ML Variable Bindings and Expressions

<aside> 🗒️ Before a program is run, the types of the variable bindings (static environment) are checked to ensure that every variable binding in the program is typed correctly.

While a program is run, the values of the variable bindings (dynamic environment) are evaluated.

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• Variables in ML are written in the following format:

  val x = e;
  

  • Let’s run through the syntax step by step:
    • val is a keyword
    • x is a variable
    • = is the assignment operator
    • e is an expression (which evaluates to a value v) of type t
    • the semicolon indicates that the variable binding has ended (optional in files but compulsory in the SML REPL)

• Static environment - the types of the preceding bindings in a file

• Dynamic environment - the values of the preceding bindings in a file

• Here’s a short program that shows how the static and dynamic environments change after each variable binding.

• Syntax → how to write something

• Semantics → what something means

  • 1. Type-checking (Done before program runs; if a type in the current static environment is incorrect, an error is thrown.)
  • 2. Evaluation (Done while program runs; looks up values in the current dynamic environment)

• At variable bindings, we…

  • type-check the expression (right-hand side) and extend the static environment
  • evaluate the expression (right-hand side) and extend the dynamic environment

• Each kind of expression (e.g. conditionals, functions, variables) has its own type-checking and evaluation rules.