Logical and control flow functions

This page lists the 17 functions of the logical and control flow family. Taxonomy/source: Logical functions. The formula function contract has every family, the engine builds, and the evaluation limits.

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Function (aliases)	Engine	Contract
`IF`	Default + full	incumbent Signature: `if` Semantics: `lazy-control` Dialect: `excel-documented` Implementation: `implemented-assisted`
`AND`	Default + full	incumbent Signature: `logical-variadic` Semantics: `logical` Dialect: `excel-documented` Implementation: `implemented-assisted`
`OR`	Default + full	incumbent Signature: `logical-variadic` Semantics: `logical` Dialect: `excel-documented` Implementation: `implemented-assisted`
`NOT`	Default + full	incumbent Signature: `unary-value` Semantics: `logical` Dialect: `excel-documented` Implementation: `implemented-assisted`
`IFS`	Default + full	required target Signature: `ifs` Semantics: `lazy-control` Dialect: `excel-documented` Implementation: `implemented-assisted`
`SWITCH`	Default + full	required target Signature: `switch` Semantics: `lazy-control` Dialect: `excel-documented` Implementation: `implemented-assisted`
`XOR`	Default + full	required target Signature: `logical-variadic` Semantics: `logical` Dialect: `excel-documented` Implementation: `implemented-assisted`
`TRUE`	Default + full	required target Signature: `zero` Semantics: `logical` Dialect: `excel-documented` Implementation: `implemented-assisted`
`FALSE`	Default + full	required target Signature: `zero` Semantics: `logical` Dialect: `excel-documented` Implementation: `implemented-assisted`
`LET`	Default + full	required target Signature: `let` Semantics: `let-binding` Dialect: `excel-documented` Implementation: `implemented-assisted`
`LAMBDA`	Full only	optional analysis Signature: `lambda-lambda` Semantics: `analysis-lambda` Dialect: `analysis-lambda` Implementation: `analysis-lambda`
`MAP`	Full only	optional analysis Signature: `lambda-map` Semantics: `analysis-lambda` Dialect: `analysis-lambda` Implementation: `analysis-lambda`
`REDUCE`	Full only	optional analysis Signature: `lambda-reduce` Semantics: `analysis-lambda` Dialect: `analysis-lambda` Implementation: `analysis-lambda`
`SCAN`	Full only	optional analysis Signature: `lambda-scan` Semantics: `analysis-lambda` Dialect: `analysis-lambda` Implementation: `analysis-lambda`
`BYROW`	Full only	optional analysis Signature: `lambda-byrow` Semantics: `analysis-lambda` Dialect: `analysis-lambda` Implementation: `analysis-lambda`
`BYCOL`	Full only	optional analysis Signature: `lambda-bycol` Semantics: `analysis-lambda` Dialect: `analysis-lambda` Implementation: `analysis-lambda`
`MAKEARRAY`	Full only	optional analysis Signature: `lambda-makearray` Semantics: `analysis-lambda` Dialect: `analysis-lambda` Implementation: `analysis-lambda`

Signature profiles

Argument order, required/default state, accepted shapes, repetition, and return shape come directly from the inventory.

Signature: if

Return shape: contextual.

Argument	Required	Default	Accepts	Repetition
`logicalTest`	yes	none	`scalar`, `reference`	`once`
`valueIfTrue`	no	true	`scalar`, `range`, `array`, `reference`	`once`
`valueIfFalse`	no	false	`scalar`, `range`, `array`, `reference`	`once`

Signature: logical-variadic

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`logical`	yes	none	`scalar`, `range`, `array`, `reference`	`one-or-more`

Signature: unary-value

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`value`	yes	none	`scalar`, `range`, `array`, `reference`	`once`

Signature: ifs

Return shape: contextual.

Argument	Required	Default	Accepts	Repetition
`testAndValue`	yes	none	`scalar`, `range`, `array`, `reference`	`paired`

Signature: switch

Return shape: contextual.

Argument	Required	Default	Accepts	Repetition
`expression`	yes	none	`scalar`, `reference`	`once`
`valueAndResult`	yes	none	`scalar`, `range`, `array`, `reference`	`paired`
`defaultValue`	no	#N/A	`scalar`, `range`, `array`, `reference`	`once`

Signature: zero

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
none	—	—	—	—

Signature: let

Return shape: contextual.

Argument	Required	Default	Accepts	Repetition
`nameAndValue`	yes	none	`scalar`, `range`, `array`, `name`, `reference`	`paired`
`calculation`	yes	none	`scalar`, `range`, `array`, `name`, `reference`	`once`

Signature: lambda-lambda

Return shape: contextual.

Argument	Required	Default	Accepts	Repetition
`parameter`	no	none	`scalar`, `range`, `array`, `reference`	`zero-or-more`
`calculation`	yes	none	`scalar`, `range`, `array`, `reference`	`once`

Signature: lambda-map

Return shape: array.

Argument	Required	Default	Accepts	Repetition
`array`	yes	none	`scalar`, `range`, `array`, `reference`	`one-or-more`
`lambda`	yes	none	`scalar`, `range`, `array`, `reference`	`once`

Signature: lambda-reduce

Return shape: scalar.

Argument	Required	Default	Accepts	Repetition
`initialValue`	no	none	`scalar`, `range`, `array`, `reference`	`once`
`array`	yes	none	`scalar`, `range`, `array`, `reference`	`once`
`lambda`	yes	none	`scalar`, `range`, `array`, `reference`	`once`

Signature: lambda-scan

Return shape: array.

