JSON schema conversion: ⚡️ faster repetitions, min/maxLength for strings, cap number length (#6555)

* json: rename python schema converter to make import easier

* server: skip null json_schema / grammar fields

* json: deps management for primitive rules (+ allow null values)

* json: optimize repetitions for minItems/maxItems and regexps: `a{,3}` goes from `"a"? "a"? "a"?` (explosive combos) to `(a (a (a)?)?)?`

* grammars: add troubleshooting section to readme

* json: cap length of numbers to 15 digits before/after decimal point

(avoids infinite gen, e.g. "one third" -> `0.333333333333...`)

* json: unify all repetition code (w/ or w/o sep)

* json: support string minLength/maxLength

* server+json: update server/README w/ result_format

* nits

* json: fix type error w/ python 3.8

* json: fix server/README (json_schema in /completion vs. result_format in /v1/chat/completions)

* json: simplify DOT `{"type": "string", "pattern": "^.$"}`

* json: remove recursion in opt_repetitions (avoids Python stack overflow)

* json: rm dead code

* json: rm useless assert & ggml.h import

7 files changed, 2028 insertions, 1719 deletions

diff --git a/examples/json-schema-to-grammar.py b/examples/json_schema_to_grammar.py
index 91dd734c..826cd3f7 100755
--- a/examples/json-schema-to-grammar.py
+++ b/examples/json_schema_to_grammar.py
@@ -6,37 +6,94 @@ import re
 import sys
 from typing import Any, Dict, List, Set, Tuple, Union
 
+def _build_repetition(item_rule, min_items, max_items, separator_rule=None, item_rule_is_literal=False):
+    if not separator_rule:
+        if min_items == 0 and max_items == 1:
+            return f'{item_rule}?'
+        elif min_items == 1 and max_items is None:
+            return f'{item_rule}+'
+
+    result = ''
+
+    if min_items > 0:
+        if item_rule_is_literal and separator_rule is None:
+            result = '"' + (item_rule[1:-1] * min_items) + '"'
+        else:
+            result = (f' {separator_rule} ' if separator_rule else ' ').join([item_rule] * min_items)
+
+    def opt_repetitions(up_to_n, prefix_with_sep=False):
+        '''
+            - n=4, no sep:             '(a (a (a (a)?)?)?)?'
+            - n=4, sep=',', prefix:    '("," a ("," a ("," a ("," a)?)?)?)?'
+            - n=4, sep=',', no prefix: '(a ("," a ("," a ("," a)?)?)?)?'
+        '''
+
+        content = f'{separator_rule} {item_rule}' if prefix_with_sep and separator_rule else item_rule
+        if up_to_n == 0:
+            return ''
+        elif up_to_n == 1:
+            return f'({content})?'
+        elif separator_rule and not prefix_with_sep:
+            return f'({content} {opt_repetitions(up_to_n - 1, prefix_with_sep=True)})?'
+        else:
+            return (f'({content} ' * up_to_n).rstrip() + (')?' * up_to_n)
+
+    if min_items > 0 and max_items != min_items:
+        result += ' '
+
+    if max_items is not None:
+        result += opt_repetitions(max_items - min_items, prefix_with_sep=min_items > 0)
+    else:
+        item_operator = f'({separator_rule + " " if separator_rule else ""}{item_rule})'
+
+        if min_items == 0 and separator_rule:
+            result = f'({item_rule} {item_operator}*)?'
+        else:
+            result += f'{item_operator}*'
+
+    return result
+
+
+class BuiltinRule:
+    def __init__(self, content: str, deps: list = None):
+        self.content = content
+        self.deps = deps or []
+
+_up_to_15_digits = _build_repetition('[0-9]', 0, 15)
+
 # whitespace is constrained to a single space char to prevent model "running away" in
 # whitespace. Also maybe improves generation quality?
 SPACE_RULE = '" "?'
 
