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arxiv: 2505.09094 · v3 · submitted 2025-05-14 · 💻 cs.HC

PLanet: Formalizing and Analyzing Assignment Procedures in the Design of Experiments

London Bielicke , Anna Zhang , Shruti Tyagi , Emery Berger , Adam Chlipala , Eunice Jun This is my paper

Pith reviewed 2026-05-22 16:09 UTC · model grok-4.3

classification 💻 cs.HC
keywords experimental designcausal queriesdomain-specific languagematrix algebrastatic analysisconstraint satisfactionassignment procedures
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The pith

PLanet's grammar and matrix representation for experimental designs enable static analysis to identify testable causal queries under different assumptions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Experimental designs rest on assumptions about variable relationships that determine which causal questions can be answered. Existing tools leave these assumptions implicit, so researchers must reason about them manually. PLanet introduces a composable grammar of operators for building assignment procedures, expressed through matrix algebra and compiled into constraint satisfaction problems. This representation supports static analysis that automatically checks which causal queries are testable given specific assumptions. The result is more explicit design exploration and fewer overlooked assumptions about the variables involved.

Core claim

By defining a grammar of composable operators for assignment procedures and representing them in matrix algebra, PLanet compiles designs into constraint satisfaction problems. This allows a static analysis to determine the testability of causal queries under varying assumptions, making design choices and assumptions explicit without requiring full procedural code.

What carries the argument

Composable grammar of operators for assignment procedures, grounded in matrix algebra and compiled to constraint satisfaction problems over matrices.

Load-bearing premise

The matrix algebra representation and constraint satisfaction encoding must capture all relevant assumptions about variable relationships without omitting causal structure or introducing artifacts.

What would settle it

An experimental design in which PLanet's static analysis labels a causal query as testable but a manual causal graph analysis shows it is not identifiable, or the reverse.

Figures

Figures reproduced from arXiv: 2505.09094 by Adam Chlipala, Anna Zhang, Emery Berger, Eunice Jun, London Bielicke, Shruti Tyagi.

Figure 1
Figure 1. Figure 1: Composing designs in PLanet using cross and nest. In the crossed design (left), every row contains every condition of each variable but not every combination (e.g., X and Y appear with A and B, but not all combinations XA, XB, YA, YB appear in one row). In the nested design (right), the outer condition (A or B) is held fixed within each 2 × 2 block while the inner conditions (X and Y) alternate. Variables.… view at source ↗
Figure 3
Figure 3. Figure 3: Generating viable experimental plans. PLanet de￾termines the shape of the design matrix and places constraints on entries of the matrix (left) before generating a Z3 model (middle). The numbers in the matrix map directly to specific values of a bitvector encoding, which represents possible assignments to a set of variables. The last step translates the matrix to a table with all viable experimental plans (… view at source ↗
Figure 2
Figure 2. Figure 2: Our formal grammar of experimental assignment. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: PLanet’s user interface comparing two experimental designs from our user evaluation (Section 8). [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: PLanet program (left) representing an experiment [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Nested design from Sweating the Details: Emotion Recognition and the Influence of Physical Exertion in Virtual Reality Exergaming [29] implemented in PLanet and edibble. PLanet correctly and explicitly represents that both the Exercise Intensity and Emotion VE conditions are counterbalanced and that there are 72 participants. The edibble program does not cor￾rectly represent this design. edibble’s strict u… view at source ↗
Figure 7
Figure 7. Figure 7: R1’s intended experimental assignment and PLanet program. [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
read the original abstract

Experimental designs reflect assumptions about variable relationships that determine what causal queries researchers can answer through the experiment. Accounting for and communicating these assumptions is essential for drawing valid, generalizable conclusions from scientific experiments. Unfortunately, existing experimental design tools elide these details, expecting researchers to reason about design decisions and assumptions on their own. To surface assumptions and enable design exploration, we introduce a grammar of composable operators for constructing experimental assignment procedures grounded in matrix algebra. The PLanet DSL implements this grammar and compiles PLanet programs into constraint satisfaction problems over matrices. Together, PLanet's composable grammar and matrix representation enable a static analysis to determine which causal queries are testable under different assumptions. In an expressivity evaluation, PLanet was the most expressive of existing DSLs. Critical reflections with the authors of these DSLs revealed that PLanet makes design choices explicit without requiring procedural specification. Think-aloud studies showed that PLanet facilitated design exploration and surfaced assumptions researchers may otherwise overlook.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces PLanet, a domain-specific language for formalizing experimental assignment procedures via a composable grammar grounded in matrix algebra. PLanet programs are compiled into constraint satisfaction problems over matrices, which in turn support a static analysis that determines which causal queries are testable under different assumptions about variable relationships. The work reports an expressivity evaluation showing PLanet outperforms prior DSLs, critical reflections with authors of those DSLs, and think-aloud studies indicating that the approach surfaces assumptions and supports design exploration.

