#lang racket (require redex) ; An STG-like language as described in ; "Making a Fast Curry: Push/Enter vs. Eval/Apply for Higher-order Languages" ; Only lightly-tested. ; A list of differences from STG proper: ; * Right-hand sides of let-bindings have different syntax ; * Let-binding is not recursive ; * Missing semantics for top-level bindings ; * Missing semantics for primops, e.g. ; * Exceptions ; * Concurrency ; * STM ; * Missing let-no-escape ; * Missing IND (for heap indirections after thunk evaluation) ; Some other things that these semantics might want to capture ; * Selector thunks ; * Pointer tagging ; * Stack chunks / STACK_AP ; * CAFs ; Useful sanity checks: ; * Formalize Core (with typing), define translation to STG, test for ; progress given that Core type-checks (define-language L ((x y z f g h) variable-not-otherwise-mentioned) (C variable-not-otherwise-mentioned) (n integer) (lit integer real) ((a v) x lit) (k • ; unknown arity n) (e a (f k a ...) (⊕ a ...) ; saturated (let (x obj) e) (case e alt ...) ) (alt ((C x ...) e) ((x) e)) (obj val (THUNK e) BLACKHOLE) (val (FUN (x ...) e) (PAP f a ...) (CON C a ...)) ; saturated ) (define-extended-language Ev L (p (e s H)) (H ((x_!_ obj) ...)) (κ (case • alt ...) (upd x •) (• a ...)) (s (κ ...)) ) ; use the tutorial substitution (require redex/tut-subst) (define-metafunction Ev subst : (x v) ... e -> e [(subst (x v) ... e) ,(subst/proc x? (term (x ...)) (term (v ...)) (term e))]) (define x? (redex-match Ev x)) ; We need to do some negative matches, a metafunction will be easiest (define-metafunction Ev [(lit? e) ,(redex-match? Ev lit (term e))]) (define-metafunction Ev [(heapval? e H) ,(redex-match Ev (x_i ((x_0 obj_0) ... (x_i val_i) (x_i+1 obj_i+1) ...)) (term (e H))) ]) ; eval/apply reduction semantics (define red (reduction-relation Ev #:domain p (--> ((let (x obj) e) s ((x_1 obj_1) ...)) ((subst (x x_0) e) s ((x_0 obj) (x_1 obj_1) ...)) (fresh x_0) "Let") (--> ((case x_i alt_0 ... ((C_i y_i ..._i_) e_i) alt_i+1 ...) s H) ((subst (y_i a_i) ... e_i) s H) (where ((x_0 obj_0) ... (x_i (CON C_i a_i ..._i_)) (x_i+1 obj_i+1) ...) H) "CaseCon") (--> ((case x_i alt ... ((x) e)) s H) ((subst (x x_i) e) s H) (where ((x_0 obj_0) ... (x_i val_i) (x_i+1 obj_i+1) ...) H) (side-condition ; this terri-bad side condition (not (redex-match ; NB: not redex-match? which is buggy Ev ((CON C_i a_i ...) alt_0 ... ((C_i y_i ...) e_i) alt_i+1 ...) (term (val_i alt ...))))) "CaseAnyHeap") (--> ((case lit alt ... ((x) e)) s H) ((subst (x lit) e) s H) "CaseAnyLit") ; I kind of like the original presentation, where we have an execution ; code that tells us whether or not we need to enter the scrutinee (--> ((case e alt ...) (κ ...) H) (e ((case • alt ...) κ ...) H) (where #f (lit? e)) (where #f (heapval? e H)) "Case") (--> (lit ((case • alt ...) κ ...) H) ((case lit alt ...) (κ ...) H) "RetLit") (--> (x_i ((case • alt ...) κ ...) H) ((case x_i alt ...) (κ ...) H) (where ((x_0 obj_0) ... (x_i val_i) (x_i+1 obj_i+1) ...) H) "Ret") (--> (x_i s ((x_0 obj_0) ... (x_i (THUNK e)) (x_i+1 obj_i+1) ...)) (e ((upd x_i •) ,@(term s)) ; nifty idiom for splicing in ((x_0 obj_0) ... (x_i BLACKHOLE) (x_i+1 obj_i+1) ...)) "Thunk") (--> (y_j ((upd x_i •) κ ...) H) (y_j (κ ...) ((x_0 obj_x0) ... (x_i val_j) (x_i+1 obj_i+1) ...)) (where ((x_0 obj_x0) ... (x_i BLACKHOLE) (x_i+1 obj_i+1) ...) H) (where ((y_0 obj_y0) ... (y_j val_j) (y_j+1 