Gerald Sussman on Using Languages To Construct Continuous Solutions

This is the next lecture in the series MIT 6.001 Structure and Interpretation (1986). See Hal Abelson on Language Embeddings.

At 5:36 on the problem of integration expressed by rules which increase the complexity of the expression which has to be integrated, see Knuth Bendix Completion.

9:00 On how sums are going to be expressed, ... The A1 and A2 arguments are what in the terminology of yacc are called semantic values. See this message: Infix arithmetic module, so I was only fourteen years behind, ... That's still progress, right? See my reply to Michael Vanier on July 14, 2000.

Is eelectrical engineering the same as mathematical engineering? At 36:40 the representation of arithmetic expressions could be being done as proofs based on axiomatic formulation of arithmetic over some field. Joe Hurd did this for HOL in his PhD thesis, using an interesting representation of exact rational arithmetic using multiples of 2 and 3 which he found in something written by Donald Knuth. Joe's PhD dissertation doesn't even mention this though. The principal result in this work is formal verification of the (stochastic) Miller-Rabin Primality test. See Formal verification of probabilistic algorithms. Note that the existence of such abstraction barriers as Sussman describes means that the applicability of results established in the proof depends crucially on the details such as the procedure by which random numbers are generated. For example, this HOL proof of Joe Hurd's says nothing about the reliability of a Miller-Rabin Primality test based on the Mersenne Twister. See https://gmplib.org/manual/Prime-Testing-Algorithm. Why try a few small factors beforehand?

The full playlist of 20 videos is here: MIT 6.001 Structure and Interpretation, 1986.

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