No a TVar isn't a mutex guard. As a sibling comment points out it gives you transactional semantics similar to most relational databases.

Here's an example in perhaps more familiar pseudocode.

  var x = "y is greater than 0"
  var y = 1
  
  forkAndRun {() =>
    y = y - 1
    if (y <= 0) {
      x = "y is less than or equal to 0"
    }
  }
  
  forkAndRun {() =>
    y = y + 1
    if (y > 0) {
      x = "y is greater than 0"
    }
  }

In the above example, it's perfectly possible, depending on how the forked code blocks interact with each other, to end up with

  x = "y is less than or equal to 0"
  y = 1

because we have no guarantee of atomicity/transactionality in what runs within the `forkAndRun` blocks.

The equivalent of what that Haskell code is doing is replacing `var` with a new keyword `transactional_var` and introducing another keyword `atomically` such that we can do

  transactional_var x = "y is greater than 0"
  transactional_var y = 1
  
  forkAndRun {
    atomically {() =>
      y = y - 1
      if (y <= 0) {
        x = "y is less than or equal to 0"
      }
    }
  }
  
  forkAndRun {
    atomically {() =>
      y = y + 1
      if (y > 0) {
        x = "y is greater than 0"
      }
    }
  }

and never end up with a scenario where `x` and `y` disagree with each other, because all their actions are done atomically together and `x` and `y` are specifically marked so that in an atomic block all changes to the variables either happen together or are all rolled back together (and tried again), just like in a database.

`transactional_var` is the equivalent of a `TVar` and `atomically` is just `atommically`.