Examples Gallery

.qvr programs spanning probabilistic regressions, latent-variable models, state-space models, language models, encoder-decoder networks, weighted deductions, and QIEC computations. Most full pages include a ## Try it section; CI executes runnable documentation blocks and skips blocks marked as illustrative. Pages with current model limitations identify them directly.

The measured transpilation corpus lives under docs/examples/source/. Mixed QIEC case studies whose purpose is reference-machine execution live under docs/examples/qiec/, so adding one does not silently expand the promised backend matrix.

Language feature map

Use this table when you want an example of a language feature rather than a particular statistical family.

Feature	Primary example	What to inspect
indexed families, authored handlers, computation calls, parser search, structural attachments, grouped marginalization	Amortized Bayesian Semantics	mixed entry list, effect trace, target-capability diagnostics
schema and bundle elaboration, generated search and weight effects	Schema-Bundled Chart Parser	classic chart against run_deduction
direct deduction, learned rule weights, program-to-deduction call	PCFG and CCG	inside weights, parameter store, scored parser call
structural signature, encoder, decoder, loss, typed PyTorch attachments	Term Autoencoder	Program.run("reconstruct", term) and autograd
grouped and fibred exact marginalization	Latent Dirichlet Allocation	over, via, and the per-group reduction
program templates and subprogram calls	Parametric Partial Pooling	static object arguments, prefixed sites, labeled tuple return
open sequence extent and recursive scan lowering	Vanilla RNN LM	generated scan step and trajectory site addresses
network kernel computation	Bayesian Neural Network	MLP parameter source and reference-machine boundary
measure-algebra families	Amortized Bayesian Semantics	heterogeneous Mixture value used for scoring and prediction
finite collection traversal, indexed effects, nested computation calls, lexical uncertainty	Lexical-Uncertainty RSA	map/fold normalization, traverse over worlds and lexica, lexical marginalization, observed-or-predicted interpretation

The generated transpilation support matrix records whether each measured source reaches each backend. A successful reference-machine run and a successful transpile are distinct claims; the examples state both where they differ.

Integrated QIEC case study

• Amortized Bayesian Semantics: a learnable categorial parser, structural logical-form autoencoder, indexed missing-data computation with a contamination measure, authored robustification handler, and hierarchical model with grouped exact marginalization.
• Lexical-Uncertainty RSA: the specificity model of Bergen, Levy, and Goodman (2016), with a literal listener nested inside a pragmatic speaker and a listener that traverses and marginalizes over three lexica.

Regressions

• Bayesian Linear Regression: Normal likelihood with Normal-prior weights.
• Beta Regression: Beta-distributed response with logit link.
• Gamma Regression: Gamma response with a log-shape predictor and unit rate.
• Horseshoe Regression: sparse linear regression under the horseshoe prior.
• Negative Binomial Regression: overdispersed count response.
• Continuous-gate Poisson Regression: differentiable relaxation of a zero-inflation gate.
• Item Response Theory (2PL): Rasch-style logistic IRT with item difficulty and discrimination.
• Weibull Survival: uncensored Weibull event-time regression; censored rows require an explicit survival-score term.

Latent-variable models

• Isotropic Bayesian Factor Model: low-rank factors and loadings with one shared observation scale.
• Probabilistic PCA: the isotropic factor model interpreted through its principal-component solution.
• Latent Dirichlet Allocation: topic model with Dirichlet priors on per-document and per-topic distributions.
• Gaussian Mixture Model: finite mixture with grouped marginalization over the cluster label.
• Latent Decoder and Encoder Paths: prior-decoder program plus a separately exported encoder-decoder path; the current SVI block does not use the encoder as its guide.
• Bayesian Neural Network: nonlinear regression through an MLP-parameterised Normal kernel, made Bayesian after lifting priors over its weights.
• Parametric Partial Pooling: random effects from a parametric program template, with a labeled return tuple, a score-step sum-to-zero factor, and export selection.
• Probabilistic Matrix Factorization: low-rank Bayesian completion of a sparse rating matrix.
• Bilinear Tensor Contraction: neural-tensor-layer scoring of predicate-argument pairs via an operadic three-way contraction.

State-space and time-series models

• AR(1): first-order autoregressive Normal scalar series.
• Changepoint Model: piecewise-constant means with a sampled change point.
• Conditionally Factorized Stochastic Volatility: AR(1) log-volatility conditionals with externally supplied lag values.
• Gaussian-Kernel SSM: learned transition, emission, and filtering kernels; not a closed-form Kalman filter.
• Finite-State Path Composition: product-fuzzy transition and emission relations, plus a partial discrete-program sketch.
• Continuous-State Sequence Model: Gaussian transition, emission, and separately learned recognition kernels.
• Deep Markov Model: nonlinear-MLP transition and emission cells.

Language models

• Vanilla RNN LM: single-cell Elman RNN scored by a Categorical head.
• GRU-shaped LM: stochastic reset and update gates with a simplified candidate update.
• LSTM-shaped LM: stochastic gates without a separately threaded cell state.
• Dual-RNN Masked-Token Model: two left-to-right scans combined for a masked-token target.
• Transformer-shaped LM: parallel MLP-normal branches with a Categorical head; no dot-product self-attention or causal mask.

Encoder-decoder and structured outputs

• Sequence-to-Sequence: parallel encoder-decoder branches joined by a learned merge, without attention.
• Tree-Structured Score Tensor: recursive additive scores over a parametric tree.

Weighted deductions

• PCFG: probabilistic context-free grammar with learnable production weights.
• CCG: combinatory categorial grammar with forward / backward application and composition.
• Type-Logical Grammar (Lambek): Lambek calculus with residuated slashes and tensor.
• PMCFG: probabilistic multiple context-free grammar with WH-movement via a rank-2 non-terminal.
• Schema-Bundled Chart Parser: pattern-polymorphic rule schemas bundled into a differentiable CKY chart parser.
• Term Autoencoder: a signature, encoder, decoder, and loss compressing typed lambda terms.
• Multimodal TLG: Lambek calculus extended with diamond and box modalities.
• Custom Sequent Rules: user-defined sequents over a free residuated category.
• Quantifier Scope: continuation-monad lift for generalized quantifiers.
• Montague NLI: Montague-style lambda-term LFs plus modus-ponens NLI prover.