 PRIMITIVE_RULES = {
-    'boolean': '("true" | "false") space',
-    'number': '("-"? ([0-9] | [1-9] [0-9]*)) ("." [0-9]+)? ([eE] [-+]? [0-9]+)? space',
-    'integer': '("-"? ([0-9] | [1-9] [0-9]*)) space',
-    'value'  : 'object | array | string | number | boolean',
-    'object' : '"{" space ( string ":" space value ("," space string ":" space value)* )? "}" space',
-    'array'  : '"[" space ( value ("," space value)* )? "]" space',
-    'uuid'   : '"\\"" ' + ' "-" '.join('[0-9a-fA-F]' * n for n in [8, 4, 4, 4, 12]) + ' "\\"" space',
-    'string': r''' "\"" (
-        [^"\\] |
-        "\\" (["\\/bfnrt] | "u" [0-9a-fA-F] [0-9a-fA-F] [0-9a-fA-F] [0-9a-fA-F])
-      )* "\"" space''',
-    'null': '"null" space',
+    'boolean'      : BuiltinRule('("true" | "false") space', []),
+    'decimal-part' : BuiltinRule('[0-9] ' + _up_to_15_digits, []),
+    'integral-part': BuiltinRule('[0-9] | [1-9] ' + _up_to_15_digits, []),
+    'number'       : BuiltinRule('("-"? integral-part) ("." decimal-part)? ([eE] [-+]? integral-part)? space', ['integral-part', 'decimal-part']),
+    'integer'      : BuiltinRule('("-"? integral-part) space', ['integral-part']),
+    'value'        : BuiltinRule('object | array | string | number | boolean | null', ['object', 'array', 'string', 'number', 'boolean', 'null']),
+    'object'       : BuiltinRule('"{" space ( string ":" space value ("," space string ":" space value)* )? "}" space', ['string', 'value']),
+    'array'        : BuiltinRule('"[" space ( value ("," space value)* )? "]" space', ['value']),
+    'uuid'         : BuiltinRule(r'"\"" ' + ' "-" '.join('[0-9a-fA-F]' * n for n in [8, 4, 4, 4, 12]) + r' "\"" space', []),
+    'char'         : BuiltinRule(r'[^"\\] | "\\" (["\\/bfnrt] | "u" [0-9a-fA-F] [0-9a-fA-F] [0-9a-fA-F] [0-9a-fA-F])', []),
+    'string'       : BuiltinRule(r'"\"" char* "\"" space', ['char']),
+    'null'         : BuiltinRule('"null" space', []),
 }
-OBJECT_RULE_NAMES = ['object', 'array', 'string', 'number', 'boolean', 'null', 'value']
 
 # TODO: support "uri", "email" string formats
-DATE_RULES = {
-    'date'   : '[0-9] [0-9] [0-9] [0-9] "-" ( "0" [1-9] | "1" [0-2] ) "-" ( \"0\" [1-9] | [1-2] [0-9] | "3" [0-1] )',
-    'time'   : '([01] [0-9] | "2" [0-3]) ":" [0-5] [0-9] ":" [0-5] [0-9] ( "." [0-9] [0-9] [0-9] )? ( "Z" | ( "+" | "-" ) ( [01] [0-9] | "2" [0-3] ) ":" [0-5] [0-9] )',
-    'date-time': 'date "T" time',
-    'date-string': '"\\"" date "\\"" space',
-    'time-string': '"\\"" time "\\"" space',
-    'date-time-string': '"\\"" date-time "\\"" space',
+STRING_FORMAT_RULES = {
+    'date'            : BuiltinRule('[0-9] [0-9] [0-9] [0-9] "-" ( "0" [1-9] | "1" [0-2] ) "-" ( \"0\" [1-9] | [1-2] [0-9] | "3" [0-1] )', []),
+    'time'            : BuiltinRule('([01] [0-9] | "2" [0-3]) ":" [0-5] [0-9] ":" [0-5] [0-9] ( "." [0-9] [0-9] [0-9] )? ( "Z" | ( "+" | "-" ) ( [01] [0-9] | "2" [0-3] ) ":" [0-5] [0-9] )', []),
+    'date-time'       : BuiltinRule('date "T" time', ['date', 'time']),
+    'date-string'     : BuiltinRule('"\\"" date "\\"" space', ['date']),
+    'time-string'     : BuiltinRule('"\\"" time "\\"" space', ['time']),
+    'date-time-string': BuiltinRule('"\\"" date-time "\\"" space', ['date-time']),
 }
 
-RESERVED_NAMES = set(["root", *PRIMITIVE_RULES.keys(), *DATE_RULES.keys()])
+DOTALL = '[\\U00000000-\\U0010FFFF]'
+DOT = '[^\\x0A\\x0D]'
+
+RESERVED_NAMES = set(["root", "dot", *PRIMITIVE_RULES.keys(), *STRING_FORMAT_RULES.keys()])
 
 INVALID_RULE_CHARS_RE = re.compile(r'[^a-zA-Z0-9-]+')
 GRAMMAR_LITERAL_ESCAPE_RE = re.compile(r'[\r\n"]')
@@ -46,8 +103,6 @@ GRAMMAR_LITERAL_ESCAPES = {'\r': '\\r', '\n': '\\n', '"': '\\"', '-': '\\-', ']'
 NON_LITERAL_SET = set('|.()[]{}*+?')
 ESCAPED_IN_REGEXPS_BUT_NOT_IN_LITERALS = set('[]()|{}*+?')
 
