README.md

@@ -82,8 +82,8 @@ For structured output a record writes the row for you.
 
 A record is a template seen as columns: its fields are the columns, its `format`
 the whole. `--format json|ndjson|csv|sql` writes the records; the library's
-`FakeRecord` (below) hands back the columns. Every column is a string — typed scalars
-are on the release checklist, see [`todo.md`](todo.md). Save
+`FakeRecord` (below) hands back the columns. A column is a string unless it declares a
+[datatype](#datatype), and a [`null`](#null) item draws it as null. Save
 `mydata/users.json`:
 
 ```json
@@ -164,7 +164,8 @@ r, err = f.FakeRecordTemplate(`{"format":"{x}","x":["a","b"]}`) // compile + ren
 | `WithDataFS(fsys)` | layer an `fs.FS`, such as your own `embed.FS` |
 | `WithoutShippedData()` | load only what you give |
 
-A `*Record` carries its columns via `Columns()`, and serializes them with `JSON()`
+A `*Record` carries its columns via `Columns()` — each a `Column` of `Name`,
+`DataType`, rendered `Value` and `Null` — and serializes them with `JSON()`
 (one object), `CSVHeader()`/`CSVLine()`, or `SQLInsert(table)` — the shapes the
 CLI's `--format` writes. `FakeRecord` and `FakeRecordTemplate` take a record; a
 path or template that is not one — a bare string, a choice, or a folder — errors.
@@ -255,10 +256,53 @@ Renders e.g. `bar foo baz`. Rejected at load: a `separator` without a `repeat`,
 a `separator` of `""` (the default), and a `repeat` that multiplies to more than
 1 048 576 renders along any path of nested repeats.
 
+### Datatype
+
+A record column may declare `datatype` — `integer`, `number` or `boolean` — so `json`
+writes `42` rather than `"42"` and `sql` a bare literal; a column without one is a
+string:
+
+```json
+{ "format": "",
+  "id": { "format": "{seq()}", "datatype": "integer" },
+  "paid": { "format": "{p}", "p": ["true", "false"], "datatype": "boolean" },
+  "total": { "format": "{calc(net * qty, 2)}", "net": ["19.99", "5.00"], "qty": ["3", "7"], "datatype": "number" } }
+```
+
+Writes e.g. `{"id":1,"paid":true,"total":59.97}`. A column is a field of the top-level
+template, or an item of a choice standing in for one; `datatype` anywhere else is a
+load error. So is a column that can render text its datatype rejects — `integer` takes
+`-?(0|[1-9][0-9]*)`, `number` a JSON number, `boolean` `true` or `false` — and the
+error shows such a render:
+
+```text
+order.id: datatype integer, but it can render "000", which is not an integer
+```
+
+A `{calc()}` fills an `integer` or `number` column only where it provably prints no
+`NaN` or `Inf`: each operand is a plain decimal — a sign, digits, one dot — of at most
+300 bytes, or a field holding only such a calc, and no divisor can be zero. An
+`integer` column also needs a decimals count of `0`, or integer operands and no `/`.
+
+### Null
+
+A `null` item draws a record column as null: `json` writes `null`, `sql` `NULL`, and
+`csv` an empty field, with an empty string written `""` so PostgreSQL's `COPY … CSV`
+reads both back. `Fake` renders a null as `""`. The other items' weights skew its
+odds:
+
+```json
+{ "format": "", "deleted_at": null, "middle": [null, { "format": "{n}", "n": ["Ann", "Eva"], "weight": 3 }] }
+```
+
+`deleted_at` is null every draw, `middle` a name three draws in four. Rejected at
+load: `null` anywhere but a column, naming `""`, and a column whose items declare
+different datatypes.
+
 ### Options and fields
 
-`format`, `weight`, `repeat` and `separator` are the only options; **any other
-key is a field** (see [Decisions](#decisions)). An object that does nothing a
+`format`, `weight`, `repeat`, `separator` and `datatype` are the only options; **any
+other key is a field** (see [Decisions](#decisions)). An object that does nothing a
 string can't — only a `format` — is rejected naming the string, as is a one-item
 choice naming its item.
 
@@ -437,8 +481,8 @@ tokens add cost in proportion to the output.
 
 ## Decisions
 
-- **Options and fields share one namespace.** `format`, `weight`, `repeat` and
-  `separator` are reserved; every other key is a field. Nesting fields under a
+- **Options and fields share one namespace.** `format`, `weight`, `repeat`,
+  `separator` and `datatype` are reserved; every other key is a field. Nesting fields under a
   key, or prefixing options, would tax every template to guard against a
   misspelt option.
 - **`{a|b}` stays beside nested choices.** `[[…], […]]` picks the same way, but
@@ -518,7 +562,8 @@ tokens add cost in proportion to the output.
   so `a/(b*c)` with `b` fixed at `0` and `c` varying loads and prints `Inf` every
   draw — catching it needs zero-absorbing algebra for a shape nobody writes.
 - **In data, a default written out and a constant spelled as a sample are load
-  errors.** `weight: 1`, `repeat: 1`, `separator: ""`, `int(5,5)`, `float(1,1,2)`,
+  errors.** `weight: 1`, `repeat: 1`, `separator: ""`, `datatype: "string"`,
+  `int(5,5)`, `float(1,1,2)`,
   `+5` and `05` each spell what a shorter form already spells, so each is rejected
   naming that form. The CLI's numbers follow the shell instead: `--seed 007` and
   `--repeat +3` are 7 and 3, as every command line reads them.
@@ -557,6 +602,9 @@ tokens add cost in proportion to the output.
   row — would vary per draw. A fixed column set is what the CSV and `INSERT`
   contracts rest on, so the restriction holds even where a particular choice would
   happen to agree.
+- **Null is a `null` item, not a rate.** A null is one more outcome of a column's
+  draw, so a choice's weights skew it like any other; a null-rate option would be a
+  second way to state odds.
 - **The performance gate asserts allocations, not wall-clock time.** `AllocsPerRun`
   is deterministic across machines, so a ±10% ceiling does not flake under CI load,
   while time varies with the machine and its neighbours. A rendering slowdown
@@ -612,7 +660,9 @@ hold.go         the hold: one draw per expansion for paths and operands, and its
 reference.go    reference sigils, and binding references across the tree
 graph.go        the render graph: edges, cycles, the repeat bound, tree walks
 builtins.go     the {name()} function registry and its implementations
-calc.go         the {calc()} arithmetic evaluator: parser, eval, validation
+calc.go         the {calc()} arithmetic evaluator: parser, eval, validation, and the proof a typed column's calc is finite
+datatype.go     column datatypes: DataType, where datatype and null may sit, and the load check every typed render passes
+renderlang.go   what text a node can render, as relations over a scalar's grammar
 data.go         data loading: fs.FS folders/files -> namespace tree, multi-source merge
 cmd/fejkdata/   the fejkdata CLI
 data/           shipped data (JSON), embedded at build: locale folders + a misc folder

builtins.go

@@ -5,6 +5,7 @@ import (
 	"errors"
 	"fmt"
 	"math"
+	"slices"
 	"strconv"
 	"strings"
 	"unicode"
@@ -24,36 +25,36 @@ const (
 // samples read only the rng. A time-based id (uuid v7, ulid) draws its timestamp
 // from the rng, not the wall clock, so seeded output stays reproducible.
