Before starting, load /authoring-tests.

Follow these principles when writing property-based tests:

• Write focused properties with focused arbitraries to explore slices of the input space

• Prefer arbitraries that generate the desired input space directly instead of generating a larger input space and then filtering it

• Assert only what's straightforward to infer from the input arbitraries. Asserting the full value is often infeasible. If no assertion seems feasible, then the input space is too broad

• Don't constrain an arbitrary unless the constraint is necessary to satisfy the property or to resolve a performance problem

Common properties

• "Output is always/never X for all inputs". Example: for any number n, Math.floor(n) is an integer

• "When input is X, then output is always/never Y". Example: for any array data with no duplicates, the result of removing duplicates from data is data itself

• "Complex implementation X is equivalent to simpler implementation Y". Example: "c is contained inside sorted array data for binary search" is equivalent to "c is contained inside data for linear search"

• Totality: function returns rather than throwing for all valid inputs. Example: JSON.parse(JSON.stringify(x)) never throws for serializable x

• Deterministic: always returns the same output for the same input. Example: for any date d, formatDate(d) always returns the same string

• Side-effect free: does not mutate the input or non-local state. Example: for any array data, sorted(data) leaves data unchanged

• Bounded output: output is always within a known range. Example: clamp(x, low, high) always returns a value between low and high

• Structural invariant: output always has a guaranteed shape/structure. Example: partition(predicate, data) always produces two arrays whose combined length equals data.length

• Closure under operation: applying f to valid inputs always produces a valid output of the same type/domain. Example: add(positiveInt, positiveInt) is always a positive integer

• Identity element: there exists an input that leaves output unchanged. Example: concat(xs, []) equals xs

• Absorption/annihilation: certain inputs collapse the result regardless of the other. Example: and(false, x) is always false

• Idempotent: running twice is the same as running once, either in its effect on non-local state or when passing its first output as its second input. Example: for any array data, sort(sort(data)) equals sort(data)

• Commutative: rearranging argument order doesn't affect output. Example: for any numbers a and b, add(a, b) equals add(b, a)

• Associative: regrouping arguments for multiple calls doesn't affect output. Example: concat(concat(a, b), c) equals concat(a, concat(b, c))

• Distributive: f(a ∪ b) === f(a) ∪ f(b). Example: map(f, [...xs, ...ys]) equals [...map(f, xs), ...map(f, ys)]

• Inverse/symmetry/roundtrips: f and g are inverses of each other. Example: decode(encode(x)) equals x

• Transitivity: if f(a, b) and f(b, c), then f(a, c). Example: if isAncestor(a, b) and isAncestor(b, c), then isAncestor(a, c)

• Monotonic: if input increases (or decreases), output always changes in the same direction. Example: sorting more elements never produces fewer elements

• Consistent ordering: if a comes before b in the input, the output keeps that order. Example: a stable sort never reorders equal elements relative to each other

• Prefix/suffix closure: if f(x) holds, it holds for any sub-input, or conversely, for any superset. Example: if isValid(data) then isValid(data.slice(0, n)) for all n

These aren't exhaustive. Reason from first principles when none fits.

fast-check tips

• Use fc.clone(arb, count) to produce multiple equal values instead of structuredClone or JSON.parse(JSON.stringify(...))

• Use fc.uniqueArray(arb, { minLength, maxLength }) to produce unique values instead of fc.tuple(...arbs).filter(...)