-DATE_PATTERN = '[0-9]{4}-(0[1-9]|1[0-2])-([0-2][0-9]|3[0-1])'
-TIME_PATTERN = '([01][0-9]|2[0-3])(:[0-5][0-9]){2}(\\.[0-9]{1,3})?(Z|[+-](([01][0-9]|2[0-3]):[0-5][0-9]))' # Cap millisecond precision w/ 3 digits
 
 class SchemaConverter:
     def __init__(self, *, prop_order, allow_fetch, dotall, raw_pattern):
@@ -55,7 +110,9 @@ class SchemaConverter:
         self._allow_fetch = allow_fetch
         self._dotall = dotall
         self._raw_pattern = raw_pattern
-        self._rules = {'space': SPACE_RULE}
+        self._rules = {
+            'space': SPACE_RULE,
+        }
         self._refs = {}
         self._refs_being_resolved = set()
 
@@ -65,6 +122,29 @@ class SchemaConverter:
         )
         return f'"{escaped}"'
 
+    def not_literal(self, literal: str, dotall: bool = True, maybe_escaped_underscores = False) -> str:
+        '''
+            not_literal('a') -> '[^a]'
+            not_literal('abc') -> '([^a] | "a" ([^b] | "b" ([^c])?)?)?'
+        '''
+        assert len(literal) > 0, 'Empty literal not supported'
+        def recurse(i: int):
+            c = literal[i]
+            if maybe_escaped_underscores and c == '_':
+                yield f'[^{c}\\\\]'
+                yield ' | '
+                yield f'"\\\\"? "{c}"'
+            else:
+                yield f'[^{c}]'
+            if i < len(literal) - 1:
+                yield ' | '
+                yield self._format_literal(c)
+                yield ' ('
+                yield from recurse(i + 1)
+                yield ')?'
+
+        return ''.join(('(', *recurse(0), ')'))
+
     def _add_rule(self, name, rule):
         esc_name = INVALID_RULE_CHARS_RE.sub('-', name)
         if esc_name not in self._rules or self._rules[esc_name] == rule:
@@ -169,10 +249,10 @@ class SchemaConverter:
 
             def get_dot():
                 if self._dotall:
-                    rule = '[\\U00000000-\\U0010FFFF]'
+                    rule = DOTALL
                 else:
                     # Accept any character... except \n and \r line break chars (\x0A and \xOD)
-                    rule = '[\\U00000000-\\x09\\x0B\\x0C\\x0E-\\U0010FFFF]'
+                    rule = DOT
                 return self._add_rule(f'dot', rule)
 
             def join_seq():
@@ -246,26 +326,14 @@ class SchemaConverter:
 
                     (sub, sub_is_literal) = seq[-1]
 
-                    if min_times == 0 and max_times is None:
-                        seq[-1] = (f'{sub}*', False)
-                    elif min_times == 0 and max_times == 1:
-                        seq[-1] = (f'{sub}?', False)
-                    elif min_times == 1 and max_times is None:
-                        seq[-1] = (f'{sub}+', False)
-                    else:
-                        if not sub_is_literal:
-                            id = sub_rule_ids.get(sub)
-                            if id is None:
-                                id = self._add_rule(f'{name}-{len(sub_rule_ids) + 1}', sub)
-                                sub_rule_ids[sub] = id
-                            sub = id
-
-                        seq[-1] = (
-                            ' '.join(
-                                ([f'"{sub[1:-1] * min_times}"'] if sub_is_literal else [sub] * min_times) +
-                                ([f'{sub}?'] * (max_times - min_times) if max_times is not None else [f'{sub}*'])),
-                            False
-                        )
+                    if not sub_is_literal:
+                        id = sub_rule_ids.get(sub)
+                        if id is None:
+                            id = self._add_rule(f'{name}-{len(sub_rule_ids) + 1}', sub)
+                            sub_rule_ids[sub] = id
+                        sub = id
+
+                    seq[-1] = (_build_repetition(f'"{sub}"' if sub_is_literal else sub, min_times, max_times, item_rule_is_literal=sub_is_literal), False)
                 else:
                     literal = ''
                     while i < length:
@@ -373,49 +441,47 @@ class SchemaConverter:
                     ' "]" space')
             else:
                 item_rule_name = self.visit(items, f'{name}{"-" if name else ""}item')
-                list_item_operator = f'( "," space {item_rule_name} )'
-                successive_items = ""
                 min_items = schema.get("minItems", 0)
                 max_items = schema.get("maxItems")
-                if min_items > 0:
-                    successive_items = list_item_operator * (min_items - 1)
-                    min_items -= 1
-                if max_items is not None and max_items > min_items:
-                    successive_items += (list_item_operator + "?") * (max_items - min_items - 1)
-                else:
-                    successive_items += list_item_operator + "*"
-                if min_items == 0:
-                    rule = f'"[" space ( {item_rule_name} {successive_items} )? "]" space'
-                else:
-                    rule = f'"[" space {item_rule_name} {successive_items} "]" space'
-                return self._add_rule(rule_name, rule)
+                return self._add_rule(rule_name, '"[" space ' + _build_repetition(item_rule_name, min_items, max_items, separator_rule='"," space') + ' "]" space')
 
         elif schema_type in (None, 'string') and 'pattern' in schema:
             return self._visit_pattern(schema['pattern'], rule_name)
 
         elif schema_type in (None, 'string') and re.match(r'^uuid[1-5]?$', schema_format or ''):
-            return self._add_rule(
+            return self._add_primitive(
                 'root' if rule_name == 'root' else schema_format,
                 PRIMITIVE_RULES['uuid']
             )
 