Significance. If the matrix representation and CSP encoding are shown to be sound and complete for the range of designs claimed, the work could meaningfully advance experimental design practice in HCI and related fields by making implicit causal assumptions explicit and enabling automated testability analysis. The formal grounding in matrix algebra and the combination of expressivity comparison with user studies are positive features; the result would be more impactful if it included falsifiable checks against established causal-identifiability results.

major comments (2)
  1. [Sections describing the matrix representation and static analysis (likely §3–4)] The central claim that the grammar's matrix representation and compilation to CSPs faithfully encode all relevant assumptions (independence, blocking, randomization, latent variables) so that static analysis correctly decides testability is load-bearing. Matrix algebra naturally represents linear marginals and assignments but risks distorting conditional independencies or non-linear intervention effects; the manuscript should supply either a formal soundness argument or an empirical validation against known causal diagrams for standard designs (e.g., blocked RCTs) to confirm that testability verdicts match results from the causal-inference literature.
  2. [Evaluation section (expressivity comparison and think-aloud studies)] The expressivity evaluation and think-aloud studies are presented without quantitative details on participant numbers, task protocols, or how the static-analysis outputs were validated against ground-truth causal queries. This absence weakens the claim that PLanet is the most expressive DSL and that it reliably surfaces overlooked assumptions.
minor comments (2)
  1. [Introduction and grammar definition] Clarify the precise scope of the grammar with respect to non-linear or time-varying assignment procedures; a short limitations paragraph would help readers understand where the matrix encoding may intentionally abstract away structure.
  2. [Grammar and compilation sections] Add explicit cross-references between the matrix operators and the corresponding causal assumptions they encode (e.g., which operator corresponds to blocking).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback. The comments highlight important areas where additional rigor and clarity will strengthen the manuscript. We address each major comment below and indicate the revisions planned for the next version.

read point-by-point responses

  1. Referee: The central claim that the grammar's matrix representation and compilation to CSPs faithfully encode all relevant assumptions (independence, blocking, randomization, latent variables) so that static analysis correctly decides testability is load-bearing. Matrix algebra naturally represents linear marginals and assignments but risks distorting conditional independencies or non-linear intervention effects; the manuscript should supply either a formal soundness argument or an empirical validation against known causal diagrams for standard designs (e.g., blocked RCTs) to confirm that testability verdicts match results from the causal-inference literature.

    Authors: We agree that the soundness of the matrix representation and CSP encoding is central to the contribution and that the current manuscript relies primarily on informal arguments and illustrative examples rather than a complete formal proof. We will add a dedicated subsection in the revised version that states a soundness theorem for the linear case, provides a proof sketch based on the correspondence between matrix constraints and d-separation, and includes an empirical validation table comparing PLanet's testability verdicts for blocked RCTs, randomized block designs, and Latin-square designs against established results from the causal-identifiability literature. We will also explicitly delimit the scope to linear models and note that non-linear intervention effects fall outside the current guarantees. revision: yes

  2. Referee: The expressivity evaluation and think-aloud studies are presented without quantitative details on participant numbers, task protocols, or how the static-analysis outputs were validated against ground-truth causal queries. This absence weakens the claim that PLanet is the most expressive DSL and that it reliably surfaces overlooked assumptions.

    Authors: We accept that the evaluation section would benefit from more precise and quantitative reporting. The current draft mentions the think-aloud studies and expressivity comparison at a summary level but does not include a participant table, full task protocol, or explicit validation procedure against ground-truth queries. In the revision we will expand Section 5 to add (1) a table with exact participant counts, recruitment criteria, and session durations, (2) the complete task protocol and materials, and (3) a new validation subsection that lists the ground-truth causal queries for each evaluated design and reports agreement with PLanet's static-analysis outputs. These additions will make the empirical claims more transparent and reproducible. revision: yes

Circularity Check

0 steps flagged

No significant circularity in PLanet's formalization and analysis

full rationale

The paper introduces a new composable grammar for experimental assignment procedures, represented via matrix algebra and compiled to constraint satisfaction problems to support static analysis of testable causal queries. No derivation steps, equations, or results in the abstract or context reduce a claimed outcome to its own inputs by construction, self-definition, or fitted parameters renamed as predictions. Expressivity comparisons are made against prior external DSLs, and reflections/user studies provide independent evaluation. No load-bearing self-citations, uniqueness theorems imported from authors, or ansatzes smuggled via citation appear in the material. The contribution is a constructive definition of a DSL and analysis tool rather than a circular derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The approach rests on the domain assumption that matrix algebra can faithfully encode assignment procedures and their causal implications; no free parameters or invented entities are introduced in the abstract description.

axioms (1)
  • domain assumption Experimental assignment procedures and their causal implications can be represented using matrix algebra without loss of critical structure.
    The grammar is explicitly grounded in matrix algebra per the abstract.

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