ISWIM

ISWIM
編程範型	指令式, 函數式
設計者	Peter J. Landin
釋出時間	1966年，60年前
範疇	詞法
受影響於
	ALGOL 60, Lisp
影響語言
	PAL, SASL, ML, NPL, Lucid, Haskell

ISWIM（「If you See What I Mean」的首字母縮寫），是的一種抽象的電腦程式語言或程式語言家族，它由Peter J. Landin設計，並描述在他1966年於ACM通訊發表的文章《The Next 700 Programming Languages》之中^[1]。

儘管沒有實現，它被證明為在程式語言開發中非常有影響力的語言，特別是對於函數式程式設計語言，比如SASL、ML、NPL、Haskell和它們的後繼者，還有數據流程編程語言如Lucid。

設計

ISWIM是具有函數式核心的指令式編程語言，它構成自加了語法糖的叫做「應用表達式」（AE）的lambda演算，並增加了可變變量和賦值，還有強力控制機制即對應J算子（英語：J operator）的程式點算子pp^[2]。ISWIM的操作語意，使用Landin的SECD抽象機來定義，並且使用了傳值呼叫，因而是及早求值的^[3]。

ISWIM基於了lambda演算，從而具有高階函數和詞法範疇變量，其應用表達式為了「同時」或「平行」定義而擴充了在λ和.之間的識別碼列表，為遞歸定義而採用了Y不動點算子。ISWIM的目標之一，就是要看起來更像數學表示，所以在定義結構之時，放棄了ALGOL的陳述式括號begin……end，轉而採用了越位規則和基於縮排的範疇。

ISWIM程式基於了一個單一表達式，它由where或let子句、條件表達式和函數定義所限定。ISWIM在表示法上的特色，是與CPL一起，最早使用了where子句，尤其是let子句適合表達ALGOL 60的塊結構而為後繼者語言所承襲：

AE

ISWIM

{λf.f(b+2c)+f(2b-c)}
[λx.x(x+a)]

{λ(f,b,c).f(b+2c)+f(2b-c)}
[λx.x(x+a),
  u/(u+1),
  v/(v+1)]

{λg.g({λf.f}[λx.ax²+bx+c],
  u/(u+1),
  v/(v+1))}
[λ(f,p,q).f(p+2q,2p-q)]

{λf.f(6)}[Yλf.λn.(n=0)→1 else→nf(n-1)]

{λx.xy(x+y)}
[{λy.a²+a√y}
  [a²+b²]]

{λ(a,b,f).
  {λ(g,h).
    {λk.X}
    [λ(u,v).λx.K]}
  [Yλ(g,h).
    (λx.G,λ(y,z).H)]}
[A,B,λ(x,y).F]

f(b+2c)+f(2b-c)
where f(x) = x(x+a)

f(b+2c)+f(2b-c)
where f(x) = x(x+a)
  and b = u/(u+1)
  and c = v/(v+1)

g(f where f(x) = ax²+bx+c,
  u/(u+1),
  v/(v+1))
where g(f,p,q) = f(p+2q,2p-q)

f(6) where rec f(n) = (n=0)→1; nf(n-1)

xy(x+y)
where x = a²+a√y
  where y = a²+b²

X
where k(u,v)(x) = K
where rec g(x) = G
  and h(y,z) = H
where a = A
  and b = B
  and f(x,y) = F

let f(x) = x(x+a)
f(b+2c)+f(2b-c)

let f(x) = x(x+a)
  and b = u/(u+1)
  and c = v/(v+1)
f(b+2c)+f(2b-c)

let g(f,p,q) = f(p+2q,2p-q)
g((let f(x) = ax²+bx+c; f),
  u/(u+1),
  v/(v+1))

let rec f(n) = ((n=0)→1; nf(n-1)); f(6)

let x =
  let y = a²+b²; a²+a√y
xy(x+y)

let a = A
  and b = B
  and f(x,y) = F
let rec g(x) = G
  and h(y,z) = H
let k(u,v)(x) = K
X

下面以階乘函數的應用（英語：Function application）為例展示ISWIM的等價規則，設L = (n=0)→1; nf(n-1)、G = (g where g(n) = L)並且F = (G where rec f = G)：