 var builtins = map[string]builtin{
-	"luhn":   {arity: 0, prep: derive(func(e string) string { return string(rune('0' + luhnCheck(e))) })},
-	"mod11":  {arity: 0, prep: derive(mod11Check)},
-	"ean":    {arity: 0, prep: derive(eanCheck)},
-	"uuid":   {arity: 0, prep: sample(uuidV7)},
-	"ulid":   {arity: 0, prep: sample(ulid)},
-	"nanoid": {arity: 1, check: posIntArg, prep: chars(nanoidAlphabet)},
-	"hex":    {arity: 1, check: posIntArg, prep: chars(hexDigits)},
-	"digits": {arity: 1, check: posIntArg, prep: chars("0123456789")},
-	"upper":  {arity: 1, check: posIntArg, prep: chars("ABCDEFGHIJKLMNOPQRSTUVWXYZ")},
-	"lower":  {arity: 1, check: posIntArg, prep: chars("abcdefghijklmnopqrstuvwxyz")},
+	"luhn":   {arity: 0, prep: derive(func(e string) string { return string(rune('0' + luhnCheck(e))) }), emits: always(textShape{{{decimalDigits, 1, 1}}})},
+	"mod11":  {arity: 0, prep: derive(mod11Check), emits: always(textShape{{{decimalDigits + "X", 1, 1}}})},
+	"ean":    {arity: 0, prep: derive(eanCheck), emits: always(textShape{{{decimalDigits, 1, 1}}})},
+	"uuid":   {arity: 0, prep: sample(uuidV7), emits: always(uuidShape)},
+	"ulid":   {arity: 0, prep: sample(ulid), emits: always(textShape{{{crockford[:8], 1, 1}, {crockford, 25, 25}}})},
+	"nanoid": sampleOf(nanoidAlphabet),
+	"hex":    sampleOf(hexDigits),
+	"digits": sampleOf(decimalDigits),
+	"upper":  sampleOf("ABCDEFGHIJKLMNOPQRSTUVWXYZ"),
+	"lower":  sampleOf("abcdefghijklmnopqrstuvwxyz"),
 	"base64": {arity: 1, check: posIntArg, prep: func(a []string) callFn {
 		n := atoi(a[0])
 		return func(s *session, _ string, _ []string) string {
 			return base64.StdEncoding.EncodeToString(randBytes(s, n))
 		}
-	}},
+	}, emits: base64Shape},
 	"int": {arity: 2, check: intRangeArgs, prep: func(a []string) callFn {
 		lo, span := atoi(a[0]), atoi(a[1])-atoi(a[0])+1
 		return func(s *session, _ string, _ []string) string { return strconv.Itoa(lo + s.IntN(span)) }
-	}},
+	}, emits: intShape},
 	"float": {arity: 3, check: floatArgs, prep: func(a []string) callFn {
 		lo, hi, dp := atof(a[0]), atof(a[1]), atoi(a[2])
 		return func(s *session, _ string, _ []string) string {
 			return strconv.FormatFloat(lo+s.Float64()*(hi-lo), 'f', dp, 64)
 		}
-	}},
+	}, emits: func(a []string) textShape { return printedFloat(atof(a[0]), atof(a[1]), atoi(a[2]), false) }},
 	"iban": {arity: 1, check: ibanArg, prep: func(a []string) callFn {
 		cc := a[0]
 		return func(s *session, _ string, _ []string) string { return iban(s, cc) }
-	}},
+	}, emits: ibanShape},
 	"calc":      {arity: -1, check: checkCalc, prep: calcPrep, operands: calcOperands},
 	"lowercase": {arity: 1, check: transformArg, prep: transformPrep(strings.ToLower), operands: transformOperand},
 	"uppercase": {arity: 1, check: transformArg, prep: transformPrep(strings.ToUpper), operands: transformOperand},
@@ -69,7 +70,7 @@ var builtins = map[string]builtin{
 		return func(s *session, _ string, _ []string) string {
 			return strconv.FormatUint(s.next(key), 10)
 		}
-	}},
+	}, emits: always(textShape{{{nonZeroDigits, 1, 1}, {decimalDigits, 0, 19}}})},
 }
 
 // derive and sample are the two argument-free builtin shapes: a derivation reads
@@ -94,6 +95,82 @@ func chars(alphabet string) func([]string) callFn {
 	}
 }
 
+// sampleOf is the builtin that draws n characters from an alphabet.
+func sampleOf(alphabet string) builtin {
+	return builtin{arity: 1, check: posIntArg, prep: chars(alphabet), emits: func(a []string) textShape {
+		n := atoi(a[0])
+		return textShape{{{alphabet, n, n}}}
+	}}
+}
+
+// always is the emits of a builtin whose args do not change what it can print.
+func always(s textShape) func([]string) textShape {
+	return func([]string) textShape { return s }
+}
+
+var uuidShape = textShape{{{hexDigits, 8, 8}, {"-", 1, 1}, {hexDigits, 4, 4}, {"-", 1, 1}, {"7", 1, 1}, {hexDigits, 3, 3}, {"-", 1, 1}, {"89ab", 1, 1}, {hexDigits, 3, 3}, {"-", 1, 1}, {hexDigits, 12, 12}}}
+
+const base64Alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/"
+
+func base64Shape(a []string) textShape {
+	n := atoi(a[0])
+	pad := (3 - n%3) % 3
+	size := 4*((n+2)/3) - pad
+	return textShape{{{base64Alphabet, size, size}, {"=", pad, pad}}}
+}
+
+// intShape is what int prints: a sign only below zero, and no leading zero.
+func intShape(a []string) textShape {
+	lo, hi := atoi(a[0]), atoi(a[1])
+	var s textShape
+	if lo <= 0 && hi >= 0 {
+		s = append(s, []charRun{{"0", 1, 1}})
+	}
+	if hi > 0 {
+		s = append(s, []charRun{{nonZeroDigits, 1, 1}, {decimalDigits, 0, len(a[1]) - 1}})
+	}
+	if lo < 0 {
+		s = append(s, []charRun{{"-", 1, 1}, {nonZeroDigits, 1, 1}, {decimalDigits, 0, len(a[0]) - 2}})
+	}
+	return s
+}
+
+func ibanShape(a []string) textShape {
+	cc, digits := a[0], ibanLen[a[0]]-2
+	return textShape{{{cc[:1], 1, 1}, {cc[1:], 1, 1}, {decimalDigits, digits, digits}}}
+}
+
+// shortestFraction bounds the fraction FormatFloat's shortest form prints: at most 17
+// significant digits after up to 323 zeros.
+const shortestFraction = 340
+
+// printedFloat is what strconv.FormatFloat(v, 'f', dp, 64) prints for a v in [lo, hi]
+// that is whole when integral.
+func printedFloat(lo, hi float64, dp int, integral bool) textShape {
+	digits := len(strconv.FormatFloat(math.Floor(math.Max(math.Abs(lo), math.Abs(hi))), 'f', 0, 64)) + 1 // one more for a rounding carry
+	wholes := [][]charRun{{{"0", 1, 1}}, {{nonZeroDigits, 1, 1}, {decimalDigits, 0, digits - 1}}}
+	fractions := [][]charRun{nil}
+	switch {
+	case dp > 0:
+		fractions = [][]charRun{{{".", 1, 1}, {decimalDigits, dp, dp}}}
+	case dp < 0 && !integral:
+		fractions = append(fractions, []charRun{{".", 1, 1}, {decimalDigits, 1, shortestFraction}})
+	}
+	signs := [][]charRun{nil}
+	if lo < 0 || math.Signbit(lo) {
+		signs = append(signs, []charRun{{"-", 1, 1}})
+	}
+	var s textShape
+	for _, sign := range signs {
+		for _, whole := range wholes {
+			for _, fraction := range fractions {
+				s = append(s, slices.Concat(sign, whole, fraction))
+			}
+		}
+	}
+	return s
+}
+
 const hexDigits = "0123456789abcdef"
 
 // transforms are the builtins that rewrite one operand's value; they nest, so
@@ -106,20 +183,19 @@ var transforms = map[string]func(string) string{
 
 // unwrapTransform peels nested transform calls off an operand arg, returning the
 // field it finally names and the transforms to apply, innermost last.