-        elif schema_type in (None, 'string') and schema_format in DATE_RULES:
-            for t, r in DATE_RULES.items():
-                self._add_rule(t, r)
-            return schema_format + '-string'
+        elif schema_type in (None, 'string') and f'{schema_format}-string' in STRING_FORMAT_RULES:
+            prim_name = f'{schema_format}-string'
+            return self._add_rule(rule_name, self._add_primitive(prim_name, STRING_FORMAT_RULES[prim_name]))
+
+        elif schema_type == 'string' and ('minLength' in schema or 'maxLength' in schema):
+            char_rule = self._add_primitive('char', PRIMITIVE_RULES['char'])
+            min_len = schema.get('minLength', 0)
+            max_len = schema.get('maxLength')
+
+            return self._add_rule(rule_name, r'"\"" ' + _build_repetition(char_rule, min_len, max_len) + r' "\"" space')
 
         elif (schema_type == 'object') or (len(schema) == 0):
-            for n in OBJECT_RULE_NAMES:
-                self._add_rule(n, PRIMITIVE_RULES[n])
-            return self._add_rule(rule_name, 'object')
+            return self._add_rule(rule_name, self._add_primitive('object', PRIMITIVE_RULES['object']))
 
         else:
             assert schema_type in PRIMITIVE_RULES, f'Unrecognized schema: {schema}'
             # TODO: support minimum, maximum, exclusiveMinimum, exclusiveMaximum at least for zero
-            return self._add_rule(
-                'root' if rule_name == 'root' else schema_type,
-                PRIMITIVE_RULES[schema_type]
-            )
+            return self._add_primitive('root' if rule_name == 'root' else schema_type, PRIMITIVE_RULES[schema_type])
+
+    def _add_primitive(self, name: str, rule: BuiltinRule):
+        n = self._add_rule(name, rule.content)
+
+        for dep in rule.deps:
+            dep_rule = PRIMITIVE_RULES.get(dep) or STRING_FORMAT_RULES.get(dep)
+            assert dep_rule, f'Rule {dep} not known'
+            if dep not in self._rules:
+                self._add_primitive(dep, dep_rule)
+        return n
 
     def _build_object_rule(self, properties: List[Tuple[str, Any]], required: Set[str], name: str, additional_properties: Union[bool, Any]):
         prop_order = self._prop_order
@@ -437,7 +503,7 @@ class SchemaConverter:
             value_rule = self.visit({} if additional_properties == True else additional_properties, f'{sub_name}-value')
             prop_kv_rule_names["*"] = self._add_rule(
                 f'{sub_name}-kv',
-                self._add_rule('string', PRIMITIVE_RULES['string']) + f' ":" space {value_rule}'
+                self._add_primitive('string', PRIMITIVE_RULES['string']) + f' ":" space {value_rule}'
             )
             optional_props.append("*")
 
diff --git a/examples/regex-to-grammar.py b/examples/regex-to-grammar.py
index c98118e9..5cd9210a 100644
--- a/examples/regex-to-grammar.py
+++ b/examples/regex-to-grammar.py
@@ -8,7 +8,7 @@ print(subprocess.check_output(
         "python",
         os.path.join(
         os.path.dirname(os.path.realpath(__file__)),
-        "json-schema-to-grammar.py"),
+        "json_schema_to_grammar.py"),
         *rest,
         "-",
         "--raw-pattern",
diff --git a/examples/server/README.md b/examples/server/README.md
index a6fc92ea..918ac129 100644
--- a/examples/server/README.md
+++ b/examples/server/README.md
@@ -11,6 +11,7 @@ Set of LLM REST APIs and a simple web front end to interact with llama.cpp.
  * Continuous batching
  * Multimodal (wip)
  * Monitoring endpoints
+ * Schema-constrained JSON response format
 
 The project is under active development, and we are [looking for feedback and contributors](https://github.com/ggerganov/llama.cpp/issues/4216).
 
@@ -250,6 +251,8 @@ node index.js
 
     `grammar`: Set grammar for grammar-based sampling.  Default: no grammar
 
+    `json_schema`: Set a JSON schema for grammar-based sampling (e.g. `{"items": {"type": "string"}, "minItems": 10, "maxItems": 100}` of a list of strings, or `{}` for any JSON). See [tests](../../tests/test-json-schema-to-grammar.cpp) for supported features.  Default: no JSON schema.
+
     `seed`: Set the random number generator (RNG) seed.  Default: `-1`, which is a random seed.
 
