EBNF Grammar
For a graphical representation, take a look at this website.
Expr ::= Add
Add ::= Mod (PlusMinus Add)?
Mod ::= Mul ('%' Mul)?
Mul ::= Pow (MulDiv Mul)?
Pow ::= Minus ('^' Minus)?
Minus ::= '-'? Call
Call ::= Var | Name ('(' Args ')')?
Var ::= Name | Num | Str | '(' Expr ')'
Args ::= Expr (',' Expr)?
PlusMinus ::= [+-] /* ws: explicit */
MulDiv ::= [*/] /* ws: explicit */
Num ::= ('0' | [1-9]+) ('.' [0-9]+)? /* ws: explicit */
Str ::= '"' [^"]* '"' /* ws: explicit */
Name ::= [a-z] [a-z0-9_]* /* ws: explicit */
Example
{{#invoke:Expression|Eval
| 2 * (1 + min(10, x))
| {"x": 2}
}}
2 * (1 + min(10, x)) (x=2) evaluates to
6
---This is an expression interpreter. For example, "2 * (1 + min(10, 2))" evaluates to 6.
---Variable lookup needs to be implemented externally and supplied by :lookup(name)
---through the context cx given to Expression:eval(cx).
local p = {}
---@diagnostic disable-next-line: deprecated
local table_unpack = table.unpack or unpack
---@alias Context {lookup: fun(self: self, name: string)}
---@class Expr
---@field eval fun(self: Expr, cx: Context): any
Expr = {}
function Expr:new(o)
o = o or {}
setmetatable(o, self)
self.__index = self
return o
end
---@class UnaryExpr:Expr
---@field a Expr
---@field new fun(self: self, o?: UnaryExpr): UnaryExpr
---@field _eval fun(self: self, a: any): any
UnaryExpr = Expr:new()
---@param cx Context
---@return any
function UnaryExpr:eval(cx)
return self:_eval(self.a:eval(cx))
end
---@class MinusExpr:UnaryExpr
---@field new fun(self: self, o: {a: any}): MinusExpr
MinusExpr = UnaryExpr:new()
function MinusExpr:_eval(a) return -a end
---@class BinaryExpr:Expr
---@field a Expr
---@field b Expr
---@field new fun(self: self, o?: {a: Expr, b: Expr}): self
---@field _eval fun(self: BinaryExpr, a: any, b: any): any
BinaryExpr = Expr:new()
---@param cx Context
---@return any
function BinaryExpr:eval(cx)
return self:_eval(self.a:eval(cx), self.b:eval(cx))
end
---@class AddExpr:BinaryExpr
---@field new fun(self: self, o: {a: Expr, b: Expr}): self
AddExpr = BinaryExpr:new()
function AddExpr:_eval(a, b) return a + b end
---@class ModExpr:BinaryExpr
---@field new fun(self: self, o: {a: Expr, b: Expr}): self
ModExpr = BinaryExpr:new()
function ModExpr:_eval(a, b) return a % b end
---@class SubExpr:BinaryExpr
---@field new fun(self: self, o: {a: Expr, b: Expr}): self
SubExpr = BinaryExpr:new()
function SubExpr:_eval(a, b) return a - b end
---@class MulExpr:BinaryExpr
---@field new fun(self: self, o: {a: Expr, b: Expr}): self
MulExpr = BinaryExpr:new()
function MulExpr:_eval(a, b) return a * b end
---@class DivExpr:BinaryExpr
---@field new fun(self: self, o: {a: Expr, b: Expr}): self
DivExpr = BinaryExpr:new()
function DivExpr:_eval(a, b) return a / b end
---@class PowExpr:BinaryExpr
---@field new fun(self: self, o: {a: Expr, b: Expr}): self
PowExpr = BinaryExpr:new()
function PowExpr:_eval(a, b) return a ^ b end
---@class CallExpr:Expr
---@field func Expr
---@field args Expr[]
---@field new fun(self: self, o: {func: Expr, args: Expr[]}): self
CallExpr = Expr:new()
---@param cx Context
---@return any
function CallExpr:eval(cx)
local eval_args = {}
for i, arg in ipairs(self.args) do
eval_args[i] = arg:eval(cx)
end
return self.func:eval(cx)(table_unpack(eval_args))
end
---@class VarExpr:Expr
---@field name string
---@field new fun(self: self, o: {name: string}): self
VarExpr = Expr:new()
---@param cx Context
---@return any
function VarExpr:eval(cx)
assert(cx, "Variables require a context")
assert(cx.lookup, "Missing variable lookup function")
return cx:lookup(self.name)
end
---@class ConstExpr:Expr
---@field value any
---@field new fun(self:self, o: {value: any}): self
ConstExpr = Expr:new()
---@param cx Context
---@return any
function ConstExpr:eval(cx)
return self.value
end
---@class Tokenizer
---@field str string
p.Tokenizer = {}
---Create a new tokenizer
---@param o {str: string}
---@return Tokenizer
function p.Tokenizer:new(o)
o = o or {}
setmetatable(o, self)
self.__index = self
return o
end
---Retrieves the next token without consuming
---@return {type: string, value: any, offset: number, length: number}|nil
function p.Tokenizer:peek()
if self.peeked then return self.peeked end
local str = self.str:match("^%s*(.-)$")
if #str == 0 then return end
local offset = 1 + #self.str - #str
local m
m = str:match('^"([^"]*)"')
if m then
self.peeked = { type = "lit", value = m, offset = offset, length = #m + 2 }
return self.peeked
end
m = str:match("^%p")
if m then
if m == '"' then
error("Unclosed string near: " .. str)
end
self.peeked = { type = "punct", value = m, offset = offset, length = 1 }
return self.peeked
end
m = str:match("^%a[%a%d]*")
if m then
self.peeked = { type = "name", value = m, offset = offset, length = #m }
return self.peeked
end
m = str:match("^[%d%.]+")
