Karl Marx took the 'labor theory of value' argument from David Ricardo, who had taken it from Adam Smith, who had taken it from John Locke among others.
Alfred Marshall's 'marginalism' completely displaced the labor theory, insofar as the labor theory is incapable of producing a theory explaining prices. The labor theory is now only kept around by philosophy students and unreconstructed marxists.
Yes, the labor theory of value is, in short, what it means to be labeled a "classical" economist. All economists writing before the marginal revolution took it for granted.
Also, Marx never wrote anything even resembling this: Some, like Karl Marx, argued that the value of a product is based on how much labour you put into it. Not whether people want it or not.
He actually mocked people, like Proudhon, who proposed such ideas.
I don't think he moved as far away from it as you believe. Marx's particular approach to the labor theory of value is key to his philosophical ideas about exploitation and alienation. And subsequent Marxists placed a great deal of emphasis on it, especially Rosa Luxembourg.
laut is confusing the value of the function with the cost of the algorithm. Short example...
Say a spool of wool has a market value of $5 and a sweater has a market value of $11. Marx's theory is that when you buy a sweater what you're really buying is a package containing:
1. a spool of wool
2. a single application of the wool -> sweater function.
He called 2 "socially necessary labor". The value of the labor function is therefore $11 - $5 = $6. It might take worker A an hour to perform the function and worker B three hours. The amount of labor performed by a given worker (the algorithm if you will) is totally irrelevant here. Socially necessary labor is an abstract concept and its value is determined by the market values of the inputs and outputs.
Marx would say that worker A should be making $6/hour and worker B should be making $2/hour. ie they're creating and selling a specific quantity of socially necessary labor. Since they only get paid $5 for the $6 worth of labor they create they're being exploited by the capitalist who controls their work lives.
Alfred Marshall's 'marginalism' completely displaced the labor theory, insofar as the labor theory is incapable of producing a theory explaining prices. The labor theory is now only kept around by philosophy students and unreconstructed marxists.