####### DOCUMENTATIATOIAITAT ION ########


Files:
Typechecker.hs: Simple modification of the bnfc-generated Testsyntax which calls the type-checking functions.

Typecheck.hs: Contains the type-checking functions typeCheckExp, typeCheckVar and typeCheckStm and some utility functions, responsible for the entire type-checking process.

Abssyntax.hs, Parsyntax.y, Lexsyntax.x,ErrM.hs,Printsyntax.hs,Skelsyntax.hs: The files generated by bnfc, only modification is the removal of the Bool type in Abssyntx.hs so haskell's internal type can be used.


typing rules
++++++++++++


(t is little tau, T is large tau, E is 'in', and + is that other symbol)


[Eq, NEq]

T+ e1 Eq e2:bool  <=  T+ e1:t  &  T+ e2:t

If e1 and e2 are of the same type, then Eq or NEq return bool


[Plus, Minus, Times, Div]

T+ e1 Plus e2:int  <=  T+ e1:int  &  T+ e2:int

The operators Plus/Minus/Times/Div return int if both operands are ints


[Lt, ELt, Gt, EGt]

T+ e1 Lt e2:bool  <=  T+ e1:int  &  T+ e2:int

The operators Lt/ELt/Gt/EGt return bool if both operands are ints


[Assignment]

T+ i := e:t  <=  i:t E T  &  T+ e:t

The assignemnt of e to i returns type t if both i and e have type t.


[ENeg]

T+ ENeg e:int  <=  T+ e:int

ENeg e returns int if e is of type int

[ENot]

T+ ENot e:bool  <=  e:bool

ENot e returns bool if e is of type bool

[EVar]

T+ i:t <= i:t E T

i has type t if i is defined in the context with type t.

[EInt]

T+ n:int

n has type int

[EBool]

T+ b:bool

b has type bool

[EReadI]

T+ n:int

EReadI returns an int

[EReadB]

T+ b:bool

EReadB returns a bool

[EPost]

T+ EPost i:int <= i:int E T

EPost i is of type int if i is defined in T with type int.

[SExp]

T+ e   <=  T+ e:t

[SBlock]

T+ s;SBlock ss <= T+ s => T' , T'+ ss => T''

the first statment s, in the block, is typechecked in the context T and returns the context T', the rest of the block is then recursively typeckecked in the context T' 


[SIf]

T+ if e then s1 else s2  <=  T+ e:bool  &  T+ s1  &  T+ s2

if e is of type bool and s1 and and s2 typechecks in the context T, then the same context is returned


[SWhile]

T+ while e do s  <=  T+ e:bool  &  T+ s

If e is of type bool and s typechecks in context T then the same context is returned



[SDecl]

T+ t i = e => T,i:t  <=  i!ET  &  e:t 

if i and e are of the same type and i is not declared in the current scope then i is added with type t to the context.

[SDeclD]

T+ t i => T,i:t  <=  i!ET

if i is not declared in the current scope, then i is added to the context with type t

[SNoop]

T+ s

SNoops does nothing so the same context is returned

[SPrint]

T+ e <= T+ e:t

if e has type t then SPrint returns the same context