Entire file

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	fileTypes = ( 'j', 'jl', 'jul', 'julia' );
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		{	include = '#function_call'; },
		{	include = '#type_decl'; },
		{	include = '#keyword'; },
		{	include = '#operator'; },
		{	include = '#number'; },
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				},
				{	name = 'keyword.other.julia';
					match = '\b(?:function|type|macro|quote|abstract|bitstype|typealias|module|new)\b';
				},
				{	name = 'keyword.control.julia';
					match = '\b(?:if|else|elseif|while|for|begin|let|end|do|try|catch|return|break|continue)\b';
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				{	name = 'storage.modifier.variable.julia';
					match = '\b(?:global|local|const|export|import)\b';
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				{	name = 'support.macro.julia';
					match = '@\w+\b';
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			);
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		number = {
			patterns = (
				{	name = 'constant.numeric.julia';
					match = '((\b0(x|X)[0-9a-fA-F]*)|((\b[0-9]+\.?[0-9]*)|(\.[0-9]+))((e|E)(\+|-)?[0-9]*)?(im)?|\bInf(32)?\b|\bNaN(32)?\b)';
				},
			);
		};
		operator = {
			patterns = (
				{	name = 'keyword.operator.update.julia';
					match = '(?:=|:=|\+=|-=|\*=|/=|//=|\.//=|\.\*=|\\=|\.\\=|^=|\.^=|%=|\|=|&=|\$=|<<=|>>=)';
				},
				{	name = 'keyword.operator.ternary.julia';
					match = '(?:\?|:)';
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					match = '(?:\|\||&&|!)';
				},
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					match = '(?:->|<-|-->)';
				},
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				},
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				},
				{	name = 'keyword.operator.shift.julia';
					match = '(?:<<|>>)';
				},
				{	name = 'keyword.operator.bitwise.julia';
					match = '(?:\||\&|~)';
				},
				{	name = 'keyword.operator.arithmetic.julia';
					match = '(?:\+|-|\*|\.\*|/|\./|//|\.//|%|\.%|\\|\.\\|\^|\.\^)';
				},
				{	name = 'keyword.operator.isa.julia';
					match = '(?:::)';
				},
				{	name = 'keyword.operator.dots.julia';
					match = '(?:\.(?=[a-zA-Z])|\.\.+)';
				},
				{	match = "(\w+)([.']*')";
					captures = {
						1 = { name = 'variable'; };
						2 = { name = 'keyword.operator.transposed-variable.julia'; };
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			);
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					comments = "Matches a typed variable, such as 'id::String'";
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			);
		};
	};
}

Relevant bits

function_call = {
	patterns = (
		{	name = 'meta.function.call.julia';
			begin = '([a-zA-Z0-9_]+)\w*\(';
			end = '\)';
			beginCaptures = { 1 = { name = 'support.function.julia'; }; };
			patterns = ( { include = '$self'; } );
		},
	);
};

operator = {
	patterns = (
	 {	begin = "(\()";
      		end = "(\))([.']*')";
		beginCaptures = { 1 = { name = 'keyword.bracket.julia'; }; };
		endCaptures = {
			1 = { name = 'keyword.bracket.julia'; };
			2 = { name = 'keyword.operator.transposed-sexp.julia'; };
		};
		patterns = ( { include = '$self'; } );
	},
	)
}

Test case:

transposedMatrix = myFunc(param1, param2)'