-func unwrapTransform(arg string) (leaf string, chain []func(string) string, err error) {
+func unwrapTransform(arg string) (leaf string, chain []string, err error) {
 	for {
 		name, args, isCall := funcCall(arg)
 		if !isCall {
 			return arg, chain, nil
 		}
-		fn, isTransform := transforms[name]
-		if !isTransform {
+		if _, isTransform := transforms[name]; !isTransform {
 			return "", nil, fmt.Errorf("%s(%s) is not a transform, so it cannot be an operand", name, strings.Join(args, ","))
 		}
 		if len(args) != 1 {
 			return "", nil, fmt.Errorf("%s takes 1 arg, got %d", name, len(args))
 		}
-		chain = append(chain, fn)
+		chain = append(chain, name)
 		arg = args[0]
 	}
 }
@@ -150,10 +226,14 @@ func transformPrep(outer func(string) string) func([]string) callFn {
 		if err != nil {
 			panic(fmt.Sprintf("fejkdata: transform arg %q reached prep unvalidated: %v", a[0], err))
 		}
+		fns := make([]func(string) string, len(chain))
+		for i, name := range chain {
+			fns[i] = transforms[name]
+		}
 		return func(_ *session, _ string, operands []string) string {
 			v := operands[0]
-			for i := len(chain) - 1; i >= 0; i-- {
-				v = chain[i](v)
+			for i := len(fns) - 1; i >= 0; i-- {
+				v = fns[i](v)
 			}
 			return outer(v)
 		}

calc.go

@@ -6,6 +6,7 @@ import (
 	"strconv"
 	"strings"
 	"unicode"
+	"unicode/utf8"
 )
 
 // calcNode is a parsed expression node. It evaluates over the operand values expand
@@ -154,10 +155,12 @@ func calcText(n calcNode) string {
 	return "?"
 }
 
-// neverNumeric reports a node no render of which is a number: fixed text that does
-// not parse, or a choice of only such items. text is one such render.
+// neverNumeric reports a node no render of which is a number: a null, fixed text that
+// does not parse, or a choice of only such items. text is one such render.
 func neverNumeric(n node) (text string, never bool) {
 	switch n := n.(type) {
+	case *null:
+		return "", true
 	case *template:
 		if !n.fixed || n.repeat > 1 {
 			return "", false
@@ -191,10 +194,7 @@ func calcPrep(args []string) callFn {
 		at[name] = i
 	}
 	placed := indexVars(expr, at)
-	dp := -1
-	if len(args) == 2 {
-		dp = atoi(args[1])
-	}
+	dp := calcDecimals(args)
 	return func(_ *session, _ string, operands []string) string {
 		return strconv.FormatFloat(placed.eval(operands), 'f', dp, 64)
 	}
@@ -384,3 +384,256 @@ func contains(bs []byte, b byte) bool {
 	}
 	return false
 }
+
+// calcDecimals is a calc's decimals count, or -1 for the shortest form.
+func calcDecimals(args []string) int {
+	if len(args) == 2 {
+		return atoi(args[1])
+	}
+	return -1
+}
+
+// calcLimit is the largest magnitude a proof accepts as finite, far enough below
+// math.MaxFloat64 that rounding in the bounds cannot hide an overflow.
+const calcLimit = 1e300
+
+// maxOperandLen is the longest operand text a proof bounds by its length, so that
+// bound, 10^maxOperandLen, stays within calcLimit.
+const maxOperandLen = 300
+
+// calcBound is what a proof knows of every value a calc can take: it lies in [lo, hi],
+// is at least nonZero from zero unless nonZero is 0, and is whole when integral.
+type calcBound struct {
+	lo, hi, nonZero float64
+	integral        bool
+}
+
+func magnitude(b calcBound) float64 { return math.Max(math.Abs(b.lo), math.Abs(b.hi)) }
+
+// doubt is why a proof could not show a calc finite, and the render that shows it.
+type doubt struct{ render, why string }
+
+type bounded struct {
+	b calcBound
+	d *doubt
+}
+
+// calcProof bounds a typed column's calcs from their operands' renders, to show each
+// prints a number rather than NaN or Inf.
+type calcProof struct {
+	decimal  *textLanguage
+	operands map[node]bounded
+	lengths  map[node]int
+}
+
+func newCalcProof() *calcProof {
+	p := &calcProof{operands: map[node]bounded{}, lengths: map[node]int{}}
+	p.decimal = newTextLanguage(decimalGrammar, p)
+	return p
+}
+
+// call bounds one calc token of t.
+func (p *calcProof) call(t *template, args []string) (calcBound, *doubt) {
+	expr, err := parseCalc(args[0])
+	if err != nil {
+		panic(fmt.Sprintf("fejkdata: calc(%q) reached a proof unparsed: %v", args[0], err))
+	}
+	b, d := p.expr(expr, t.fields)
+	if d != nil {
+		return b, &doubt{d.render, fmt.Sprintf("{calc(%s)}: %s", strings.Join(args, ", "), d.why)}
+	}
+	return b, nil
+}
+
+func (p *calcProof) expr(n calcNode, fields map[string]node) (calcBound, *doubt) {
+	switch n := n.(type) {
+	case calcNum:
+		v := float64(n)
+		return calcBound{v, v, v, v == math.Trunc(v)}, nil
+	case calcVar:
+		return p.operand(string(n), fields[string(n)])
+	case calcNeg:
+		b, d := p.expr(n.x, fields)
+		return calcBound{-b.hi, -b.lo, b.nonZero, b.integral}, d
+	case calcBin:
+		l, d := p.expr(n.l, fields)
+		if d != nil {
+			return l, d
+		}
+		r, d := p.expr(n.r, fields)
+		if d != nil {
+			return r, d
+		}
+		return combine(n, l, r)
+	}
+	panic(fmt.Sprintf("fejkdata: calc node %T has no bound", n))
+}
+
+// combine bounds one operation from the bounds of its sides.
+func combine(n calcBin, l, r calcBound) (calcBound, *doubt) {
+	b := calcBound{integral: l.integral && r.integral}
+	switch n.op {
+	case '+':
+		b.lo, b.hi = l.lo+r.lo, l.hi+r.hi
+	case '-':
+		b.lo, b.hi = l.lo-r.hi, l.hi-r.lo
+	case '*':
+		b.lo = min(l.lo*r.lo, l.lo*r.hi, l.hi*r.lo, l.hi*r.hi)
+		b.hi = max(l.lo*r.lo, l.lo*r.hi, l.hi*r.lo, l.hi*r.hi)
+		b.nonZero = l.nonZero * r.nonZero
+	default:
+		if r.nonZero == 0 {
+			return b, &doubt{"+Inf", fmt.Sprintf("divides by %s, which can be zero", calcText(n.r))}
+		}
+		m := magnitude(l) / r.nonZero
+		b = calcBound{lo: -m, hi: m, nonZero: l.nonZero / magnitude(r)}
+	}
+	if b.lo > 0 || b.hi < 0 {
+		b.nonZero = math.Max(b.nonZero, math.Min(math.Abs(b.lo), math.Abs(b.hi)))
+	}
+	if !(magnitude(b) <= calcLimit) {
+		return b, &doubt{"+Inf", calcText(n) + " can overflow"}
+	}
+	return b, nil
+}
+
+// operand bounds a calc operand, once per node.
+func (p *calcProof) operand(name string, n node) (calcBound, *doubt) {
+	if seen, done := p.operands[n]; done {
+		return seen.b, seen.d
+	}
+	b, d := p.measure(name, n)
+	p.operands[n] = bounded{b, d}
+	return b, d
+}
+
+// measure bounds an operand through the calc it renders when that is all it renders,
+// and otherwise from its text: a plain decimal of at most maxOperandLen bytes.
