If we look on abstract machines we could noticed analogue with modern computers (of course). What I mean? I mean this points: 1. Model of implementer (In Turing machine it is description of head, which can read/write/move, cells of memory, which are in one line and unlimited. In Markov algorithms it is description of symbol string, which also unlimited, and format of rules) 2. Program (In Turing machine it is description in special syntax (table) of states and symbols and rules how to change states and initial state) In Markov algorithms is it conversion rules.) 3. Input-Output (In Turing machine it is unlimited line of cells. In Markov algorithm it is symbol string).
So, if we try to define this three points lambda-calculus what they are could be? If "model of implementer" is the rules of reduction what "program" and "input-output" are in lambda-calculus? Is this question is correct or incorrect? If "no" what is the best way to imagine equality of this models of computation (turing machine and labmda-calculus)?