“Virtual” Format

\[\begin {align} {\cal V}^p &: \text {Closure.prog} \rightarrow \text {SparcAsm.prog} \\ {\cal V}^f &: \text {Closure.fundef} \rightarrow \text {SparcAsm.fundef} \\ {\cal V}^e &: \text {Closure.t} \rightarrow \text {SparcAsm.t} \end {align}\]

Caption of Fig 18

• Variables that occur in RHS but not in LHS are fresh.

• \(\mathtt {R_{hp}}\) is a register specifically used as heap pointer.

• \(e_1; e_2\) is a short hand notation for \(x \leftarrow e_1; e_2\).

• \(x \leftarrow E_1; E_2\) is a short hand notation for \(x_1 \rightarrow e_1; \ldots; x_n \rightarrow e_n; E_2\), where \((x_1 \rightarrow e_1; \ldots; x_n \rightarrow e_n; E_2) = E_1\).

V-Code for a Function

\[\begin {align} {\cal V}^F&(\mathtt {L_x}(y_1, \ldots, y_m)(z_1, \ldots, z_n) = e) = \\ & \mathtt {L_x}(y_1, \ldots, y_m) = \\ & z_1 \leftarrow \mathtt R_0.(4); \quad \ldots; \quad z=n \leftarrow \mathtt R_0.(4n); \\ & {\cal V}^e(e) \end {align}\]

• The implementation is a bit more complicated: Offsets into \(\mathtt R_0\) takes in account different sizes of int and float values (four and eight, respectively).

V-Code for Tupple Creation

\[\begin {align} {\cal V}^e&((x_1, \ldots, x_n)) =\\ & y \leftarrow \mathtt {R_{hp}}; \quad \mathtt {R_{hp}} \leftarrow \mathtt {R_{hp}} + 4n; \\ & y.(0) \leftarrow x_1; \quad \ldots; \quad y.(4(n - 1)) \leftarrow x_n; \\ & y \end {align}\]

• \(y\) is a fresh register

V-Code for make_closure

\[\begin {align} {\cal V}^e&(\mathit {make\_closure}\ x = (\mathtt {L_x}, (y_1, \ldots, y_m)) \text { in } e) \\ & x \leftarrow \mathtt {R_{hp}}; \quad \mathtt {R_{hp}} \leftarrow \mathtt {R_{hp}} + r(n + 1); \\ & z \leftarrow \mathtt L_x; \\ & x.(0) \leftarrow z; \\ & x.(1) \leftarrow y_1; \quad \ldots; \quad x.(m) \leftarrow y_m; \\ & {\cal V}^e(e) \end {align}\]

• \(z\) is a fresh register

V-Code for let

\[\begin {align} {\cal V}^e &(\text {let } x = e_1 \text { in } e_2) = \\ & x \leftarrow {\cal V}(e_1) \\ & {\cal V}(e_2) \end {align}\]

V-Code for let tuple

\[\begin {align} {\cal V}^e &(\text {let }(x_1, \ldots, x_n) = y \text { in } e) = \\ & x_{i_1} \leftarrow y.(4(i_1 - 1)); \\ & \ldots \\ & x_{i_m} \leftarrow y.(4(i_m - 1)); \\ & \text {where } \{x_{i_1}, \ldots, x_{i_m}\} = \{x_1, \ldots, x_n\} \cap \mathit {FV}(e) \end {align}\]

V-Code for Array Access

\[\begin {align} {\cal V}& (x.(y)) = \\ & y' \leftarrow 4 y; \\ & x.(y') \\ \\ {\cal V}& (x.(y) \leftarrow z) = \\ & y' \leftarrow 4 y; \\ & x.(y') \leftarrow z \end {align}\]