+func (p *calcProof) measure(name string, n node) (calcBound, *doubt) {
+	if t, ok := n.(*template); ok {
+		if args, isCalc := soleCalc(t); isCalc {
+			b, d := p.call(t, args)
+			return rounded(b, calcDecimals(args)), d
+		}
+	}
+	text := p.decimal.node(n, nil)
+	if w, escapes := text.escape(decimalAccept); escapes {
+		why := fmt.Sprintf("operand %q can render %s, which is not a plain decimal", name, w)
+		if w.why != "" {
+			why += ": " + w.why
+		}
+		return calcBound{}, &doubt{"NaN", why}
+	}
+	size := p.length(n)
+	if size > maxOperandLen {
+		return calcBound{}, &doubt{"NaN", fmt.Sprintf("operand %q can render more than %d bytes, too many to bound", name, maxOperandLen)}
+	}
+	ends, m := text.to[1], math.Pow(10, float64(size))
+	b := calcBound{hi: m, nonZero: 1 / m, integral: ends&decimalFractional == 0}
+	if ends&decimalNegative != 0 {
+		b.lo = -m
+	}
+	if ends&decimalZero != 0 {
+		b.nonZero = 0
+	}
+	return b, nil
+}
+
+// soleCalc reports a template that renders one calc and nothing else, with its args.
+func soleCalc(t *template) ([]string, bool) {
+	if t.repeat != 1 || len(t.ops) != 1 || t.ops[0].kind != 'b' {
+		return nil, false
+	}
+	name, args, _ := funcCall(t.format[1 : len(t.format)-1])
+	return args, name == "calc"
+}
+
+// rounded is b once printed to dp decimals, which moves a value by up to half a unit.
+func rounded(b calcBound, dp int) calcBound {
+	if dp < 0 {
+		return b
+	}
+	half := math.Pow(10, -float64(dp)) / 2
+	return calcBound{b.lo - half, b.hi + half, math.Max(0, b.nonZero-half), b.integral || dp == 0}
+}
+
+// length is the most bytes a render of n can take, anything past maxOperandLen
+// reported as maxOperandLen+1.
+func (p *calcProof) length(n node) int {
+	if size, done := p.lengths[n]; done {
+		return size
+	}
+	size := 0
+	switch n := n.(type) {
+	case *choice:
+		for _, it := range n.items {
+			size = max(size, p.length(it))
+		}
+	case *template:
+		size = p.formatLength(n)*n.repeat + len(n.separator)*(n.repeat-1)
+	}
+	size = min(size, maxOperandLen+1)
+	p.lengths[n] = size
+	return size
+}
+
+func (p *calcProof) formatLength(t *template) int {
+	size := 0
+	_ = eachToken(t.format, func(tok ftoken) error {
+		if tok.kind == 'l' {
+			size += utf8.RuneLen(tok.r)
+		} else {
+			size += p.tokenLength(t, tok.body)
+		}
+		size = min(size, maxOperandLen+1)
+		return nil
+	})
+	return size
+}
+
+// tokenLength is the most bytes one token can print. A transform never lengthens a
+// render that reads as a decimal: it maps each non-ASCII rune, two bytes or more, to at
+// most two ASCII letters.
+func (p *calcProof) tokenLength(t *template, body string) int {
+	name, args, isFunc := funcCall(body)
+	var arms []arm
+	switch _, isTransform := transforms[name]; {
+	case !isFunc:
+		arms = splitArms(body, t.refs)
+	case isTransform:
+		leaf, _, _ := unwrapTransform(args[0])
+		arms = []arm{splitArm(leaf, t.refs)}
+	case name == "calc":
+		b, d := p.call(t, args)
+		if d != nil {
+			return len(d.render)
+		}
+		return shapeLength(printedFloat(b.lo, b.hi, calcDecimals(args), b.integral))
+	default:
+		return shapeLength(builtins[name].emits(args))
+	}
+	size := 0
+	for _, a := range arms {
+		for _, leaf := range pathLeaves(t.fields[a.key], a.tail) {
+			size = max(size, p.length(leaf))
+		}
+	}
+	return size
+}
+
+// shapeLength is the most bytes a shape can emit, anything past maxOperandLen reported
+// as maxOperandLen+1.
+func shapeLength(s textShape) int {
+	longest := 0
+	for _, alt := range s {
+		size := 0
+		for _, run := range alt {
+			if run.max < 0 {
+				return maxOperandLen + 1
+			}
+			size += run.max
+		}
+		longest = max(longest, size)
+	}
+	return min(longest, maxOperandLen+1)
+}

datatype.go

@@ -0,0 +1,140 @@
+package fejkdata
+
+import (
+	"errors"
+	"fmt"
+)
+
+// DataType is what a record column holds, which decides how a record writes its value.
+type DataType int
+
+// The datatypes a column declares with "datatype"; a column without one is a string.
+const (
+	DataTypeString DataType = iota
+	DataTypeInteger
+	DataTypeNumber
+	DataTypeBoolean
+)
+
+var dataTypeNames = [...]string{"string", "integer", "number", "boolean"}
+
+// String is the datatype as data spells it.
+func (d DataType) String() string {
+	if d < 0 || int(d) >= len(dataTypeNames) {
+		return fmt.Sprintf("DataType(%d)", int(d))
+	}
+	return dataTypeNames[d]
+}
+
+// position is where a JSON value sits, which decides whether it may carry a datatype or
+// be null.
+type position int
+
+const (
+	inFormat position = iota // rendered by a format, so neither
+	atTop                    // a category or an inline template, whose fields are the columns
+	inColumn                 // a column, or a choice item standing in for one
+)
+
+// datatypeOf reads a template's "datatype" (default DataTypeString).
+func datatypeOf(m map[string]any, pos position) (DataType, error) {
+	v, ok := m["datatype"]
+	if !ok {
+		return DataTypeString, nil
+	}
+	name, ok := v.(string)
+	if !ok {
+		return 0, fmt.Errorf("datatype must be a string, got %T", v)
+	}
+	if name == DataTypeString.String() {
+		return 0, fmt.Errorf("datatype %q is the default, so it has no effect; drop it", name)
+	}
+	for d := DataTypeInteger; d <= DataTypeBoolean; d++ {
+		if name != d.String() {
+			continue
+		}
+		if pos != inColumn {
+			return 0, errors.New("datatype only types a record column — a field of the top-level template — so it has no effect here")
+		}
+		return d, nil
+	}
+	return 0, fmt.Errorf(`datatype takes "integer", "number" or "boolean", got %q`, name)
+}
+
+// columnDatatype is the datatype a column's items declare. They must agree, since a
+// column holds one; a column only ever null is a string.
+func columnDatatype(n node) (DataType, error) {
+	var declared []DataType
+	var collect func(node)
+	collect = func(n node) {
+		switch n := n.(type) {
+		case *choice:
+			for _, it := range n.items {
+				collect(it)
+			}
+		case *template:
+			declared = append(declared, n.datatype)
+		}
+	}
+	collect(n)
+	if len(declared) == 0 {
+		return DataTypeString, nil
+	}
+	for _, d := range declared {
+		if d != declared[0] {
+			return declared[0], fmt.Errorf("its items declare %s and %s; a column holds one datatype, so give every item the same", declared[0], d)
+		}
+	}
+	return declared[0], nil
+}
+
+// datatypeSpec is what a datatype's text must satisfy: a grammar, the states a render
+// may end in, and how an error names the datatype.
+type datatypeSpec struct {
+	grammar *grammar
+	accept  uint32
+	noun    string
+}
+
+var datatypeSpecs = map[DataType]datatypeSpec{
+	DataTypeInteger: {numberGrammar, integerAccept, "an integer"},
+	DataTypeNumber:  {numberGrammar, numberAccept, "a number"},
+	DataTypeBoolean: {booleanGrammar, booleanAccept, "a boolean"},
+}
+
+// datatypeCheck proves every render of a typed column is text its datatype takes. One
+// check covers a scope, so a node several columns reach is read once per grammar.