     `ignore_eos`: Ignore end of stream token and continue generating.  Default: `false`
@@ -365,6 +368,8 @@ Notice that each `probs` is an array of length `n_probs`.
 
     See [OpenAI Chat Completions API documentation](https://platform.openai.com/docs/api-reference/chat). While some OpenAI-specific features such as function calling aren't supported, llama.cpp `/completion`-specific features such as `mirostat` are supported.
 
+    The `response_format` parameter supports both plain JSON output (e.g. `{"type": "json_object"}`) and schema-constrained JSON (e.g. `{"type": "json_object", "schema": {"type": "string", "minLength": 10, "maxLength": 100}}`), similar to other OpenAI-inspired API providers.
+
     *Examples:*
 
     You can use either Python `openai` library with appropriate checkpoints:
diff --git a/examples/server/json-schema-to-grammar.mjs.hpp b/examples/server/json-schema-to-grammar.mjs.hpp
index ef1d5dcf..da5035bf 100644
--- a/examples/server/json-schema-to-grammar.mjs.hpp
+++ b/examples/server/json-schema-to-grammar.mjs.hpp
@@ -2,1643 +2,1825 @@ unsigned char json_schema_to_grammar_mjs[] = {
   0x2f, 0x2f, 0x20, 0x57, 0x41, 0x52, 0x4e, 0x49, 0x4e, 0x47, 0x3a, 0x20,
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-  0x61, 0x2d, 0x74, 0x6f, 0x2d, 0x67, 0x72, 0x61, 0x6d, 0x6d, 0x61, 0x72,
+  0x6d, 0x20, 0x6a, 0x73, 0x6f, 0x6e, 0x5f, 0x73, 0x63, 0x68, 0x65, 0x6d,
+  0x61, 0x5f, 0x74, 0x6f, 0x5f, 0x67, 0x72, 0x61, 0x6d, 0x6d, 0x61, 0x72,
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+  0x64, 0x20, 0x5b, 0x6c, 0x61, 0x73, 0x74, 0x4b, 0x65, 0x79, 0x2c, 0x20,
+  0x67, 0x72, 0x6f, 0x75, 0x70, 0x5d, 0x3b, 0x0a, 0x20, 0x20, 0x7d, 0x0a,
+  0x7d, 0x0a
 };
-unsigned int json_schema_to_grammar_mjs_len = 19690;
+unsigned int json_schema_to_grammar_mjs_len = 21866;
diff --git a/examples/server/public/json-schema-to-grammar.mjs b/examples/server/public/json-schema-to-grammar.mjs
index 17bd60fd..8e0be1b4 100644
--- a/examples/server/public/json-schema-to-grammar.mjs
+++ b/examples/server/public/json-schema-to-grammar.mjs
@@ -1,33 +1,95 @@
-// WARNING: This file was ported from json-schema-to-grammar.py, please fix bugs / add features there first.
+// WARNING: This file was ported from json_schema_to_grammar.py, please fix bugs / add features there first.
 const SPACE_RULE = '" "?';
 