	`f(6) where rec f(n) = (n=0)→1; nf(n-1)`		`let rec f(n) = ((n=0)→1; nf(n-1)); f(6)`
$\equiv$	`f(6) where rec f(n) = L`	$\equiv$	`let rec f(n) = L; f(6)`
$\equiv$	`f(6) where rec f = (g where g(n) = L)`	$\equiv$	`let rec f = (let g(n) = L; g); f(6)`
$\equiv$	`f(6) where rec f = G`	$\equiv$	`let rec f = G; f(6)`
$\equiv$	`f(6) where f = (G where rec f = G)`	$\equiv$	`let f = (let rec f = G; G); f(6)`
$\equiv$	`(G where rec f = G)(6)`	$\equiv$	`(let rec f = G; G)(6)`
$\equiv$	`(G where f = (G where rec f = G))(6)`	$\equiv$	`(let f = (let rec f = G; G); G)(6)`
$\equiv$	`(G where f = F)(6)`	$\equiv$	`(let f = F; G)(6)`
$\equiv$	`((g where g(n) = L) where f = F)(6)`	$\equiv$	`(let f = F; (let g(n) = L; g))(6)`
$\equiv$	`((g where g(n) = (n=0)→1; nf(n-1)) where f = F)(6)`	$\equiv$	`(let f = F; (let g(n) = ((n=0)→1; nf(n-1)); g))(6)`
$\equiv$	`(g where g(n) = (n=0)→1; nF(n-1))(6)`	$\equiv$	`(let g(n) = ((n=0)→1; nF(n-1)); g)(6)`
$\equiv$	`((n=0)→1; nF(n-1)) where n = 6`	$\equiv$	`let n = 6; ((n=0)→1; nF(n-1))`
$\equiv$	`6(F(5))`	$\equiv$	`6(F(5))`
$\equiv$	`6((G where rec f = G)(5))`	$\equiv$	`6((let rec f = G; G)(5))`
$\equiv$	`6(f(5) where f = (G where rec f = G))`	$\equiv$	`6(let f = (let rec f = G; G); f(5))`
$\equiv$	`6(f(5) where rec f = G)`	$\equiv$	`6(let rec f = G; f(5))`
$\equiv$	`6(f(5) where rec f = (g where g(n) = L))`	$\equiv$	`6(let rec f = (let g(n) = L; g); f(5))`
$\equiv$	`6(f(5) where rec f(n) = L)`	$\equiv$	`6(let rec f(n) = L; f(5))`
$\equiv$	`6(f(5) where rec f(n) = (n=0)→1; nf(n-1))`	$\equiv$	`6(let rec f(n) = ((n=0)→1; nf(n-1)); f(5))`

在ISWIM論文中首次出現了用來定義結構的代數資料類型定義，這是通過自然語言的either……or……和……and……描述完成的，但明確的表示出了「積（英語：Product type）之和」^[4]：

ISWIM

Standard ML

an  $\mathrm {aexpression}$  ( $\mathrm {aexp}$ ) is
  either  $simple$ , and has
    a  $body$ , which is an  $\mathrm {identifier}$ 
  or a  $combination$ , in which case it has
    a  $rator$ , which is an  $\mathrm {aexp}$ ,
    and a  $rand$ , which is an  $\mathrm {aexp}$ ,
  or a  $conditional$ , ……
  or  $one{\text{-}}armed$ , ……
  or a  $listing$ , ……
  or  $beet$ , …… .

datatype aexp
  = SIMPLE of body 
  | COMBINATION of rator * rand
  | CONDITIONAL ……
  | ONE_ARMED ……
  | LISTING ……
  | BEET ……
and body = BODY of identifier
and rator = RATOR of aexp
and rand = RAND of aexp

實現和衍生

沒有進行過直接實現ISWIM的嘗試，但Arthur Evans的PAL^[5]，和John C. Reynolds（英語：John C. Reynolds）的Gedanken^[6]，取得了Landin的多數概念，包括強力的控制轉移操作，這兩者都是動態型別語言。Robin Milner的ML，可以被認為等價於沒有J算子，而有類型推論的ISWIM。

從ISWIM衍生出的另一條路線，是去掉指令式特徵即賦值和J算子，而只留下純函數式語言^[7]，接着就有可能切換到惰性求值。這條路線導致了SASL、Hope、KRC、Miranda、Haskell、Clean。