+type datatypeCheck struct {
+	languages map[*grammar]*textLanguage
+	proof     *calcProof
+}
+
+func (c *datatypeCheck) check(path string, n node) error {
+	t, ok := n.(*template)
+	if !ok || t.datatype == DataTypeString {
+		return nil
+	}
+	spec := datatypeSpecs[t.datatype]
+	w, escapes := c.language(spec.grammar).node(t, nil).escape(spec.accept)
+	if !escapes {
+		return nil
+	}
+	msg := fmt.Sprintf("%s: datatype %s, but it can render %s, which is not %s", path, t.datatype, w, spec.noun)
+	if w.why != "" {
+		msg += ": " + w.why
+	}
+	return errors.New(msg)
+}
+
+func (c *datatypeCheck) language(g *grammar) *textLanguage {
+	if c.proof == nil {
+		c.proof = newCalcProof()
+		c.languages = map[*grammar]*textLanguage{}
+	}
+	l, made := c.languages[g]
+	if !made {
+		l = newTextLanguage(g, c.proof)
+		c.languages[g] = l
+	}
+	return l
+}

fejkdata.go

@@ -162,6 +162,8 @@ func paths(n node) []string {
 			}
 		}
 		return out
+	case *null:
+		return []string{""}
 	case *choice:
 		out := []string{""}
 		for p := range n.shared {

graph.go

@@ -186,7 +186,10 @@ func checkScope(s nodeScope) error {
 	if err := s(func(path string, n node) error { return repeatCheck(path, n, mem) }); err != nil {
 		return err
 	}
-	return s(heldCheck)
+	if err := s(heldCheck); err != nil {
+		return err
+	}
+	return s((&datatypeCheck{}).check)
 }
 
 type reachMemo map[node]int

node.go

@@ -32,6 +32,12 @@ type choice struct {
 
 func (*choice) isNode() {}
 
+// null is a record column's missing value, rendered as "". It is not zero-sized, so two
+// nulls are two map keys.
+type null struct{ _ byte }
+
+func (*null) isNode() {}
+
 // template renders a format string, substituting {tokens} from fields. A bare
 // JSON string is a template with no fields. repeat (default 1) renders that format
 // that many times and joins the results with separator (default ""), each render
@@ -41,6 +47,7 @@ type template struct {
 	fields    map[string]node
 	repeat    int
 	separator string
+	datatype  DataType
 	ops       []op                  // format compiled once (see compileOps); what expand walks
 	grow      int                   // minimum output size, to size the render buffer
 	fixed     bool                  // no op varies, so every render is lit
@@ -66,26 +73,37 @@ func (t *template) field(seg string) (node, bool) {
 	return n, ok
 }
 
-// compile converts parsed JSON into a node tree, validating structure up front.
-// Only a choice's items carry a weight, so one here would be inert whatever its type.
+// compile converts parsed JSON — a category or an inline template — into a node tree,
+// validating structure up front.
 func compile(v any) (node, error) {
+	return compileAt(v, atTop)
+}
+
+// compileAt compiles a node that is no choice's item. Only a choice's items carry a
+// weight, so one here would be inert whatever its type.
+func compileAt(v any, pos position) (node, error) {
 	if m, ok := v.(map[string]any); ok {
 		if _, weighted := m["weight"]; weighted {
 			return nil, fmt.Errorf("weight only skews a choice's items, so it has no effect here; it is an option and can never be a field")
 		}
 	}
-	return compileItem(v)
+	return compileItem(v, pos)
 }
 
 // compileItem compiles one node, allowing the weight a choice item may carry.
-func compileItem(v any) (node, error) {
+func compileItem(v any, pos position) (node, error) {
 	switch v := v.(type) {
 	case string:
 		return compileString(v)
 	case []any:
-		return compileChoice(v)
+		return compileChoice(v, pos)
 	case map[string]any:
-		return compileTemplate(v)
+		return compileTemplate(v, pos)
+	case nil:
+		if pos != inColumn {
+			return nil, fmt.Errorf(`null is a record column's value; here it only renders "", so write ""`)
+		}
+		return &null{}, nil
 	default:
 		return nil, fmt.Errorf("a template value must be a string, a list or an object, not %s", jsonKind(v))
 	}
@@ -99,8 +117,6 @@ func jsonKind(v any) string {
 		return "a number"
 	case bool:
 		return "a boolean"
-	case nil:
-		return "null"
 	}
 	return fmt.Sprintf("%T", v)
 }
@@ -136,7 +152,11 @@ func (t *template) compileFormat() error {
 	return checkNoRepeatedRead(t.format, c, t.refs)
 }
 
-func compileChoice(items []any) (node, error) {
+func compileChoice(items []any, pos position) (node, error) {
+	itemPos := inFormat
+	if pos == inColumn {
+		itemPos = inColumn
+	}
 	if len(items) == 0 {
 		return nil, fmt.Errorf("empty choice")
 	}
@@ -160,7 +180,7 @@ func compileChoice(items []any) (node, error) {
 		}
 		total += w
 		cum[i] = total
-		n, err := compileItem(raw)
+		n, err := compileItem(raw, itemPos)
 		if err != nil {
 			return nil, err
 		}
@@ -203,22 +223,26 @@ func checkNoRepeatedItem(items []any) error {
 	return nil
 }
 
-func compileTemplate(m map[string]any) (node, error) {
-	o, err := readOptions(m)
+func compileTemplate(m map[string]any, pos position) (node, error) {
+	o, err := readOptions(m, pos)
 	if err != nil {
 		return nil, err
 	}
-	fields, err := compileFields(m)
+	fieldPos := inFormat
+	if pos == atTop && o.repeat == 1 {
+		fieldPos = inColumn
+	}
+	fields, err := compileFields(m, fieldPos)
 	if err != nil {
 		return nil, err
 	}
-	if len(fields) == 0 && o.repeat == 1 && !o.weighted {
+	if len(fields) == 0 && o.repeat == 1 && !o.weighted && o.datatype == DataTypeString {
 		return nil, fmt.Errorf("an object holding only a format is a string; write %q", o.format)
 	}
 	if err := checkTokens(o.format, fields); err != nil {
 		return nil, err
 	}
-	t := &template{format: o.format, fields: fields, repeat: o.repeat, separator: o.separator}
+	t := &template{format: o.format, fields: fields, repeat: o.repeat, separator: o.separator, datatype: o.datatype}
 	if err := t.compileFormat(); err != nil {
 		return nil, err
 	}
@@ -227,13 +251,14 @@ func compileTemplate(m map[string]any) (node, error) {
 
 // templateOptions is what a template object's option keys say.
 type templateOptions struct {
+	datatype  DataType
 	format    string
 	repeat    int
 	separator string
 	weighted  bool
 }
 
-func readOptions(m map[string]any) (templateOptions, error) {
+func readOptions(m map[string]any, pos position) (templateOptions, error) {
 	var o templateOptions
 	format, ok := m["format"].(string)
 	if !ok {
@@ -245,6 +270,9 @@ func readOptions(m map[string]any) (templateOptions, error) {
 		return o, err
 	}
 	o.repeat = repeat
+	if o.datatype, err = datatypeOf(m, pos); err != nil {
+		return o, err
+	}
 	if sv, ok := m["separator"]; ok {
 		if o.separator, ok = sv.(string); !ok {
 			return o, fmt.Errorf("separator must be a string, got %T", sv)
@@ -262,7 +290,7 @@ func readOptions(m map[string]any) (templateOptions, error) {
 
 // compileFields compiles every non-option key of a template object, in name order
 // so which of several bad fields is reported does not vary.
