Complex sentence: A program is the transcription of an algorithm in a programming language, and being every (Turing-complete) programming language equivalent to Church's lambda calculus by virtue of the Church-Turing thesis, a program is thus the transcription of a mathematical function.
Split into simpler sentences: A program is the transcription of an algorithm in a programming language. Since every (Turing-complete) programming language implements the Church's lambda calculus by virtue of the Church-Turing thesis, a program is thus the transcription of a mathematical function.