參照

^ Landin, P. J. The Next 700 Programming Languages (PDF). Communications of the ACM (Association for Computing Machinery). March 1966, 9 (3): 157–165 [2021-08-28]. S2CID 13409665. doi:10.1145/365230.365257. （原始內容 (PDF)存檔於2022-03-23）.
^ Landin, P.J. A Generalization of Jumps and Labels (PDF). 1965.
Thielecke, H. An Introduction to Landin's "A Generalization of Jumps and Labels". Higher-Order and Symbolic Computation. December 1998, 11 (2): 117–123. S2CID 1562780. doi:10.1023/A:1010060315625.
^ Gordon Plotkin（英語：Gordon Plotkin）. Call-by-Name, Call-by Value and the Lambda Calculus (PDF) (報告). 1975 [2020-04-26]. （原始內容 (PDF)存檔於2020-02-01）.
^ Turner, D. A., Some History of Functional Programming Languages (PDF), Lecture Notes in Computer Science 7829, Berlin, Heidelberg: Springer Berlin Heidelberg: 1–20, 2013 [2024-01-28], ISBN 978-3-642-40446-7, doi:10.1007/978-3-642-40447-4_1, The ISWIM paper also has the first appearance of algebraic type definitions used to define structures. This is done in words, but the sum-of-products idea is clearly there.
^ Arthur Evans. PAL: a language designed for teaching programming linguistics. Proceedings ACM National Conference. ACM National Conference. Association for Computing Machinery. 1968.
A. Evans. PAL -- A Reference Manual and a Primer (PDF) (報告). Department of Electrical Engineering, Massachusetts Institute of Technology. February 1968 [2021-09-09]. （原始內容 (PDF)存檔於2022-03-06）.
A. Evans. Appendix 2.1. The Complete Syntax for PAL (PDF) (報告). February 1968 [2021-09-10]. （原始內容 (PDF)存檔於2022-03-06）.
J. M. Wozencraft, A. Evans. Notes on Programming Linguistics (PDF). M.I.T. Department of Electrical Engineering. 1971 [2021-09-11]. （原始內容 (PDF)存檔於2022-03-06）.
^ John C. Reynolds（英語：John C. Reynolds）. GEDANKEN: a simple typeless language which permits functional data structures and co-routines (PDF) (報告). Argonne National Laboratory. September 1969 [2021-09-09]. （原始內容 (PDF)存檔於2021-09-09）.
John C. Reynolds（英語：John C. Reynolds）. Definitional interpreters for higher-order programming languages. ACM '72: Proceedings of the ACM annual conference - Volume. August 1972 [2022-11-19]. doi:10.1145/800194.805852. （原始內容存檔於2022-11-27）.
^ Ivanović, Mirjana; Budimac, Zoran. A definition of an ISWIM-like language via Scheme. ACM SIGPLAN Notices. April 1993, 28 (4): 29–38. S2CID 14379260. doi:10.1145/152739.152743.

本條目部分或全部內容出自以GFDL授權發佈的《自由線上電腦詞典》（FOLDOC）。

[1] Landin, P. J. The Next 700 Programming Languages (PDF). Communications of the ACM (Association for Computing Machinery). March 1966, 9 (3): 157–165 [2021-08-28]. S2CID 13409665. doi:10.1145/365230.365257. （原始內容 (PDF)存檔於2022-03-23）.

[2] Landin, P.J. A Generalization of Jumps and Labels (PDF). 1965.
Thielecke, H. An Introduction to Landin's "A Generalization of Jumps and Labels". Higher-Order and Symbolic Computation. December 1998, 11 (2): 117–123. S2CID 1562780. doi:10.1023/A:1010060315625.

[3] Gordon Plotkin（英語：Gordon Plotkin）. Call-by-Name, Call-by Value and the Lambda Calculus (PDF) (報告). 1975 [2020-04-26]. （原始內容 (PDF)存檔於2020-02-01）.

[4] Turner, D. A., Some History of Functional Programming Languages (PDF), Lecture Notes in Computer Science 7829, Berlin, Heidelberg: Springer Berlin Heidelberg: 1–20, 2013 [2024-01-28], ISBN 978-3-642-40446-7, doi:10.1007/978-3-642-40447-4_1, The ISWIM paper also has the first appearance of algebraic type definitions used to define structures. This is done in words, but the sum-of-products idea is clearly there.

[5] Arthur Evans. PAL: a language designed for teaching programming linguistics. Proceedings ACM National Conference. ACM National Conference. Association for Computing Machinery. 1968.
A. Evans. PAL -- A Reference Manual and a Primer (PDF) (報告). Department of Electrical Engineering, Massachusetts Institute of Technology. February 1968 [2021-09-09]. （原始內容 (PDF)存檔於2022-03-06）.
A. Evans. Appendix 2.1. The Complete Syntax for PAL (PDF) (報告). February 1968 [2021-09-10]. （原始內容 (PDF)存檔於2022-03-06）.
J. M. Wozencraft, A. Evans. Notes on Programming Linguistics (PDF). M.I.T. Department of Electrical Engineering. 1971 [2021-09-11]. （原始內容 (PDF)存檔於2022-03-06）.

[6] John C. Reynolds（英語：John C. Reynolds）. GEDANKEN: a simple typeless language which permits functional data structures and co-routines (PDF) (報告). Argonne National Laboratory. September 1969 [2021-09-09]. （原始內容 (PDF)存檔於2021-09-09）.
John C. Reynolds（英語：John C. Reynolds）. Definitional interpreters for higher-order programming languages. ACM '72: Proceedings of the ACM annual conference - Volume. August 1972 [2022-11-19]. doi:10.1145/800194.805852. （原始內容存檔於2022-11-27）.

[7] Ivanović, Mirjana; Budimac, Zoran. A definition of an ISWIM-like language via Scheme. ACM SIGPLAN Notices. April 1993, 28 (4): 29–38. S2CID 14379260. doi:10.1145/152739.152743.

[1]

[2]

[3]

[4]

[5]

[6]

[7]