Transformation of Applicative Specifications into Imperative ...
Transformation of Applicative Specifications into Imperative ... Transformation of Applicative Specifications into Imperative ...
APPENDIX C. FORMAL SPECIFICATIONS OF TRANSFORMATIONS BracketedExpr(bve) → let (b, env ′ , types ′ ) = CheckValueExpr( bve, Unknown, typings, func, trans, env, types) in (b, updateENV(env ′ , et, trans), types ′ ) end, ValueInfixExpr(first, op, second) → let (b, env ′ , types ′ ) = CheckValueExprList( 〈first, second〉, 〈Unknown, Unknown〉, typings, func, trans, env, types) in (b, updateENV(env ′ , et, trans), types ′ ) end, ValuePrefixExpr(op, operand) → let (b, env ′ , types ′ ) = CheckValueExpr( operand, Unknown, typings, func, trans, env, types) in (b, updateENV(env ′ , et, trans), types ′ ) end, LetExpr(ldl, lve) → let (b, env ′ , types ′ ) = CheckLetDefList( ldl, typings, func, trans, env, types), (b ′ , env ′′ , types ′′ ) = CheckValueExpr( lve, et, typings, func, trans, env ′ , types ′ ) in (b ∧ b ′ , env ′′ , types ′′ ) end, Make_IfExpr(ie) → CheckIfExpr( ie, et, typings, func, trans, env, types), CaseExpr(cond, cbl) → let 164
C.1. FORMAL SPECIFICATION OF THE TRANSFORMER end, (b, env ′ , types ′ ) = CheckValueExpr( cond, Unknown, typings, func, trans, env, types), (b ′ , env ′′ , types ′′ ) = CheckCaseBranchList( cbl, et, typings, func, trans, env ′ , types ′ ) in (b ∧ b ′ , env ′′ , types ′′ ) end /∗Checks for transformability of a list of value expressions.∗/ /∗ Arguments: ======= vel: the list of value expressions etl: the list of the corresponding expected types of the value expressions Results: ===== Bool: true if the list is transformable, false otherwise ∗/ CheckValueExprList : ValueExpr ∗ × ExpType ∗ × TYPINGS × FUNC × TRANS × ENV × TYPES → Bool × ENV × TYPES CheckValueExprList( vel, etl, typings, func, trans, env, types) ≡ if vel = 〈〉 then (true, env, types) else let (b, env ′ , types ′ ) = CheckValueExpr( hd vel, hd etl, typings, func, trans, env, types) in if ∼ b then (b, env ′ , types ′ ) else CheckValueExprList( tl vel, tl etl, typings, func, trans, env ′ , 165
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APPENDIX C. FORMAL SPECIFICATIONS OF TRANSFORMATIONS<br />
BracketedExpr(bve) →<br />
let<br />
(b, env ′ , types ′ ) =<br />
CheckValueExpr(<br />
bve, Unknown, typings, func, trans, env,<br />
types)<br />
in<br />
(b, updateENV(env ′ , et, trans), types ′ )<br />
end,<br />
ValueInfixExpr(first, op, second) →<br />
let<br />
(b, env ′ , types ′ ) =<br />
CheckValueExprList(<br />
〈first, second〉, 〈Unknown, Unknown〉,<br />
typings, func, trans, env, types)<br />
in<br />
(b, updateENV(env ′ , et, trans), types ′ )<br />
end,<br />
ValuePrefixExpr(op, operand) →<br />
let<br />
(b, env ′ , types ′ ) =<br />
CheckValueExpr(<br />
operand, Unknown, typings, func, trans,<br />
env, types)<br />
in<br />
(b, updateENV(env ′ , et, trans), types ′ )<br />
end,<br />
LetExpr(ldl, lve) →<br />
let<br />
(b, env ′ , types ′ ) =<br />
CheckLetDefList(<br />
ldl, typings, func, trans, env, types),<br />
(b ′ , env ′′ , types ′′ ) =<br />
CheckValueExpr(<br />
lve, et, typings, func, trans, env ′ ,<br />
types ′ )<br />
in<br />
(b ∧ b ′ , env ′′ , types ′′ )<br />
end,<br />
Make_IfExpr(ie) →<br />
CheckIfExpr(<br />
ie, et, typings, func, trans, env, types),<br />
CaseExpr(cond, cbl) →<br />
let<br />
164
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