Referential transparency is the property that an expression can always be replaced by its value, anywhere it appears, without changing what the program does. If a function call always produces the same result given the same inputs, then any occurrence of that call denotes simply that result, and a reader or a compiler can substitute one for the other freely. The Haskell site lists referential transparency among the language’s defining features, alongside immutability and lazy evaluation.
The property depends on functions being pure. As the Haskell site puts it, every function in Haskell is “a function in the mathematical sense,” meaning its output is determined entirely by its inputs and it produces no hidden effects such as I/O or mutation. Once a function can quietly change or read external state, the same call may yield different results at different times, and the simple substitution that referential transparency promises no longer holds.
This is closely tied to why functional programs are easier to reason about. In “Why Functional Programming Matters,” John Hughes emphasizes that the absence of side effects lets functional programs be understood and manipulated more like ordinary mathematical expressions than like sequences of state changes.
The practical payoff is the freedom to substitute equals for equals. That freedom is what lets compilers reorder, cache, or eliminate computations safely, lets programmers refactor with confidence, and lets independent expressions be evaluated in parallel, because none of them can interfere with one another through hidden state.