Language "SIMPLE"

Syntax
  Exp : exp ::= '(' exp ')'
             |  value
             |  lexp
             |  lexp '=' exp
             |  '++' lexp
             |  '-' exp
             |  exp '(' exps? ')'
             |  'sizeOf' '(' exp ')'
             |  'read' '(' ')'
             |  exp '+' exp
             |  exp '-' exp
             |  exp '*' exp
             |  exp '/' exp
             |  exp '%' exp
             |  exp '<' exp
             |  exp '<=' exp
             |  exp '>' exp
             |  exp '>=' exp
             |  exp '==' exp
             |  exp '!=' exp
             |  '!' exp
             |  exp '&&' exp
             |  exp '||' exp

Rule
  [[ '(' Exp ')' ]] : exp = [[ Exp ]]

Semantics
  rval[[ _:exp ]] : =>values
Rule
  rval[[ V ]] = val[[ V ]]
Rule
  rval[[ LExp ]] = assigned(lval[[ LExp ]])
Rule
  rval[[ LExp '=' Exp ]] = give(
                             rval[[ Exp ]],
                             sequential(
                               assign(lval[[ LExp ]], given),
                               given))
Rule
  rval[[ '++' LExp ]] = give(
                          lval[[ LExp ]],
                          sequential(
                            assign(given, integer-add(assigned(given), 1)),
                            assigned(given)))
Rule
  rval[[ '-' Exp ]] = integer-negate(rval[[ Exp ]])
Rule
  rval[[ Exp '(' Exps? ')' ]] = apply(rval[[ Exp ]], tuple(rvals[[ Exps? ]]) )
Rule
  rval[[ 'sizeOf' '(' Exp ')' ]] = length(vector-elements(rval[[ Exp ]]))
Rule
  rval[[ 'read' '(' ')' ]] = read
Rule
  rval[[ Exp1 '+' Exp2 ]]  = integer-add(rval[[ Exp1 ]],rval[[ Exp2 ]])
Rule
  rval[[ Exp1 '-' Exp2 ]]  = integer-subtract(rval[[ Exp1 ]],rval[[ Exp2 ]])
Rule
  rval[[ Exp1 '*' Exp2 ]]  = integer-multiply(rval[[ Exp1 ]],rval[[ Exp2 ]])
Rule
  rval[[ Exp1 '/' Exp2 ]]  = checked integer-divide(rval[[ Exp1 ]],rval[[ Exp2 ]])
Rule
  rval[[ Exp1 '%' Exp2 ]]  = checked integer-modulo(rval[[ Exp1 ]],rval[[ Exp2 ]])
Rule
  rval[[ Exp1 '<' Exp2 ]]  = is-less(rval[[ Exp1 ]],rval[[ Exp2 ]])
Rule
  rval[[ Exp1 '<=' Exp2 ]] = is-less-or-equal(rval[[ Exp1 ]],rval[[ Exp2 ]])
Rule
  rval[[ Exp1 '>' Exp2 ]]  = is-greater(rval[[ Exp1 ]],rval[[ Exp2 ]])
Rule
  rval[[ Exp1 '>=' Exp2 ]] = is-greater-or-equal(rval[[ Exp1 ]],rval[[ Exp2 ]])
Rule
  rval[[ Exp1 '==' Exp2 ]] = is-equal(rval[[ Exp1 ]],rval[[ Exp2 ]])
Rule
  rval[[ Exp1 '!=' Exp2 ]] = not(is-equal(rval[[ Exp1 ]],rval[[ Exp2 ]]))
Rule
  rval[[ '!' Exp ]]        = not(rval[[ Exp ]])
Rule
  rval[[ Exp1 '&&' Exp2 ]] = if-else(rval[[ Exp1 ]],rval[[ Exp2 ]],false)
Rule
  rval[[ Exp1 '||' Exp2 ]] = if-else(rval[[ Exp1 ]],true,rval[[ Exp2 ]])

Syntax
  Exps : exps ::= exp (',' exps)?

Semantics
  rvals[[ _:exps? ]] : (=>values)*
Rule
  rvals[[  ]] = ( )
Rule
  rvals[[ Exp ]] = rval[[ Exp ]]
Rule
  rvals[[ Exp ',' Exps ]] = rval[[ Exp ]] , rvals[[ Exps ]]

Syntax
  LExp : lexp ::= id | lexp '[' exps ']'

Rule
  [[ LExp '[' Exp ','     Exps ']' ]] : lexp =
  [[ LExp '[' Exp ']' '[' Exps ']' ]]

Semantics
  lval[[ _:lexp ]] : =>variables
Rule
  lval[[ Id ]] = bound(id[[ Id ]])
Rule
   lval[[ LExp '[' Exp ']' ]] =
     checked index(integer-add(1,rval[[ Exp ]]),vector-elements(rval[[ LExp ]]))