Argument	Required	Default	Accepts	Repetition
`initialValue`	no	none	`scalar`, `range`, `array`, `reference`	`once`
`array`	yes	none	`scalar`, `range`, `array`, `reference`	`once`
`lambda`	yes	none	`scalar`, `range`, `array`, `reference`	`once`

Signature: lambda-byrow

Return shape: array.

Argument	Required	Default	Accepts	Repetition
`array`	yes	none	`scalar`, `range`, `array`, `reference`	`once`
`lambda`	yes	none	`scalar`, `range`, `array`, `reference`	`once`

Signature: lambda-bycol

Return shape: array.

Argument	Required	Default	Accepts	Repetition
`array`	yes	none	`scalar`, `range`, `array`, `reference`	`once`
`lambda`	yes	none	`scalar`, `range`, `array`, `reference`	`once`

Signature: lambda-makearray

Return shape: array.

Argument	Required	Default	Accepts	Repetition
`rows`	yes	none	`scalar`, `range`, `array`, `reference`	`once`
`columns`	yes	none	`scalar`, `range`, `array`, `reference`	`once`
`lambda`	yes	none	`scalar`, `range`, `array`, `reference`	`once`

Semantic profiles

These values are normative for the listed Sheetwrite subset. function-defined and contextual are explicit limitations: consult the formula guides' function-specific sections rather than assuming another spreadsheet's edge behavior.

Semantics: lazy-control

Dimension	Contract
shape	scalar: accepted range: contextual array: contextual broadcast: function-defined result: contextual
coercion	blank: function-defined text: function-defined boolean: function-defined error: trap-selected
text	case: insensitive wildcard: literal
environment	locale: invariant dateSystem: function-defined
numeric	tolerance: function-defined domain: function-defined iteration: kind: none maximum: none
calculation	dependencies: contextual lazy: lazy-branches spill: contextual fill: relative-reference-rewrite copy: relative-reference-rewrite structuralRewrite: ast-reference-rewrite
persistence	snapshot: formula-source history: formula-source collaboration: formula-source xlsxSource: rewrite-on-structural-edit

Semantics: logical

Dimension	Contract
shape	scalar: accepted range: accepted array: contextual broadcast: function-defined result: scalar
coercion	blank: false text: function-defined boolean: preserved error: propagate
text	case: insensitive wildcard: literal
environment	locale: invariant dateSystem: not-applicable
numeric	tolerance: exact domain: all-inputs iteration: kind: none maximum: none
calculation	dependencies: tracked lazy: eager spill: scalar fill: relative-reference-rewrite copy: relative-reference-rewrite structuralRewrite: ast-reference-rewrite
persistence	snapshot: formula-source history: formula-source collaboration: formula-source xlsxSource: rewrite-on-structural-edit

Semantics: let-binding

Dimension	Contract
shape	scalar: accepted range: accepted array: accepted broadcast: function-defined result: contextual
coercion	blank: preserved text: preserved boolean: preserved error: propagate
text	case: insensitive wildcard: literal
environment	locale: invariant dateSystem: function-defined
numeric	tolerance: function-defined domain: function-defined iteration: kind: none maximum: none
calculation	dependencies: contextual lazy: lazy-bindings spill: contextual fill: relative-reference-rewrite copy: relative-reference-rewrite structuralRewrite: ast-reference-rewrite
persistence	snapshot: formula-source history: formula-source collaboration: formula-source xlsxSource: rewrite-on-structural-edit

Semantics: analysis-lambda

Dimension	Contract
shape	scalar: accepted range: accepted array: accepted broadcast: none result: contextual
coercion	blank: function-defined text: function-defined boolean: function-defined error: propagate
text	case: not-applicable wildcard: not-applicable
environment	locale: invariant dateSystem: not-applicable
numeric	tolerance: binary64 domain: function-defined iteration: kind: bounded maximum: 2000000
calculation	dependencies: tracked lazy: function-defined spill: contextual fill: relative-reference-rewrite copy: relative-reference-rewrite structuralRewrite: ast-reference-rewrite
persistence	snapshot: formula-source history: formula-source collaboration: formula-source xlsxSource: rewrite-on-structural-edit

Dialect profiles

Dialect: excel-documented

Dialect	Status
Microsoft Excel	documented
Google Sheets	unverified
OpenFormula	unverified

Limitations: Google Sheets and OpenFormula results require producer evidence before compatibility is claimed.

Dialect: analysis-lambda

Dialect	Status
Microsoft Excel	documented
Google Sheets	unverified
OpenFormula	unverified

Limitations: Available only in @sheetwrite/formulas. Named ranges are supported, but workbook-defined named formulas are not available. LAMBDA uses lexical parameters and LET bindings. Calls are limited to depth 64 and 2000000 work units. Helpers reject nested arrays.

Implementation profiles

Implementation: implemented-assisted

Layer	Status and source/evidence
Parser	implemented `packages/wasm/src/calc.rs`
Evaluator	implemented `packages/wasm/src/eval/mod.rs` `packages/wasm/src/eval/functions.rs`
Formula assist	implemented `packages/core/src/formula-assist.ts`
Evidence	source-linked `packages/wasm/src/tests.rs` `packages/core/test/formula-assist.test.ts`

Implementation: analysis-lambda

Layer	Status and source/evidence
Parser	implemented `packages/wasm/src/calc.rs`
Evaluator	implemented `packages/wasm/src/eval/analysis/lambda.rs`
Formula assist	implemented `packages/core/src/formula-assist.ts`
Evidence	source-linked `packages/wasm/src/eval/analysis/lambda.rs`

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