obj_j+1) ...) H) "Update") (--> ((f_i n a ..._n_) s H) ((subst (x a) ... e) s H) (where ((f_0 obj_0) ... (f_i (FUN (x ..._n_) e)) (f_i+1 obj_i+1) ...) H) (side-condition (= (length (term (a ...))) (length (term (x ...))) (term n))) "KnownCall") ; Primop rule is omitted ; n.b. named ellipses do not carry over (--> ((f_i • a ...) s H) ((subst (x a) ... e) s H) (where ((f_0 obj_0) ... (f_i (FUN (x ...) e)) (f_i+1 obj_i+1) ...) H) (side-condition (= (length (term (a ...))) (length (term (x ...))))) "Exact") (--> ((f_i k a_1→n ..._1→n a_n+1→m ...) (κ ...) (name H ((f_0 obj_0) ... (f_i (FUN (x ..._1→n) e)) (f_i+1 obj_i+1) ...))) ((subst (x a_1→n) ... e) ((• a_n+1→m ...) κ ...) H) (side-condition (> (length (term (a_n+1→m ...))) 0)) "CallK") (--> ((f_i k a ..._1→m) s (name H ((f_1 obj_1) ... (f_i (FUN (x_1→m ..._1→m x_m+1→n ...) e)) (f_i+1 obj_i+1) ...))) (f_0 s ((f_0 (PAP f_i a ...)) ,@(term H))) (fresh f_0) (side-condition (> (length (term (x_m+1→n ...))) 0)) "PAP") (--> ((f_i • a ...) (κ ...) H) (f_i ((• a ...) κ ...) H) (where ((f_0 obj_0) ... (f_i (THUNK e)) (f_i+1 obj_i+1) ...) H) "TCall") (--> ((f_i k a_m ...) s H) ((g • a_n ... a_m ...) s H) (where ((f_0 obj_0) ... (f_i (PAP g a_n ...)) (f_i+1 obj_i+1) ...) H) "PCall") (--> (f_i ((• a ...) κ ...) H) ((f_i • a ...) (κ ...) H) ; technically CON should not be allowed, but we'll get stuck one step later (where ((f_0 obj_0) ... (f_i val) (f_i+1 obj_i+1) ...) H) "RetFun") )) (define dH (term ((f (FUN (x y z) (⊕ x y z))) (g (THUNK f)) (h (PAP f 0)) (y (THUNK z)) (z (CON C_I 0))))) ; XXX these tests are pretty fragile (define dHc (term ((f (FUN (x y z) (⊕ x y z))) (g (THUNK f)) (h (PAP f 0)) (y (CON C_I 0)) (z (CON C_I 0))))) ; Case (test-->> red (term ((case z ((C_I x) (⊕ x 1)) ((x) x)) () ,dH)) (term ((⊕ 0 1) () ,dH))) (test-->> red (term ((case y ((C_I x) (⊕ x 1)) ((x) x)) () ,dH)) (term ((⊕ 0 1) () ,dHc))) (test-->> red (term ((case z ((C_J x) (⊕ x 1)) ((x) x)) () ,dH)) (term (z () ,dH))) (test-->> red (term ((case y ((C_J x) (⊕ x 1)) ((x) x)) () ,dH)) (term (z () ,dHc))) (test-->> red (term ((case 0 ((C_J x) (⊕ x 1)) ((x) x)) () ,dH)) (term (0 () ,dH))) ; KnownCall/Exact/CallK/PAP (test-->> red (term ((f • 0) () ,dH)) (term (f_0 () ((f_0 (PAP f 0)) ,@dH)))) (test-->> red (term ((f 3 0) () ,dH)) (term (f_0 () ((f_0 (PAP f 0)) ,@dH)))) (test-->> red (term ((f • 0 1 2 3) () ,dH)) (term ((⊕ 0 1 2) ((• 3)) ,dH))) (test-->> red (term ((f 3 0 1 2 3) () ,dH)) (term ((⊕ 0 1 2) ((• 3)) ,dH))) (test-->> red (term ((f • 0 1 2) () ,dH)) (term ((⊕ 0 1 2) () ,dH))) (test-->> red (term ((f 3 0 1 2) () ,dH)) (term ((⊕ 0 1 2) () ,dH))) ; TCall/Thunk/Update (define dHe (term ((f (FUN (x y z) (⊕ x y z))) (g (FUN (x y z) (⊕ x y z))) (h (PAP f 0)) (y (THUNK z)) (z (CON C_I 0))))) (test-->> red (term ((g • 0) () ,dH)) (term (f_0 () ((f_0 (PAP f 0)) ,@dHe)))) (test-->> red (term ((g • 0 1 2 3) () ,dH)) (term ((⊕ 0 1 2) ((• 3)) ,dHe))) (test-->> red (term ((g • 0 1 2) () ,dH)) (term ((⊕ 0 1 2) () ,dHe))) ; PCall (test-->> red (term ((h • 1) () ,dH)) (term (f_0 () ((f_0 (PAP f 0 1)) ,@dH)))) (test-->> red (term ((h 2 1) () ,dH)) (term (f_0 () ((f_0 (PAP f 0 1)) ,@dH)))) (test-->> red (term ((h • 1 2 3) () ,dH)) (term ((⊕ 0 1 2) ((• 3)) ,dH))) (test-->> red (term ((h 3 1 2 3) () ,dH)) (term ((⊕ 0 1 2) ((• 3)) ,dH))) (test-->> red (term ((h • 1 2) () ,dH)) (term ((⊕ 0 1 2) () ,dH))) (test-->> red (term ((h 3 1 2) () ,dH)) (term ((⊕ 0 1 2) () ,dH)))