-func compileFields(m map[string]any) (map[string]node, error) {
+func compileFields(m map[string]any, pos position) (map[string]node, error) {
 	fields := make(map[string]node, len(m))
 	keys := make([]string, 0, len(m))
 	for k := range m {
@@ -276,7 +304,10 @@ func compileFields(m map[string]any) (map[string]node, error) {
 		if err := checkName(k); err != nil {
 			return nil, fmt.Errorf("field %w", err)
 		}
-		n, err := compile(m[k])
+		n, err := compileAt(m[k], pos)
+		if err == nil && pos == inColumn {
+			_, err = columnDatatype(n)
+		}
 		if err != nil {
 			return nil, fmt.Errorf("field %q: %w", k, err)
 		}
@@ -360,10 +391,10 @@ func checkName(name string) error {
 }
 
 // isOption reports whether a template key configures the node instead of naming a
-// field. These four names can never be fields.
+// field. These names can never be fields.
 func isOption(name string) bool {
 	switch name {
-	case "format", "repeat", "separator", "weight":
+	case "datatype", "format", "repeat", "separator", "weight":
 		return true
 	}
 	return false

path.go

@@ -60,7 +60,7 @@ func walkPath(n node, tail []string, w pathWalk) error {
 		}
 		return nil
 	}
-	return fmt.Errorf("cannot descend into %T at %q", n, tail[0])
+	return fmt.Errorf("no field %q", tail[0])
 }
 
 // carriedByAll is the choice rule a path that must resolve on every call obeys:

record.go

@@ -9,10 +9,14 @@ import (
 	"strings"
 )
 
-// Column is one rendered column of a record.
+// Column is one rendered column of a record. Value is the rendered text, which a
+// serializer quotes for DataTypeString and writes bare for any other datatype; a Null
+// column has no Value.
 type Column struct {
 	Name     string
+	DataType DataType
 	Value    string
+	Null     bool
 }
 
 // Record is one record rendered from a template: every direct field is a column,
@@ -28,70 +32,93 @@ func (r *Record) Columns() []Column {
 	return append([]Column(nil), r.columns...)
 }
 
-// JSON renders the record as one JSON object, every column a string.
+// JSON renders the record as one JSON object.
 func (r *Record) JSON() string {
-	m := make(map[string]string, len(r.columns))
-	for _, c := range r.columns {
-		m[c.Name] = c.Value
+	var b strings.Builder
+	b.WriteByte('{')
+	for i, c := range r.columns {
+		if i > 0 {
+			b.WriteByte(',')
 		}
-	b, _ := json.Marshal(m)
+		b.WriteString(jsonString(c.Name))
+		b.WriteByte(':')
+		b.WriteString(literal(c, jsonString, "null"))
+	}
+	b.WriteByte('}')
+	return b.String()
+}
+
+func jsonString(s string) string {
+	b, _ := json.Marshal(s)
 	return string(b)
 }
 
 // CSVHeader renders the column names as one CSV header line.
 func (r *Record) CSVHeader() string {
-	return csvLine(r.names())
+	fields := make([]string, len(r.columns))
+	for i, c := range r.columns {
+		fields[i] = csvField(c.Name)
+	}
+	return strings.Join(fields, ",")
 }
 
-// CSVLine renders the column values as one CSV row.
+// CSVLine renders the column values as one CSV row: a null column an empty field and an
+// empty string "", the convention PostgreSQL's COPY reads a null by.
 func (r *Record) CSVLine() string {
-	return csvLine(r.values())
-}
-
-func (r *Record) names() []string {
-	out := make([]string, len(r.columns))
+	fields := make([]string, len(r.columns))
 	for i, c := range r.columns {
-		out[i] = c.Name
-	}
-	return out
-}
-
-func (r *Record) values() []string {
-	out := make([]string, len(r.columns))
-	for i, c := range r.columns {
-		out[i] = c.Value
-	}
-	return out
-}
-
-func csvLine(cols []string) string {
-	var b strings.Builder
-	w := csv.NewWriter(&b)
-	_ = w.Write(cols)
-	w.Flush()
-	line := strings.TrimSuffix(b.String(), "\n")
-	if line == "" {
-		return `""` // a blank line is a row every CSV reader drops
+		fields[i] = literal(c, csvField, "")
 	}
+	if line := strings.Join(fields, ","); line != "" {
 		return line
 	}
+	return `""` // a blank line is a row every CSV reader drops
+}
 
-// SQLInsert renders the record as one INSERT statement into table: identifiers in
-// ANSI double quotes, every value a single-quoted string literal.
+func csvField(s string) string {
+	if s == "" {
+		return `""`
+	}
+	var b strings.Builder
+	w := csv.NewWriter(&b)
+	_ = w.Write([]string{s})
+	w.Flush()
+	return strings.TrimSuffix(b.String(), "\n")
+}
+
+// SQLInsert renders the record as one INSERT statement into table, identifiers in ANSI
+// double quotes.
 func (r *Record) SQLInsert(table string) string {
 	cols := make([]string, len(r.columns))
 	vals := make([]string, len(r.columns))
 	for i, c := range r.columns {
 		cols[i] = quoteIdent(c.Name)
-		vals[i] = "'" + strings.ReplaceAll(c.Value, "'", "''") + "'"
+		vals[i] = literal(c, sqlString, "NULL")
 	}
 	return fmt.Sprintf("INSERT INTO %s (%s) VALUES (%s);", quoteIdent(table), strings.Join(cols, ", "), strings.Join(vals, ", "))
 }
 
+func sqlString(s string) string {
+	return "'" + strings.ReplaceAll(s, "'", "''") + "'"
+}
+
 func quoteIdent(s string) string {
 	return `"` + strings.ReplaceAll(s, `"`, `""`) + `"`
 }
 
+// literal spells a column the way a serializer writes it: quoted for a string, bare for
+// any other datatype, whose every render the load check proved a literal, and nullText
+// for a null.
+func literal(c Column, quote func(string) string, nullText string) string {
+	switch {
+	case c.Null:
+		return nullText
+	case c.DataType == DataTypeString:
+		return quote(c.Value)
+	}
+	return c.Value
+}
+
 // FakeRecord renders a path as one record: the template it names, with each direct
 // field drawn as a column. Only a category-level template is a record — a path
 // that descends into a field, or that names a folder or a choice, is an error.
@@ -116,7 +143,7 @@ func (f *Generator) FakeRecord(path string) (*Record, error) {
 // columns, or why it is not a record.
 type recordShape struct {
 	t       *template
-	columns []string
+	columns []Column
 	err     error
 }
 
@@ -140,7 +167,7 @@ func (f *Generator) recordShapeOf(n node) recordShape {
 type RecordTemplate struct {
 	g       *Generator
 	t       *template
-	columns []string
+	columns []Column
 }
 
 // Fake renders the record with one draw.
@@ -175,7 +202,7 @@ func (f *Generator) FakeRecordTemplate(input string) (*Record, error) {
 
 // recordOf is the fence both record entry points pass. The columns come back with
 // the template, fixed for every draw the caller goes on to make.
-func recordOf(n node) (*template, []string, error) {
+func recordOf(n node) (*template, []Column, error) {
 	t, ok := n.(*template)
 	if !ok {
 		return nil, nil, errors.New("names a choice, not a template; a record is a template whose fields are its columns")
@@ -183,13 +210,18 @@ func recordOf(n node) (*template, []string, error) {
 	if t.repeat != 1 {
 		return nil, nil, fmt.Errorf("carries repeat %d, which composes its format into one string; a record projects columns instead — drop the repeat and render the record again for more rows", t.repeat)
 	}
-	columns := recordColumns(t)
-	if len(columns) == 0 {
+	names := recordColumns(t)
+	if len(names) == 0 {
 		return nil, nil, errors.New("has no fields, so no columns")
 	}
-	if err := checkColumnRefs(t, columns); err != nil {
+	if err := checkColumnRefs(t, names); err != nil {
 		return nil, nil, err
 	}
+	columns := make([]Column, len(names))
+	for i, name := range names {
+		datatype, _ := columnDatatype(t.fields[name]) // compile refused a column whose items disagree
+		columns[i] = Column{Name: name, DataType: datatype}
+	}
 	return t, columns, nil
 }
 
@@ -262,11 +294,16 @@ func columnRefs(t *template, columns []string) ([]columnRef, error) {
 
 // renderRecord draws each column once, in the name order recordOf fixed, over one
 // reference scope shared across them.