+function _buildRepetition(itemRule, minItems, maxItems, opts={}) {
+  const separatorRule = opts.separatorRule ?? '';
+  const itemRuleIsLiteral = opts.itemRuleIsLiteral ?? false
+
+  if (separatorRule === '') {
+    if (minItems === 0 && maxItems === 1) {
+      return `${itemRule}?`;
+    } else if (minItems === 1 && maxItems === undefined) {
+      return `${itemRule}+`;
+    }
+  }
+
+  let result = '';
+  if (minItems > 0) {
+    if (itemRuleIsLiteral && separatorRule === '') {
+      result = `"${itemRule.slice(1, -1).repeat(minItems)}"`;
+    } else {
+      result = Array.from({ length: minItems }, () => itemRule)
+        .join(separatorRule !== '' ? ` ${separatorRule} ` : ' ');
+    }
+  }
+
+  const optRepetitions = (upToN, prefixWithSep=false) => {
+    const content = separatorRule !== '' && prefixWithSep ? `${separatorRule} ${itemRule}` : itemRule;
+    if (upToN === 0) {
+      return '';
+    } else if (upToN === 1) {
+      return `(${content})?`;
+    } else if (separatorRule !== '' && !prefixWithSep) {
+      return `(${content} ${optRepetitions(upToN - 1, true)})?`;
+    } else {
+      return Array.from({ length: upToN }, () => `(${content}`).join(' ').trim() + Array.from({ length: upToN }, () => ')?').join('');
+    }
+  };
+
+  if (minItems > 0 && maxItems !== minItems) {
+    result += ' ';
+  }
+
+  if (maxItems !== undefined) {
+    result += optRepetitions(maxItems - minItems, minItems > 0);
+  } else {
+    const itemOperator = `(${separatorRule !== '' ? separatorRule + ' ' : ''}${itemRule})`;
+
+    if (minItems === 0 && separatorRule !== '') {
+      result = `(${itemRule} ${itemOperator}*)?`;
+    } else {
+      result += `${itemOperator}*`;
+    }
+  }
+
+  return result;
+}
+
+class BuiltinRule {
+  constructor(content, deps) {
+    this.content = content;
+    this.deps = deps || [];
+  }
+}
+
+const UP_TO_15_DIGITS = _buildRepetition('[0-9]', 0, 15);
+
 const PRIMITIVE_RULES = {
-  boolean: '("true" | "false") space',
-  number: '("-"? ([0-9] | [1-9] [0-9]*)) ("." [0-9]+)? ([eE] [-+]? [0-9]+)? space',
-  integer: '("-"? ([0-9] | [1-9] [0-9]*)) space',
-  value: 'object | array | string | number | boolean',
-  object: '"{" space ( string ":" space value ("," space string ":" space value)* )? "}" space',
-  array: '"[" space ( value ("," space value)* )? "]" space',
-  uuid: '"\\"" ' + [8, 4, 4, 4, 12].map(n => [...new Array(n)].map(_ => '[0-9a-fA-F]').join('')).join(' "-" ') + ' "\\"" space',
-  string: ` "\\"" (
-        [^"\\\\] |
-        "\\\\" (["\\\\/bfnrt] | "u" [0-9a-fA-F] [0-9a-fA-F] [0-9a-fA-F] [0-9a-fA-F])
-      )* "\\"" space`,
-  null: '"null" space',
+  boolean        : new BuiltinRule('("true" | "false") space', []),
+  'decimal-part' : new BuiltinRule('[0-9] ' + UP_TO_15_DIGITS, []),
+  'integral-part': new BuiltinRule('[0-9] | [1-9] ' + UP_TO_15_DIGITS, []),
+  number         : new BuiltinRule('("-"? integral-part) ("." decimal-part)? ([eE] [-+]? integral-part)? space', ['integral-part', 'decimal-part']),
+  integer        : new BuiltinRule('("-"? integral-part) space', ['integral-part']),
+  value          : new BuiltinRule('object | array | string | number | boolean | null', ['object', 'array', 'string', 'number', 'boolean', 'null']),
+  object         : new BuiltinRule('"{" space ( string ":" space value ("," space string ":" space value)* )? "}" space', ['string', 'value']),
+  array          : new BuiltinRule('"[" space ( value ("," space value)* )? "]" space', ['value']),
+  uuid           : new BuiltinRule('"\\"" ' + [8, 4, 4, 4, 12].map(n => [...new Array(n)].map(_ => '[0-9a-fA-F]').join('')).join(' "-" ') + ' "\\"" space', []),
+  char           : new BuiltinRule(`[^"\\\\] | "\\\\" (["\\\\/bfnrt] | "u" [0-9a-fA-F] [0-9a-fA-F] [0-9a-fA-F] [0-9a-fA-F])`, []),
+  string         : new BuiltinRule(`"\\"" char* "\\"" space`, ['char']),
+  null           : new BuiltinRule('"null" space', []),
 };
-const OBJECT_RULE_NAMES = ['object', 'array', 'string', 'number', 'boolean', 'null', 'value'];
 
 // TODO: support "uri", "email" string formats
-const DATE_RULES = {
-    'date'   : '[0-9] [0-9] [0-9] [0-9] "-" ( "0" [1-9] | "1" [0-2] ) "-" ( \"0\" [1-9] | [1-2] [0-9] | "3" [0-1] )',
-    'time'   : '([01] [0-9] | "2" [0-3]) ":" [0-5] [0-9] ":" [0-5] [0-9] ( "." [0-9] [0-9] [0-9] )? ( "Z" | ( "+" | "-" ) ( [01] [0-9] | "2" [0-3] ) ":" [0-5] [0-9] )',
-    'date-time': 'date "T" time',
-    'date-string': '"\\"" date "\\"" space',
-    'time-string': '"\\"" time "\\"" space',
-    'date-time-string': '"\\"" date-time "\\"" space',
-};
+const STRING_FORMAT_RULES = {
+  'date'            : new BuiltinRule('[0-9] [0-9] [0-9] [0-9] "-" ( "0" [1-9] | "1" [0-2] ) "-" ( \"0\" [1-9] | [1-2] [0-9] | "3" [0-1] )', []),
+  'time'            : new BuiltinRule('([01] [0-9] | "2" [0-3]) ":" [0-5] [0-9] ":" [0-5] [0-9] ( "." [0-9] [0-9] [0-9] )? ( "Z" | ( "+" | "-" ) ( [01] [0-9] | "2" [0-3] ) ":" [0-5] [0-9] )', []),
+  'date-time'       : new BuiltinRule('date "T" time', ['date', 'time']),
+  'date-string'     : new BuiltinRule('"\\"" date "\\"" space', ['date']),
+  'time-string'     : new BuiltinRule('"\\"" time "\\"" space', ['time']),
+  'date-time-string': new BuiltinRule('"\\"" date-time "\\"" space', ['date-time']),
+}
 
