The core of ATS is a call-by-value functional programming language. I will
explain the meaning of *call-by-value* in a moment. As
for functional programming, there is really no precise definition. The
most important aspect of functional programming that I want to explore is
the notion of binding, which relates names to expressions.

ATS is both syntax-rich and feature-rich, and its grammar is probably more complex than most existing programming languages. In ATS, there are a large variety of forms of expressions, which I will introduce gradually.

Let us first start with some integer arithmetic expressions (IAEs): 1, ~2, 1+2, 1+2*3-4, (1+2)/(3-4), etc. Note that the negative sign is represented by the tilde symbol (~) in ATS. There is also support for floating point numbers, and some floating point constants are given here: 1.0, ~2.0, 3., 0.12345, 2.71828, 31416E-4, etc. Note that 3. and 31416E-4 are the same as 3.0 and 3.1416, respectively. What I really want to emphasize at this point is that 1 and 1.0 are two distinct numbers in ATS: the former is an integer while the latter is a floating point number (of double precision).

There are also boolean constants: true and false. We can form boolean expressions such as 1 >= 0, not(2-1 >= 2), (1 < 2) andalso (2 < 3) and (~1 > 1) orelse (~1 <= 1), where not, andalso and orelse stand for negation, conjunction and disjunction, respectively. For programmers familiar with C-like syntax, I point out that operators && and || are synonyms for andalso and orelse, respectively.

Other commonly used constant values include characters and strings. For instance, following are some character constants: 'a', 'B', '\n' (newline), '\t' (tab), '\(' (left parenthesis), ')' (right parenthesis), '\{' (left curly brace), '}' (right curly brace), etc; following are some string constants: "My name is Zoe", "Don't call me \"Chloe\"", "this is a newline:\n", etc.

Given a (function) name, say, foo, and an expression exp, the expression foo(exp) is a function application or function call. The parentheses in foo(exp) may be dropped if no ambiguity is created by doing so. For instance, print("Hello") is a function application, which can also be written as print "Hello". If foo is a nullary function, then a function application foo() can be formed. If foo is a binary function, then a function application foo(exp1, exp2) can be formed for expressions exp1 and exp2. Functions of more arguments can be treated accordingly.

Note that we cannot write +(1,2) as the name + has already been given the infix status requiring that it be treated as an infix operator. However, we can write op+(1,2), where op is a keyword in ATS that can be used to temporarily suspend the infix status of any name immediately following it. I will explain in detail the issue of fixity (prefix, infix and postfix) elsewhere.

Values are essentially expressions of certain special forms, which cannot be reduced or simplified further. For instance, integer constants such as 1 and ~2 are values, but the integer expression 1+2 is not a value, which can be reduced to the value 3. Evaluation refers to the computational process that reduces a given expression into a value. However, certain expressions such as 1/0 cannot be reduced to a value, and evaluating such an expression must abort at some point. I will gradually present more information on evaluation.