-func renderRecord(s *session, t *template, columns []string) *Record {
+func renderRecord(s *session, t *template, columns []Column) *Record {
 	scope := &draws{variant: map[string]node{}, value: map[string]string{}}
-	r := &Record{columns: make([]Column, len(columns))}
-	for i, name := range columns {
-		r.columns[i] = Column{Name: name, Value: render(s, t.fields[name], scope)}
+	r := &Record{columns: append([]Column(nil), columns...)}
+	for i := range r.columns {
+		n := drawn(s, t.fields[r.columns[i].Name])
+		if _, isNull := n.(*null); isNull {
+			r.columns[i].Null = true
+		} else {
+			r.columns[i].Value = render(s, n, scope)
+		}
 	}
 	return r
 }

render.go

@@ -56,6 +56,8 @@ func render(s *session, n node, refScope *draws) string {
 	switch n := n.(type) {
 	case *choice:
 		return render(s, pick(s, n), refScope)
+	case *null:
+		return ""
 	case *template:
 		if n.repeat == 1 {
 			if n.fixed {

renderlang.go

@@ -0,0 +1,403 @@
+package fejkdata
+
+import (
+	"slices"
+	"strconv"
+	"strings"
+	"unicode/utf8"
+)
+
+// grammar is a deterministic automaton over a scalar's text: state 0 is dead, 1 the
+// start, and each state lists the runes that leave it and where they lead.
+type grammar [][]arc
+
+type arc struct {
+	on string
+	to int
+}
+
+func (g *grammar) run(q int, s string) int {
+	for _, r := range s {
+		if q = g.step(q, r); q == 0 {
+			return 0
+		}
+	}
+	return q
+}
+
+func (g *grammar) step(q int, r rune) int {
+	for _, a := range (*g)[q] {
+		if strings.ContainsRune(a.on, r) {
+			return a.to
+		}
+	}
+	return 0
+}
+
+const (
+	decimalDigits = "0123456789"
+	nonZeroDigits = "123456789"
+)
+
+// numberGrammar reads a JSON number. States: 2 "-", 3 "0", 4 more integer digits, 5 ".",
+// 6 fraction digits, 7 "e", 8 its sign, 9 exponent digits.
+var numberGrammar = &grammar{
+	nil,
+	{{"-", 2}, {"0", 3}, {nonZeroDigits, 4}},
+	{{"0", 3}, {nonZeroDigits, 4}},
+	{{".", 5}, {"eE", 7}},
+	{{decimalDigits, 4}, {".", 5}, {"eE", 7}},
+	{{decimalDigits, 6}},
+	{{decimalDigits, 6}, {"eE", 7}},
+	{{"+-", 8}, {decimalDigits, 9}},
+	{{decimalDigits, 9}},
+	{{decimalDigits, 9}},
+}
+
+const (
+	integerAccept uint32 = 1<<3 | 1<<4
+	numberAccept         = integerAccept | 1<<6 | 1<<9
+)
+
+var booleanGrammar = &grammar{
+	nil,
+	{{"t", 2}, {"f", 6}},
+	{{"r", 3}}, {{"u", 4}}, {{"e", 5}}, nil,
+	{{"a", 7}}, {{"l", 8}}, {{"s", 9}}, {{"e", 10}}, nil,
+}
+
+const booleanAccept uint32 = 1<<5 | 1<<10
+
+// decimalGrammar reads what a calc operand must render to be proven finite: a sign,
+// digits and at most one dot. Past the sign, states 4–9 are positive and 10–15 their
+// negatives: 4 zero digits, 5 a nonzero integer, 6 a leading dot, 7 zero with a dot,
+// 8 a nonzero integer with a zero fraction, 9 a nonzero fraction.
+var decimalGrammar = &grammar{
+	nil,
+	{{"+", 2}, {"-", 3}, {"0", 4}, {nonZeroDigits, 5}, {".", 6}},
+	{{"0", 4}, {nonZeroDigits, 5}, {".", 6}},
+	{{"0", 10}, {nonZeroDigits, 11}, {".", 12}},
+	{{"0", 4}, {nonZeroDigits, 5}, {".", 7}},
+	{{decimalDigits, 5}, {".", 8}},
+	{{"0", 7}, {nonZeroDigits, 9}},
+	{{"0", 7}, {nonZeroDigits, 9}},
+	{{"0", 8}, {nonZeroDigits, 9}},
+	{{decimalDigits, 9}},
+	{{"0", 10}, {nonZeroDigits, 11}, {".", 13}},
+	{{decimalDigits, 11}, {".", 14}},
+	{{"0", 13}, {nonZeroDigits, 15}},
+	{{"0", 13}, {nonZeroDigits, 15}},
+	{{"0", 14}, {nonZeroDigits, 15}},
+	{{decimalDigits, 15}},
+}
+
+const (
+	decimalAccept     uint32 = 1<<4 | 1<<5 | 1<<7 | 1<<8 | 1<<9 | 1<<10 | 1<<11 | 1<<13 | 1<<14 | 1<<15
+	decimalNegative   uint32 = 0xfc00
+	decimalZero       uint32 = 1<<4 | 1<<7 | 1<<10 | 1<<13
+	decimalFractional uint32 = 1<<9 | 1<<15
+)
+
+// relation is what a node's renders do to a grammar: from each state, the states a
+// render can end in, and one render reaching each.
+type relation struct {
+	g  *grammar
+	to []uint32
+	w  []witness // w[from*len(to)+to]
+}
+
+// witness is one render, cut past witnessCap bytes, and why it can occur when the text
+// alone does not say.
+type witness struct {
+	text string
+	cut  bool
+	why  string
+}
+
+const witnessCap = 60
+
+func (w witness) then(next witness) witness {
+	if w.why == "" {
+		w.why = next.why
+	}
+	if w.cut {
+		return w
+	}
+	w.text += next.text
+	w.cut = next.cut
+	if len(w.text) > witnessCap {
+		end := witnessCap
+		for !utf8.RuneStart(w.text[end]) {
+			end--
+		}
+		w.text, w.cut = w.text[:end], true
+	}
+	return w
+}
+
+func (w witness) String() string {
+	if w.cut {
+		return strconv.Quote(w.text + "…")
+	}
+	return strconv.Quote(w.text)
+}
+
+func newRelation(g *grammar) *relation {
+	n := len(*g)
+	return &relation{g: g, to: make([]uint32, n), w: make([]witness, n*n)}
+}
+
+func (r *relation) add(from, to int, w witness) {
+	if r.to[from]&(1<<to) == 0 {
+		r.to[from] |= 1 << to
+		r.w[from*len(r.to)+to] = w
+	}
+}
+
+// textRelation is the relation of a render that is always s.
+func textRelation(g *grammar, s, why string) *relation {
+	r := newRelation(g)
+	w := witness{why: why}.then(witness{text: s})
+	for q := range r.to {
+		r.add(q, g.run(q, s), w)
+	}
+	return r
+}
+
+// union is the renders of either relation; a nil relation has none.
+func union(a, b *relation) *relation {
+	if a == nil {
+		return b
+	}
+	if b == nil {
+		return a
+	}
+	u := newRelation(a.g)
+	for _, r := range []*relation{a, b} {
+		for from, ends := range r.to {
+			for to := range r.to {
+				if ends&(1<<to) != 0 {
+					u.add(from, to, r.w[from*len(r.to)+to])
+				}
+			}
+		}
+	}
+	return u
+}
+
+// then is a render of r followed by a render of next.
