singleton-bayes

singleton-bayes explores dependent-style Bayesian programming in ordinary Haskell. It combines singletons and monad-bayes so inference stays in familiar probabilistic monads while model structure is indexed at the type level.

Why this library is unique

In much of the Haskell PPL ecosystem, one typically chooses between:

• dynamic model selection with runtime tags, or
• static models with one fixed latent/evidence shape.

singleton-bayes makes a different trade: model families are higher-kinded (model :: k -> Type), and each index carries its own latent and evidence types. Singleton witnesses transport that index from runtime to types, so one program can remain generic while each branch stays precise.

Toward a fuller inference framework: heart-failure counselling

DependentBayes.Clinical is a working inference model that shows what this abstraction is for.

A clinical workup is indexed by the ClinicalPhase kind. HeartModel :: ClinicalPhase -> Type satisfies the higher-kinded class constraint DependentModel (model :: k -> Type) at k = ClinicalPhase. Three closed type families then map each phase index to structurally distinct latent, evidence, and prediction types:

Phase	LatentState	Evidence	Prediction
'RiskAssessment	RiskScore	PatientVitals	RiskScore
'BehaviorGap	(RiskScore, ComplianceScore)	(PatientVitals, BehaviorSurvey)	same
'CounselAction	(RiskScore, ComplianceScore)	(PatientVitals, BehaviorSurvey)	[ClinicalAction]

The central clinical insight is the belief–behaviour gap: a patient's heart-failure risk inferred from objective vitals may substantially exceed the risk implied by their self-reported behaviour. At the 'CounselAction phase the predict hook converts the continuous posterior (risk, compliance) into a typed recommendation list, and the demo now packages that output with a clinician-facing rationale and a patient-facing explanation:

deriveActions :: RiskScore -> ComplianceScore -> [ClinicalAction]
deriveActions risk compliance =
  case (risk >= 0.60, risk - compliance >= 0.25) of
    (True,  True)  -> [ReferToCardiologist, MedicationCounseling, ReduceSodiumIntake, RecommendExercise]
    (True,  False) -> [MedicationCounseling, ContinueMonitoring, RecommendExercise]
    (False, True)  -> [ReduceSodiumIntake, RecommendExercise, ContinueMonitoring]
    (False, False) -> [ContinueMonitoring]

-- A clinician-guided package that also makes the reasoning visible to the patient.
data Recommendation = Recommendation
  { recommendationActions :: [ClinicalAction]
  , clinicianRationale     :: String
  , patientExplanation     :: String
  }

A patient with systolic BP 145 mmHg, ejection fraction 40 %, low self-reported exercise and medication adherence yields risk ≈ 0.72, compliance ≈ 0.30 — a gap of 0.42 — and the full intervention stack. The demo now surfaces both the action list and the explanation text so the recommendation can be discussed as part of the clinician-patient relationship rather than as a standalone machine output.

The type checker enforces this routing: [ClinicalAction] is the Prediction type only at 'CounselAction. Passing SCounselAction where a 'RiskAssessment-indexed function is expected is a compile error.

The three convenience wrappers hide the singleton machinery from callers entirely:

heartRiskPosterior        :: (MonadDistribution m, MonadFactor m)
                          => PatientVitals -> m RiskScore
heartBehaviorGapPosterior :: (MonadDistribution m, MonadFactor m)
                          => (PatientVitals, BehaviorSurvey) -> m (RiskScore, ComplianceScore)
heartCounsel              :: (MonadDistribution m, MonadFactor m)
                          => (PatientVitals, BehaviorSurvey)
                          -> m ((RiskScore, ComplianceScore), [ClinicalAction])

Modules

• DependentBayes.Types: index kind (Mode) and type families
• DependentBayes.Singleton: polymorphic singleton data family
• DependentBayes.Singleton.Mode: Mode-specific singleton instances
• DependentBayes.Singleton.Clinical: ClinicalPhase-specific singleton instances
• DependentBayes.Core: DependentModel class and posterior combinators
• DependentBayes.Example: toy model showing index-specific types
• DependentBayes.Clinical.Types: ClinicalPhase kind (separated to break import cycle)
• DependentBayes.Clinical: heart-failure counselling model; Beta priors, Normal likelihoods, deriveActions, and the new Recommendation wrapper for shared decision support

Quick try

cabal run singleton-bayes-demo

License

MIT