One of the very common notations for syntactic substitution is $[\ /\ ]$.
However, there seems to be an inconsistency in the literature about its usage. 


* Many write $[t/x]$ for "substitute $t$ for $x$" (Girard, Buss, ...).
* Others use $[x/t]$ for "replace $x$ with $t$" (van Dalen, Troelstra, Martin-Löf, ...).


I am wondering about the history of this notation. 
In particular, 
who was the first person to use this notation for 
syntactic substitution in logic?



History of the notation for substitution
Some early examples of the form $[t/x]$ are due to Haskell Curry.


See:


* Haskell Curry & Robert Feys & William Craig, [Combinatory Logic. Volume I](https://books.google.it/books/about/Combinatory_Logic.html?id=avrcMwEACAAJ&redir_esc=y) (1958), page 54:



> 
> Let $a$ and $b$ be obs and let $x$ be a variable; it is required to define the ob $b^\*$ which is obtained by substitution of $a$ for $x$ in $b$. [...]
> 
> 
> We shall adopt the notation 
> 
> 
> $$[a/x] b$$
> 
> 
> for the $b^\*$ so defined. 
> 
> 
> 


See also:


* Haskell Curry, [Foundations of Mathematical Logic](https://books.google.it/books?id=27dkTJFrLZIC&pg=PA114) (1963), page 114:



> 
> In general, if there are no bound variables to restrict the substitution, we define the result of substituting an ob $M$ for $x$, symbolized as 
> 
> 
> $$[M/x]X$$ 
> 
> 
> as that ob $X^\*$ whose construction is obtained from a construction of $X$ by 
>  replacing subconstructions leading to $x$ by constructions of $M$. 
> 
> 
> 




---


For $[x/t]$, see :


* Alfred Tarski, [A simplified formalization of predicate logic with identity](http://link.springer.com/article/10.1007%2FBF01972461), (1964) page 62:



> 
> Let $\varphi(\alpha/\beta)$ be the formula obtained from the formula $\varphi$ by proper substitution of the variable $\beta$ for the variable $\alpha$.
> 
> 
> 


We may suppose that Tarski has "simplified" the notation used by Kurt Gödel in [1930](https://books.google.it/books?id=v4tBTBlU05sC&pg=PA600), with 



> 
> $$\text {Subst } a (^v\_b)$$
> 
> 
> 


and Alonzo Church in [1932](https://www.jstor.org/stable/1968337?seq=1#page_scan_tab_contents) (and see: [The calculi of lambda-conversion](https://books.google.it/books?id=v6_SCwAAQBAJ&pg=PA9) (1941)):



> 
> $$S^x\_NM|.$$
> 
> 
> 


A "variant" of Tarski's form is used by e.g. Enderton, with: $\alpha\_t^x$.


