Core Transforms and Analysis

Strata Core Transforms and Analysis

Table of Contents

  1. 1. Introduction
  2. 2. Program Transforms
  3. 3. Configuring the Pipeline
  4. 4. Analysis Modes
  5. 5. SMT Analysis

1. Introduction🔗

This document describes the transforms and analyses available for Strata Core programs. Transforms are program-to-program rewrites that are independent of any specific analysis. Analyses consume a (possibly transformed) Core program and produce verification results. For the language definition itself, see the Strata Core Language Definition.

2. Program Transforms🔗

Program transforms are applied to a Strata Core program before analysis. They are independent of the choice of analysis and can be composed in sequence. The strata transform CLI command applies one or more passes to a Core program:

strata transform file.core.st --pass <name> [--procedures <procs>] [--pass <name> ...]

Passes are applied left to right. The --procedures and --functions flags bind to the most recent --pass.

2.1. Procedure Inlining (inlineProcedures)🔗

Replaces procedure call sites with the body of the callee, substituting actuals for formals. The --procedures flag restricts which procedures are inlined; if omitted, all eligible procedures are inlined.

2.2. Call Elimination (callElim)🔗

Replaces each procedure call with the contract-based encoding described in the language reference: assert preconditions, havoc outputs, assume postconditions. This is the standard modular verification encoding.

2.3. Loop Elimination (loopElim)🔗

Replaces loops with their invariant-based abstraction: assert the invariant, havoc the modified variables, assume the invariant and the negation of the guard.

2.4. Procedure Filtering (filterProcedures)🔗

Removes all procedures except those named in the --procedures flag (and any procedures they transitively depend on).

2.5. Irrelevant Axiom Removal (removeIrrelevantAxioms)🔗

Removes axioms that do not mention any of the functions named in the --functions flag, reducing the size of the analysis problem.

Additional internal transforms (e.g., PrecondElim, DetToKleene, StructuredToUnstructured) are used by the analysis pipelines but are not currently exposed via the CLI.

3. Configuring the Pipeline🔗

The transforms above run as a pipeline: an ordered list of phases, each declaring what it requires of the program it receives, what it establishes, and what it leaves standing. A list composes when every phase's requirements are met by the phases before it, and the back end accepts it when the list also delivers what obligation extraction needs. Both are checked before anything runs, so an unworkable order is reported rather than attempted.

strata verify --display-phases prints the default order as a pasteable argument, along with the phases available outside it, and --display-phase-contracts prints what each phase requires, delivers and preserves. Those two commands are the vocabulary: this document deliberately does not list the phases, because the tool's output cannot fall out of date and prose can.

--phases <list> runs a list of your own. With no file to verify it reports whether the list composes, which is the cheapest way to try an order out. Order matters and the checks will tell you so: naming a phase before the one that establishes what it requires is refused, with the phase that would have established it named in the message.

--phases is also refused for inputs whose verifier cannot honour it, .csimp.st and the B3 files, because those are verified through their own translation rather than the Core pipeline.

A phase list may assert a fact instead of establishing it. For every fact with an executable check there is an assert<Fact> phase — assertNoLoops and the like — which checks the fact on the program and passes it through. That is how a list can stand where another order runs a transform: if the input already has the property, checking it is cheaper than rewriting the program to produce it.

A tool that keeps a registry of pipelines gates this further. stratainternal accepts --pipeline <name> to run a registered pipeline, and refuses a --phases list that no entry holds, answering with the three ways forward: enable unregistered pipelines in a development build, run an existing pipeline by name if your package already uses that exact list, or register the list by adding the entry the refusal prints. Where unregistered pipelines are enabled the list runs and the run says so. Registration is what lets a change to the phase vocabulary be carried to the packages that depend on one, rather than silently changing what they verify.

A registered entry may also state facts it assumes of its input, and those are where the assert forms earn their place: a command line cannot prove anything, so --pipeline puts an assert<Fact> phase in front for each assumed fact and reports which ones it added. The entry's own phases are unchanged; the checks are the price of arriving without a proof.

From Lean there is a second route. A front end that proves facts of the program it emits can assume them instead, through the validating entry points that take those facts and the proof that they hold, and then omit the phases that would have established them. A command line has no way to supply such a proof, which is why the flags offer nothing equivalent.

--no-cse, --function-inlining and --unroll-bounded-quantifiers are unknown options: a pipeline names the phases it runs, so no option reshapes it. To run those phases, name them with --phases (--display-phases prints the default order to start from).

Migrating is mechanical but not a drop-in: a script or CI job still passing one of these exits with an unknown-option error, and --phases names the whole order rather than toggling one phase. Start from --display-phases and edit that list. On stratainternal an unregistered --phases list is refused, so a caller of a registered pipeline uses --pipeline <name> instead.

4. Analysis Modes🔗

Strata supports three analysis modes, selected via --check-mode. These modes are independent of the specific analysis being used — they control how results are classified.

  1. deductive (default): Prove correctness — every assertion must hold on all inputs.

  2. bugFinding: Find bugs assuming incomplete preconditions — only definite bugs are errors.

  3. bugFindingAssumingCompleteSpec: Find bugs assuming complete preconditions — any counterexample is an error.

Each verification condition produces two queries: a satisfiability check (P ∧ Q) asking whether the property can be true given the path condition, and a validity check (P ∧ ¬Q) asking whether it can be false. The combination determines the outcome and severity in each mode.

5. SMT Analysis🔗

The SMT analysis translates a Strata Core program into SMT-LIB queries and delegates reasoning to an external SMT solver.

5.1. Type Encoding🔗

Abstract types are encoded as uninterpreted sorts. Algebraic datatypes are encoded using the declare-datatypes command; the generated functions (constructors, testers, accessors) are mapped to the corresponding SMT functions (e.g., Option..isNone maps to is-None).

5.2. Function Encoding🔗

Functions with bodies are inlined by the partial evaluator where possible. Functions without bodies are declared as uninterpreted functions.

Recursive functions are simplified by the partial evaluator but are encoded as uninterpreted functions in the SMT encoding. For recursive functions with @[cases], per-constructor axioms are generated: for each constructor C of the ADT at the @[cases] parameter, an axiom representing the corresponding rewrite rule (e.g., List.length Nil = 0 and forall h t, List.length (Cons h t) = 1 + List.length t). Recursive functions without @[cases] are encoded as pure uninterpreted functions with no axioms.

Termination checking is always on for rec functions. Strata supports two termination modes:

  • Structural (ADT): The TermCheck pipeline phase generates a D..adtRank : D → Int uninterpreted function with per-constructor axioms establishing that recursive fields have strictly smaller rank, and a f$$term verification procedure that asserts adtRank(callArg) < adtRank(callerParam) at each recursive call site.

  • Int-valued: For functions with an int-valued decreases expression, the f$$term procedure asserts two obligations at each recursive call site: 0 <= call_measure (non-negativity) and call_measure < caller_measure (strict decrease), where call_measure is the decreases expression with formals substituted by the actual arguments at the call site.

5.3. Axiom Encoding🔗

Axioms are emitted as universally quantified SMT assertions.