-- # The Meaning of Programs

-- What is computation? what a computer does.

-- computation environment:
-- * machine
-- * language
-- * program
-- 
-- Fundamentally, programming is about ideas: a program is a snapshot of
-- an idea, a codification of the mental structures of the programmer(s)
-- involved.
--  
-- ## The Meaning of "Meaning"
--  
-- /semantics/ is the connection between words and meanings: while "dog"
-- is an arrangment of shapes on a page, an actual dog is a very separate
-- things. Semantics relates concrete signifiers and abstract meanings,
-- and attempts to study the fundamental nature of the abstract meanings.
--  
-- *Formal semantics* is the attempt at formalising the meanings of
-- programmings, and using this formalisation to reason about
-- languages. In order to specify a programming language, we need to
-- define both its *syntax* (the representation) and its *semantics* (the
-- meaning).
--  
-- Most languages lack a formal specification and opt to use a canonical
-- reference implementation. An alternative is to write a prose
-- specification, which is the approach of C++. A third approach is to
-- mathematically specify the language such that automated mathematical
-- analysis can be done.
--  
-- ### Syntax
--  
-- The language's syntax is what differentiates valid examples of code like

y x = x + 1

-- from nonsense like `$%EHI`. In general, a parser reads a string
-- (like "y x = x + 1") and turns it into an /abstract syntax
-- tree/. Syntax is ultimately only concerned with the surface
-- appearance of the program

-- ### Operational Semantics

-- A practical means of thinking about the meaning of a program is
--   *what it does*.