-const RESERVED_NAMES = {'root': true, ...PRIMITIVE_RULES, ...DATE_RULES};
+const RESERVED_NAMES = {'root': true, ...PRIMITIVE_RULES, ...STRING_FORMAT_RULES};
 
 const INVALID_RULE_CHARS_RE = /[^\dA-Za-z-]+/g;
 const GRAMMAR_LITERAL_ESCAPE_RE = /[\n\r"]/g;
@@ -158,7 +220,7 @@ export class SchemaConverter {
         rule = '[\\U00000000-\\U0010FFFF]';
       } else {
         // Accept any character... except \n and \r line break chars (\x0A and \xOD)
-        rule = '[\\U00000000-\\x09\\x0B\\x0C\\x0E-\\U0010FFFF]';
+        rule = '[^\\x0A\\x0D]';
       }
       return this._addRule('dot', rule);
     };
@@ -259,26 +321,19 @@ export class SchemaConverter {
 
           let [sub, subIsLiteral] = seq[seq.length - 1];
 
-          if (minTimes === 0 && maxTimes === Infinity) {
-            seq[seq.length - 1] = [`${sub}*`, false];
-          } else if (minTimes === 0 && maxTimes === 1) {
-            seq[seq.length - 1] = [`${sub}?`, false];
-          } else if (minTimes === 1 && maxTimes === Infinity) {
-            seq[seq.length - 1] = [`${sub}+`, false];
-          } else {
-            if (!subIsLiteral) {
-              let id = subRuleIds[sub];
-              if (id === undefined) {
-                id = this._addRule(`${name}-${Object.keys(subRuleIds).length + 1}`, sub);
-                subRuleIds[sub] = id;
-              }
-              sub = id;
+          if (!subIsLiteral) {
+            let id = subRuleIds[sub];
+            if (id === undefined) {
+              id = this._addRule(`${name}-${Object.keys(subRuleIds).length + 1}`, sub);
+              subRuleIds[sub] = id;
             }
-
-            const repeatedSub = Array.from({ length: minTimes }, () => subIsLiteral ? `"${sub.slice(1, -1).repeat(minTimes)}"` : sub);
-            const optionalSub = maxTimes !== undefined ? Array.from({ length: maxTimes - minTimes }, () => `${sub}?`) : [`${sub}*`];
-            seq[seq.length - 1] = [repeatedSub.concat(optionalSub).join(' '), false];
+            sub = id;
           }
+
+          seq[seq.length - 1] = [
+            _buildRepetition(subIsLiteral ? `"${sub}"` : sub, minTimes, maxTimes, {itemRuleIsLiteral: subIsLiteral}),
+            false
+          ];
         } else {
           let literal = '';
           while (i < length) {
@@ -394,47 +449,48 @@ export class SchemaConverter {
         );
       } else {
         const itemRuleName = this.visit(items, `${name ?? ''}${name ? '-' : ''}item`);
-        const listItemOperator = `( "," space ${itemRuleName} )`;
-        let successiveItems = '';
-        let minItems = schema.minItems || 0;
+        const minItems = schema.minItems || 0;
         const maxItems = schema.maxItems;
-        if (minItems > 0) {
-          successiveItems = listItemOperator.repeat(minItems - 1);
-          minItems--;
-        }
-        if (maxItems !== undefined && maxItems > minItems) {
-          successiveItems += `${listItemOperator}?`.repeat(maxItems - minItems - 1);
-        } else {
-          successiveItems += `${listItemOperator}*`;
-        }
-        const rule = minItems === 0
-          ? `"[" space ( ${itemRuleName} ${successiveItems} )? "]" space`
-          : `"[" space ${itemRuleName} ${successiveItems} "]" space`;
-        return this._addRule(ruleName, rule);
+        return this._addRule(ruleName, '"[" space ' + _buildRepetition(itemRuleName, minItems, maxItems, {separatorRule: '"," space'}) + ' "]" space');
       }
     } else if ((schemaType === undefined || schemaType === 'string') && 'pattern' in schema) {
       return this._visitPattern(schema.pattern, ruleName);
     } else if ((schemaType === undefined || schemaType === 'string') && /^uuid[1-5]?$/.test(schema.format || '')) {
-      return this._addRule(
-          ruleName === 'root' ? 'root' : schemaFormat,
-          PRIMITIVE_RULES['uuid'])
-    } else if ((schemaType === undefined || schemaType === 'string') && schema.format in DATE_RULES) {
-      for (const [t, r] of Object.entries(DATE_RULES)) {
-        this._addRule(t, r);
-      }
-      return schemaFormat + '-string';
+      return this._addPrimitive(
+        ruleName === 'root' ? 'root' : schemaFormat,
+        PRIMITIVE_RULES['uuid']
+      );
+    } else if ((schemaType === undefined || schemaType === 'string') && `${schema.format}-string` in STRING_FORMAT_RULES) {
+      const primName = `${schema.format}-string`
+      return this._addRule(ruleName, this._addPrimitive(primName, STRING_FORMAT_RULES[primName]));
+    } else if (schemaType === 'string' && ('minLength' in schema || 'maxLength' in schema)) {
+      const charRuleName = this._addPrimitive('char', PRIMITIVE_RULES['char']);
+      const minLen = schema.minLength || 0;
+      const maxLen = schema.maxLength;
+      return this._addRule(ruleName, '"\\\"" ' + _buildRepetition(charRuleName, minLen, maxLen) + ' "\\\"" space');
     } else if ((schemaType === 'object') || (Object.keys(schema).length === 0)) {
-      for (const n of OBJECT_RULE_NAMES) {
-        this._addRule(n, PRIMITIVE_RULES[n]);
-      }
-      return this._addRule(ruleName, 'object');
+      return this._addRule(ruleName, this._addPrimitive('object', PRIMITIVE_RULES['object']));
     } else {
       if (!(schemaType in PRIMITIVE_RULES)) {
         throw new Error(`Unrecognized schema: ${JSON.stringify(schema)}`);
       }
       // TODO: support minimum, maximum, exclusiveMinimum, exclusiveMaximum at least for zero
-      return this._addRule(ruleName === 'root' ? 'root' : schemaType, PRIMITIVE_RULES[schemaType]);
+      return this._addPrimitive(ruleName === 'root' ? 'root' : schemaType, PRIMITIVE_RULES[schemaType]);
+    }
+  }
+
+  _addPrimitive(name, rule) {
+    let n = this._addRule(name, rule.content);
+    for (const dep of rule.deps) {
+      const depRule = PRIMITIVE_RULES[dep] || STRING_FORMAT_RULES[dep];
+      if (!depRule) {
+        throw new Error(`Rule ${dep} not known`);
+      }
+      if (!(dep in this._rules)) {
+        this._addPrimitive(dep, depRule);
+      }
     }
+    return n;
   }
 
