A program that acquires how to execute sentences

One writes example sequences of sentences so that one sequence solves an instance of a problem, and writes how each example runs on a computer. For instance, the one writes a sentence "From 1 to 10, repeat Body", and also writes how the sentence Body repeats its execution on the computer. Then the one gives them to a program, pI, and lets the initial program generalize how the example sequences run and generate a procedure, pg. When the program, pI, gets a new example sequence to solve a new instance of the problem, the program, pI, executes the procedure, pG. For instance, the one writes a sentence "From 5 to 8, repeat Body", and then the procedure, pG, repeats the sentence Body four times. As a result of generating a procedure, pG, the program, pI, acquires implicitly rules of a grammar that produce sentences. Since the generated procedures, pG's, describe how to execute sentences of conditional branches, varying number of repetitions, and varying depth of recursive calls, this paper argues our program, pI, acquires a grammar of a language that is equivalent to that used in a conventional programming language.

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