+func (r *relation) then(next *relation) *relation {
+	c := newRelation(r.g)
+	n := len(r.to)
+	for from, mids := range r.to {
+		for mid := 0; mid < n; mid++ {
+			if mids&(1<<mid) == 0 {
+				continue
+			}
+			for to := 0; to < n; to++ {
+				if next.to[mid]&(1<<to) != 0 && c.to[from]&(1<<to) == 0 {
+					c.add(from, to, r.w[from*n+mid].then(next.w[mid*n+to]))
+				}
+			}
+		}
+	}
+	return c
+}
+
+// power is k renders of r in a row, k at least 1, composed by squaring.
+func (r *relation) power(k int) *relation {
+	var out *relation
+	for base := r; ; base = base.then(base) {
+		if k&1 == 1 {
+			if out == nil {
+				out = base
+			} else {
+				out = out.then(base)
+			}
+		}
+		if k >>= 1; k == 0 {
+			return out
+		}
+	}
+}
+
+// closure is any number of renders of r in a row, where r includes the empty render.
+func (r *relation) closure() *relation {
+	for {
+		next := r.then(r)
+		if slices.Equal(next.to, r.to) {
+			return r
+		}
+		r = next
+	}
+}
+
+// escape finds a render from the start that ends outside accept, preferring one that
+// carries a reason.
+func (r *relation) escape(accept uint32) (witness, bool) {
+	var found witness
+	escapes := false
+	for to := range r.to {
+		if (r.to[1]&^accept)&(1<<to) == 0 {
+			continue
+		}
+		if w := r.w[len(r.to)+to]; !escapes || found.why == "" && w.why != "" {
+			found, escapes = w, true
+		}
+	}
+	return found, escapes
+}
+
+// textShape is the text a builtin can emit: alternatives, each a sequence of runs.
+type textShape [][]charRun
+
+// charRun is between min and max characters, each one of chars; max -1 is unbounded.
+// chars is ASCII, so a run of k characters is k bytes.
+type charRun struct {
+	chars    string
+	min, max int
+}
+
+// textLanguage is what one grammar makes of the renders a check reads, worked out once
+// per node and fold.
+type textLanguage struct {
+	g     *grammar
+	proof *calcProof
+	memo  map[languageKey]*relation
+	empty *relation
+}
+
+type languageKey struct {
+	n    node
+	fold string
+}
+
+// fold is the transforms a render passes through before the grammar reads it, innermost
+// first. Each rewrites rune by rune, so folding a render is folding each of its pieces.
+type fold []string
+
+func (f fold) apply(s string) string {
+	for _, name := range f {
+		s = transforms[name](s)
+	}
+	return s
+}
+
+func newTextLanguage(g *grammar, proof *calcProof) *textLanguage {
+	return &textLanguage{g: g, proof: proof, memo: map[languageKey]*relation{}, empty: textRelation(g, "", "")}
+}
+
+func (l *textLanguage) node(n node, f fold) *relation {
+	key := languageKey{n, strings.Join(f, ",")}
+	if r, done := l.memo[key]; done {
+		return r
+	}
+	r := l.empty // a null renders ""
+	switch n := n.(type) {
+	case *choice:
+		r = nil
+		for _, it := range n.items {
+			r = union(r, l.node(it, f))
+		}
+	case *template:
+		r = l.format(n, f)
+		if n.repeat > 1 {
+			r = r.then(l.text(f.apply(n.separator)).then(r).power(n.repeat - 1))
+		}
+	}
+	l.memo[key] = r
+	return r
+}
+
+func (l *textLanguage) text(s string) *relation { return textRelation(l.g, s, "") }
+
+// format reads a template's format the way expand renders it: literal runs and tokens
+// in turn.
+func (l *textLanguage) format(t *template, f fold) *relation {
+	r := l.empty
+	var lit strings.Builder
+	_ = eachToken(t.format, func(tok ftoken) error {
+		if tok.kind == 'l' {
+			lit.WriteRune(tok.r)
+			return nil
+		}
+		r = r.then(l.text(f.apply(lit.String()))).then(l.token(t, tok.body, f))
+		lit.Reset()
+		return nil
+	})
+	return r.then(l.text(f.apply(lit.String())))
+}
+
+// token reads one {…} token: a field read, a transform over one, a calc, or what a
+// builtin emits.
+func (l *textLanguage) token(t *template, body string, f fold) *relation {
+	name, args, isFunc := funcCall(body)
+	if !isFunc {
+		var r *relation
+		for _, a := range splitArms(body, t.refs) {
+			r = union(r, l.read(t, a, f))
+		}
+		return r
+	}
+	if _, isTransform := transforms[name]; isTransform {
+		leaf, chain, _ := unwrapTransform(args[0])
+		inner := slices.Clone(chain)
+		slices.Reverse(inner)
+		return l.read(t, splitArm(leaf, t.refs), append(append(inner, name), f...))
+	}
+	if name == "calc" {
+		return l.calc(t, args, f)
+	}
+	return l.shape(builtins[name].emits(args), f)
+}
+
+// read is one arm of a token: every node its path can land on.
+func (l *textLanguage) read(t *template, a arm, f fold) *relation {
+	var r *relation
+	for _, leaf := range pathLeaves(t.fields[a.key], a.tail) {
+		r = union(r, l.node(leaf, f))
+	}
+	return r
+}
+
+func (l *textLanguage) calc(t *template, args []string, f fold) *relation {
+	b, d := l.proof.call(t, args)
+	if d != nil {
+		return textRelation(l.g, f.apply(d.render), d.why)
+	}
+	return l.shape(printedFloat(b.lo, b.hi, calcDecimals(args), b.integral), f)
+}
+
+func (l *textLanguage) shape(s textShape, f fold) *relation {
+	var r *relation
+	for _, alt := range s {
+		seq := l.empty
+		for _, run := range alt {
+			seq = seq.then(l.run(run, f))
+		}
+		r = union(r, seq)
+	}
+	return r
+}
+
+// run reads a charRun: min characters, then up to max-min more.
+func (l *textLanguage) run(c charRun, f fold) *relation {
+	one := newRelation(l.g)
+	for from := range one.to {
+		for _, ch := range c.chars {
+			s := f.apply(string(ch))
+			one.add(from, l.g.run(from, s), witness{text: s})
+		}
+	}
+	more := l.empty
+	switch optional := union(one, l.empty); {
+	case c.max < 0:
+		more = optional.closure()
+	case c.max > c.min:
+		more = optional.power(c.max - c.min)
+	}
+	if c.min == 0 {
+		return more
+	}
+	return one.power(c.min).then(more)
+}

template.go

@@ -72,6 +72,9 @@ type builtin struct {
 	// operands names the fields the call reads, which expand renders for it; nil
 	// for a builtin that reads none.
 	operands func(args []string) []string
+	// emits is the text a call can print, for the datatype check; nil for calc and the
+	// transforms, whose text the check derives from what they read.
+	emits func(args []string) textShape
 }
 
 // funcCall splits a "{token}" body shaped name(args) into its parts; ok is false

todo.md

@@ -6,11 +6,6 @@ The record API lands first, so the data update can use it.
 
 ### Record API
 
-- Typed columns — a column declares its type, so `json` writes `42` rather than
-  `"42"` and `sql` an unquoted literal: string, integer, number, boolean, and a
-  way to write null. A template that can render a value its type rejects is a
-  load error. The option key is reserved from then on, so a common column name
-  like `type` is a poor pick.
 - Struct-filling — fill a Go struct from `fake:"…"` tags holding a path or an
   inline template, for parity with gofakeit and go-faker. The field's Go type is
   the column type, through the same conversion and load checks as typed columns,