   _buildObjectRule(properties, required, name, additionalProperties) {
@@ -462,7 +518,7 @@ export class SchemaConverter {
       const valueRule = this.visit(additionalProperties === true ? {} : additionalProperties, `${subName}-value`);
       propKvRuleNames['*'] = this._addRule(
         `${subName}-kv`,
-        `${this._addRule('string', PRIMITIVE_RULES['string'])} ":" space ${valueRule}`);
+        `${this._addPrimitive('string', PRIMITIVE_RULES['string'])} ":" space ${valueRule}`);
       optionalProps.push('*');
     }
 
diff --git a/examples/server/server.cpp b/examples/server/server.cpp
index b08a09a5..634e653a 100644
--- a/examples/server/server.cpp
+++ b/examples/server/server.cpp
@@ -859,7 +859,7 @@ struct server_context {
         slot.sparams.min_keep          = json_value(data, "min_keep",          default_sparams.min_keep);
 
         // process "json_schema" and "grammar"
-        if (data.contains("json_schema") && data.contains("grammar")) {
+        if (data.contains("json_schema") && !data["json_schema"].is_null() && data.contains("grammar") && !data["grammar"].is_null()) {
             send_error(task, "Either \"json_schema\" or \"grammar\" can be specified, but not both", ERROR_TYPE_INVALID_REQUEST);
             return false;
         } else if (data.contains("json_schema") && !data.contains("grammar")) {
diff --git a/examples/ts-type-to-grammar.sh b/examples/ts-type-to-grammar.sh
index a7ad0017..9abba2a3 100755
--- a/examples/ts-type-to-grammar.sh
+++ b/examples/ts-type-to-grammar.sh
@@ -1,7 +1,7 @@
 #!/bin/bash
 #
 # ./examples/ts-type-to-grammar.sh "{a:string,b:string,c?:string}"
-# python examples/json-schema-to-grammar.py https://json.schemastore.org/tsconfig.json
+# python examples/json_schema_to_grammar.py https://json.schemastore.org/tsconfig.json
 #
 set -euo pipefail
 
@@ -25,4 +25,4 @@ npx ts-json-schema-generator --unstable --no-top-ref --path "$DTS_FILE" --type M
 # https://github.com/YousefED/typescript-json-schema
 # npx typescript-json-schema --defaultProps --required "$DTS_FILE" MyType | tee "$SCHEMA_FILE" >&2
 
-./examples/json-schema-to-grammar.py "$SCHEMA_FILE"
+./examples/json_schema_to_grammar.py "$SCHEMA_FILE"