Initial import.

uc/hs-simple/README.txt

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+## understanding computation
+

uc/hs-simple/meaning.hs

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+-- # 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*. *operational semantics* defines rules for how
+-- programs run on some machine (often an *abstract machine*). 
+
+-- ### Small-Step Semantics
+--
+-- Let's imagine an abstract machine that evaluates by directly
+-- operating on the syntax, reducing it iteratively to bring about the
+-- final result.
+--
+-- For example, to evaluate (1 * 2) + (3 * 4):
+
+-- 0. Compute the left-hand multiplication (1 * 2 -> 2), simplifying
+-- the expression to 2 + (3 * 4).
+
+-- 0. Compute the right-hand multiplication (3 * 14 -> 12),
+-- simplifying the expression to 2 + 12.
+
+-- 0. Carry out the addition, resulting in 14.
+
+-- We determine that 14 is the result because it cannot be simplified
+-- any further. It is a special type of algebraic expression (a
+-- *value*) with its own meaning.
+
+-- We can write down formal rules like these describing how to proceed
+-- with each small reduction step; these rules are written in a
+-- *metalanguage* (which is often mathematical notation).
+
+-- Let's explore the semantics of a toy language called SIMPLE. There
+-- is a formal mathematical language to this, but we'll use a
+-- programming language to make it more clear.
+
+class AST a where
+  reduce :: a -> Number
+  reducible :: a -> Bool
+
+data Number = Number { value :: Integer } deriving (Show)
+
+instance AST Number where
+  reduce (Number value) = (Number value)
+  reducible (Number _) = False
+
+data Add = Add {  leftAdd :: Number
+                 , rightAdd :: Number
+} deriving (Show)
+
+instance AST Add where
+  reduce (Add x y) = Number (value x + value y)
+  reducible (Add _ _) = True
+
+data Multiply = Multiply {  leftMult :: Number
+                           ,rightMult :: Number
+} deriving (Show)
+
+-- We can use these to build an AST by hand:
+
+-- print Add(Multiply (Number 2) Multiply (Number 3))
+

uc/hs-simple/meaning.md

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+-- # 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*.

uc/hs-simple/programs_and_machines.lhs

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+
+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/.