Language "IMP" 

#1 Arithmetic expressions

Syntax 
  AExp : aexp ::= num
               |  id 
               |  aexp '+' aexp 
               |  aexp '/' aexp
               |  '(' aexp ')'

Semantics		
  eval-arith[[ _:aexp ]] : =>integers

Rule

  eval-arith[[ N ]] = int-val[[ N ]]
Rule
  eval-arith[[ I ]] = assigned(bound(id[[ I ]]))
Rule
  eval-arith[[ AExp1 '+' AExp2 ]] = 
	integer-add(eval-arith[[ AExp1 ]], eval-arith[[ AExp2 ]])
Rule
  eval-arith[[ AExp1 '/' AExp2 ]] = 
	checked integer-divide(eval-arith[[ AExp1 ]], eval-arith[[ AExp2 ]])
Rule
  eval-arith[[ '(' AExp ')' ]] = eval-arith[[ AExp ]]

Syntax
  N : num ::= '-'?_decimal
Lexis
  D : decimal ::= ('0'-'9')+
Semantics
  int-val[[ _:num ]] : integers

Rule

  int-val[[ D ]] = decimal-natural(\"D\")
Rule
  int-val[[ '-' D ]] = integer-negate(int-val[[ D ]])

Lexis
  I : id ::= ('A'-'Z'|'a'-'z')+
Semantics
  id[[ _:id ]] : ids

Rule

  id[[ I ]] = \"I\"

Lexis
  keyword ::= 'else' | 'false' | 'if' | 'true' | 'while'