaker = cache(function(val, qud){
  return Infer({method: 'enumerate'},
   function(){
    var utterance = utterancePrior()
    observe(litListener(utterance,qud), val)
    return utterance
  })
})

// Pragmatic listener, jointly infers the price state, speaker valence, and QUD
var pragListener = function(utterance) {
  return Infer({method: 'enumerate'},
   function(){
    var state = statePrior()
    var valence = valencePrior(state)
    var qud = qudPrior()
    var qudfn = qudFns[qud]
    observe(speaker(qudfn(state,valence), qud), utterance)
    return {state: state, valence: valence}
  })
}

viz.auto(pragListener(10000))