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-rw-r--r--docs/stg-spec/fast-curry.rkt247
1 files changed, 247 insertions, 0 deletions
diff --git a/docs/stg-spec/fast-curry.rkt b/docs/stg-spec/fast-curry.rkt
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+#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))) \ No newline at end of file
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