Lambda-terms use the following syntax:

• Variables are any valid identifier, e.g. x, y, x1, a_long_varname
• Application is denoted using parenthesis around the function: (u)v for u applied to v.
• Lambda-abstraction is denoted with brackets: [x]x is the usual identity combinator and [x][y]x is the K combinator.

For example the S combinator is spelled: [x][y][z]((x)z)(y)z.

Simple terms use a similar syntax: variables and abstraction are denoted as in lambda-terms. Bunch application is denoted using angles around the function term instead of parentheses and braces to delimitate the bunch, with the dot acting as the delimiter inside the bunch. However as a bunch is a product of simple terms some nice simplifications may be applied to this strict syntax:

• Application of u to the empty bunch: <u>{};
• Application of u to a bunch with a single factor v: <u>{v} or simply <u>v;
• Application to a bunch with twice the same factor: <u>{v . v} or <u>{(v)^2} or <u>(v)^2 or when v is just a variable <u>v^2;
• Application to a bunch with 2 distinct factors v1 and v2 with respective multiplicity 2 and 1: <u>{v1 . v1 . v2} or <u>{(v1)^2 . v2} or, when v1 is just a variable <u>{v1^2 . v2}.

For example a term appearing in the Taylor expansion of ([x](x)x)[f][x](f)(f)x (delta applied to the Church numeral 2) is <[x]<x>x^3>{([f][x]<f><f>x)^3 . [f][x]<f>(<f>x^2)^2}.