Are there tools / programs out there that try to compute and run all possible programs for some simple, custom language? Like something you might do if you were to naively run AIXI.

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miniKanren is a logic/relational language. It's been used to solve questions related to programs. For example, once you give miniKanren a description of the untyped λ-calculus extended with integers you can ask it "give me programs that result in 2" and it'll enumerate programs from the constant "2" to "1 + 1" to more complicated versions using λ-expressions. It can even find quines (if the described language supports it).

See https://en.m.wikipedia.org/wiki/Iota_and_Jot This is a way to enumerate all possible programs as binary numbers.

miniKanren is a logic/relational language. It's been used to solve questions related to programs. For example, once you give miniKanren a description of the untyped λ-calculus extended with integers you can ask it "give me programs that result in 2" and it'll enumerate programs from the constant "2" to "1 + 1" to more complicated versions using λ-expressions. It can even find quines (if the described language supports it).

http://minikanren.org/