if m then
if m == "0" or m:match("^[1-9]%d*$") or m:match("^0%.%d+$") or m:match("^[1-9]%d*%.%d+$") then
self.peeked = { type = "lit", value = tonumber(m), offset = offset, length = #m }
return self.peeked
else
error("Invalid numeric literal: " .. m)
end
end
error("Invalid token near: " .. str:sub(1, 5))
end
---Consumes the currently peeked token
function p.Tokenizer:eat()
local token = self.peeked
if token then
self.str = self.str:sub(token.offset + token.length)
self.peeked = nil
end
end
---Retrieves the next token
---@return {type: string, value: any, offset: number, length: number}|nil
function p.Tokenizer:next()
local token = self:peek()
self:eat()
return token
end
function p.Tokenizer:iter()
return function()
return self:next()
end
end
function p.Tokenizer:syntax_error_message()
return "Invalid syntax near: " .. self.str:sub(1, 10)
end
---Parses a token of the given types
---@param tokens Tokenizer
---@param accepted string
---@return any|nil value The token value if it was found or nil
local function parse_type(tokens, accepted)
local token = tokens:peek()
if token and token.type == accepted then
tokens:eat()
return token.value
end
end
---Parses a punctuation token with the given symbol
---@param tokens Tokenizer
---@param punct string
---@return string|nil
local function parse_punct(tokens, punct)
local token = tokens:peek()
if token and token.type == "punct" and token.value == punct then
tokens:eat()
return punct
end
end
---Creates a parses function for a binary expression
---@param ops table<string, BinaryExpr> Map from operator to expression type
---@param parse_next fun(tokens: Tokenizer): Expr|nil
---@param rec any
---@return fun(tokens: Tokenizer): Expr|nil
local function make_parse_binary(ops, parse_next, rec)
local function parse_binary(tokens)
local a = parse_next(tokens)
if not a then return end
local peek = tokens:peek()
if not peek or peek.type ~= "punct" then return a end
local Op = ops[peek.value]
if not Op then return a end
tokens:eat()
local b = assert((rec and parse_binary or parse_next)(tokens), tokens:syntax_error_message())
return Op:new { a = a, b = b }
end
return parse_binary
end
---Parses a variable expression
---@param tokens Tokenizer
---@return Expr|nil
local function parse_var(tokens)
local next = tokens:next()
if not next then return end
if next.type == "name" then return VarExpr:new { name = next.value } end
if next.type == "lit" then return ConstExpr:new { value = next.value } end
if next.type == "punct" and next.value == "(" then
local expr = assert(p.parse_expr(tokens), tokens:syntax_error_message())
if parse_punct(tokens, ")") then return expr end
end
error(tokens:syntax_error_message())
end
---Parses a call expression
---@param tokens Tokenizer
---@return Expr|nil
local function parse_call(tokens)
local name = parse_type(tokens, "name")
if not name then return parse_var(tokens) end
local func = VarExpr:new { name = name }
if not parse_punct(tokens, "(") then return func end
local args = {}
local peek = assert(tokens:peek(), tokens:syntax_error_message())
if peek.type == "punct" and peek.value == ")" then
tokens:eat()
else
local done = false
repeat
local arg = assert(p.parse_expr(tokens), tokens:syntax_error_message())
table.insert(args, arg)
local peek = tokens:peek()
if not (peek and peek.type == "punct") then error(tokens:syntax_error_message()) end
if peek.value == ")" then
done = true
else
assert(peek.value == ",", tokens:syntax_error_message())
end
tokens:eat()
until done
end
return CallExpr:new { func = func, args = args }
end
---Parses a unary minus expression
---@param tokens Tokenizer
---@return Expr|nil
local function parse_minus(tokens)
if parse_punct(tokens, "-") then
local expr = assert(parse_call(tokens), tokens:syntax_error_message())
return MinusExpr:new { a = expr }
end
return parse_call(tokens)
end
local parse_pow = make_parse_binary({ ["^"] = PowExpr }, parse_minus, false)
local parse_mul_div = make_parse_binary({ ["*"] = MulExpr, ["/"] = DivExpr }, parse_pow, true)
local parse_mod = make_parse_binary({ ["%"] = ModExpr }, parse_mul_div, false)
local parse_add_sub = make_parse_binary({ ["+"] = AddExpr, ["-"] = SubExpr }, parse_mod, true)
---Parses a variable expression
---@param tokens Tokenizer
---@return Expr|nil
function p.parse_expr(tokens)
return parse_add_sub(tokens)
end
function p.Eval(frame)
local tok = p.Tokenizer:new { str = frame.args[1] }
---@type table<string, any>
local vars = mw.text.jsonDecode(frame.args[2] or "{}")
local expr = assert(p.parse_expr(tok), "Invalid expression: " .. tok.str)
if tok:peek() then error("Leftover tokens: " .. tok.str) end
local cx = {}
---@param name string
function cx:lookup(name)
return vars[name] or math[name] or error("Variable not found: " .. name)
end
return expr:eval(cx)
end
return p