Transformation of Applicative Specifications into Imperative ...
Transformation of Applicative Specifications into Imperative ... Transformation of Applicative Specifications into Imperative ...
APPENDIX C. FORMAL SPECIFICATIONS OF TRANSFORMATIONS /∗Checks for transformability of a map expression. ∗/ /∗ Arguments: ======= me: the map expression et: the expected type of the components of the map expression Results: ===== Bool: true if the map expression is transformable, false otherwise ∗/ CheckMapExpr : MapExpr × MapType × TYPINGS × FUNC × TRANS × ENV × TYPES → Bool × ENV × TYPES CheckMapExpr(me, et, typings, func, trans, env, types) ≡ case me of EnumeratedMapExpr(ovel) → CheckOptValueExprPairList( ovel, et, typings, func, trans, env, types), ComprehendedMapExpr(vep, typlist, or) → let (b1, env1, types1) = CheckValueExprList( 〈first(vep), second(vep)〉, 〈tedom(et), terange(et)〉, typings, func, trans, env, types), (b2, env2, types2) = CheckOptRestriction( or, Known(TypeLiteral(BOOL)), typings, func, trans, env1, types1) in (b1 ∧ b2, env2, types2) end end, /∗Checks for transformability of an optional value expression list.∗/ /∗ Arguments: ======= 168
C.1. FORMAL SPECIFICATION OF THE TRANSFORMER ovel: the optional value expression list et: the expected type of the components of the value expression list Results: ===== Bool: true if the optional value expression list is transformable, false otherwise ∗/ CheckOptValueExprList : OptionalValueExprList × ExpType × TYPINGS × FUNC × TRANS × ENV × TYPES → Bool × ENV × TYPES CheckOptValueExprList( ovel, et, typings, func, trans, env, types) ≡ case ovel of ValueExprList(vel) → CheckValueExprList( vel, toExpTypeList(et, len vel), typings, func, trans, env, types), NoValueExprList → (true, env, types) end, /∗Checks for transformability of an optional value expression pair list.∗/ /∗ Arguments: ======= ovel: the optional value expression pair list et: the expected type of the components of the value expression pair list Results: ===== Bool: true if the optional value expression pair list is transformable, false otherwise ∗/ CheckOptValueExprPairList : OptionalValueExprPairList × MapType × TYPINGS × FUNC × TRANS × ENV × TYPES → Bool × ENV × TYPES CheckOptValueExprPairList( ovel, et, typings, func, trans, env, types) ≡ case ovel of ValueExprPairList(vel) → CheckValueExprPairList( 169
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APPENDIX C. FORMAL SPECIFICATIONS OF TRANSFORMATIONS<br />
/∗Checks for transformability <strong>of</strong> a map expression.<br />
∗/<br />
/∗<br />
Arguments:<br />
=======<br />
me: the map expression<br />
et: the expected type <strong>of</strong> the components <strong>of</strong> the<br />
map expression<br />
Results:<br />
=====<br />
Bool: true if the map expression is transformable,<br />
false otherwise<br />
∗/<br />
CheckMapExpr :<br />
MapExpr × MapType × TYPINGS × FUNC × TRANS ×<br />
ENV × TYPES →<br />
Bool × ENV × TYPES<br />
CheckMapExpr(me, et, typings, func, trans, env, types) ≡<br />
case me <strong>of</strong><br />
EnumeratedMapExpr(ovel) →<br />
CheckOptValueExprPairList(<br />
ovel, et, typings, func, trans, env, types),<br />
ComprehendedMapExpr(vep, typlist, or) →<br />
let<br />
(b1, env1, types1) =<br />
CheckValueExprList(<br />
〈first(vep), second(vep)〉,<br />
〈tedom(et), terange(et)〉, typings,<br />
func, trans, env, types),<br />
(b2, env2, types2) =<br />
CheckOptRestriction(<br />
or, Known(TypeLiteral(BOOL)), typings,<br />
func, trans, env1, types1)<br />
in<br />
(b1 ∧ b2, env2, types2)<br />
end<br />
end,<br />
/∗Checks for transformability <strong>of</strong> an optional value<br />
expression list.∗/<br />
/∗<br />
Arguments:<br />
=======<br />
168