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refactor(ocaml): refactoring ocaml lambda #15

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merged 4 commits into from
Nov 9, 2023
+5,473 −8
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refactor(ocaml): refactoring ocaml lambda #15

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c13eeb6
refactor(ocaml): refactoring ocaml lambda
henrylee97 Nov 8, 2023
17db2e9
refactor: rename source code name
henrylee97 Nov 8, 2023
b2ae1b4
[fix] lambda-12 syntax
sdw0316 Nov 8, 2023
92ace6a
fix: fix cases with syntax errors
henrylee97 Nov 8, 2023
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2 changes: 2 additions & 0 deletions OCaml/lambda-1/.dockerignore
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.dockerignore
Dockerfile
6 changes: 6 additions & 0 deletions OCaml/lambda-1/Dockerfile
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FROM ghcr.io/sambyeol/ocaml-devcontainer:4.14.1-debian-root

USER root
RUN mkdir -p /workspace
WORKDIR /workspace
COPY . /workspace
0 functional/OCaml/lambda/bugs/bug_1/bug.ml → OCaml/lambda-1/buggy/src.ml
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0 functional/OCaml/lambda/src/testcases → OCaml/lambda-1/buggy/testcases
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12 changes: 12 additions & 0 deletions OCaml/lambda-1/metadata.json
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{
"language": "ocaml",
"id": "lambda-1",

"buggyPath": "buggy",
"referencePath": null,

"buildCommand": "ocamlc src.ml",
"testCommand": null,

"categories": ["functional"]
}
2 changes: 2 additions & 0 deletions OCaml/lambda-10/.dockerignore
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.dockerignore
Dockerfile
6 changes: 6 additions & 0 deletions OCaml/lambda-10/Dockerfile
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FROM ghcr.io/sambyeol/ocaml-devcontainer:4.14.1-debian-root

USER root
RUN mkdir -p /workspace
WORKDIR /workspace
COPY . /workspace
0 functional/OCaml/lambda/bugs/bug_10/bug.ml → OCaml/lambda-10/buggy/src.ml
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35 changes: 35 additions & 0 deletions OCaml/lambda-10/buggy/testcases
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{
V ("X") => false;
(C (P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))), V "z")) => false;
(C (V "h", C (C (V "f", V "f"), V "y"))) => false;
(P ("y", P ("g", C (V "f", V "f")))) => false;
(C (C (V "b", P ("c", V "c")), P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(C (V "h", V "y")) => false;
(P ("g", P ("x", V "y"))) => false;
(C (P ("y", P ("c", C (C (V "f", V "f"), V "c"))), C (C (V "f", V "f"), V "y"))) => false;
(C (P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))), P ("b", C (V "f", V "f")))) => false;
(C (C (C (V "z", P ("x", V "y")), P ("y", P ("c", C (C (V "f", V "f"), V "c")))), C (V "x", V "h"))) => false;
(P ("h", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(P ("c", V "c")) => true;
(P ("h", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("h", P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("g", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("x", P ("c", V "c"))) => true;
(P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => true;
(P ("h", C (P ("x", P ("c", V "c")), V "h"))) => true;
(P ("a", P ("b", C(V "a", V "b")))) => true;
C ((P (("x", V ("x"))), P (("x", V ("x"))))) => true;
C ((P (("x", V ("x"))), V ("x"))) => false;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_0"))))))) => false;
P (("x_1", P (("x_0", C ((V ("x_1"), V ("x_1"))))))) => true;
P (("x_0", P (("x_1", P (("x_2", C ((V ("x_0"), V ("x_1"))))))))) => true;
P (("x", P (("x", P (("x", V ("x"))))))) => true;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_1"))))))) => false;
P (("x_0", C ((P (("x_1", V ("x_1"))), V ("x_1"))))) => false;
P (("x_0", C ((V ("x_0"), V ("x_1"))))) => false;
P (("x_1", C ((P (("x_0", C ((V ("x_0"), V ("x_1"))))), V ("x_1"))))) => true;
C ((P (("x", V ("x"))), C ((V ("x"), P (("x", V ("x"))))))) => false;
C ((C ((V ("x"), P (("x", V ("x"))))), P (("x", V ("x"))))) => false;
}
12 changes: 12 additions & 0 deletions OCaml/lambda-10/metadata.json
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{
"language": "ocaml",
"id": "lambda-10",

"buggyPath": "buggy",
"referencePath": null,

"buildCommand": "ocamlc src.ml",
"testCommand": null,

"categories": ["functional"]
}
2 changes: 2 additions & 0 deletions OCaml/lambda-100/.dockerignore
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.dockerignore
Dockerfile
6 changes: 6 additions & 0 deletions OCaml/lambda-100/Dockerfile
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FROM ghcr.io/sambyeol/ocaml-devcontainer:4.14.1-debian-root

USER root
RUN mkdir -p /workspace
WORKDIR /workspace
COPY . /workspace
0 functional/OCaml/lambda/bugs/bug_100/bug.ml → OCaml/lambda-100/buggy/src.ml
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35 changes: 35 additions & 0 deletions OCaml/lambda-100/buggy/testcases
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{
V ("X") => false;
(C (P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))), V "z")) => false;
(C (V "h", C (C (V "f", V "f"), V "y"))) => false;
(P ("y", P ("g", C (V "f", V "f")))) => false;
(C (C (V "b", P ("c", V "c")), P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(C (V "h", V "y")) => false;
(P ("g", P ("x", V "y"))) => false;
(C (P ("y", P ("c", C (C (V "f", V "f"), V "c"))), C (C (V "f", V "f"), V "y"))) => false;
(C (P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))), P ("b", C (V "f", V "f")))) => false;
(C (C (C (V "z", P ("x", V "y")), P ("y", P ("c", C (C (V "f", V "f"), V "c")))), C (V "x", V "h"))) => false;
(P ("h", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(P ("c", V "c")) => true;
(P ("h", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("h", P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("g", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("x", P ("c", V "c"))) => true;
(P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => true;
(P ("h", C (P ("x", P ("c", V "c")), V "h"))) => true;
(P ("a", P ("b", C(V "a", V "b")))) => true;
C ((P (("x", V ("x"))), P (("x", V ("x"))))) => true;
C ((P (("x", V ("x"))), V ("x"))) => false;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_0"))))))) => false;
P (("x_1", P (("x_0", C ((V ("x_1"), V ("x_1"))))))) => true;
P (("x_0", P (("x_1", P (("x_2", C ((V ("x_0"), V ("x_1"))))))))) => true;
P (("x", P (("x", P (("x", V ("x"))))))) => true;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_1"))))))) => false;
P (("x_0", C ((P (("x_1", V ("x_1"))), V ("x_1"))))) => false;
P (("x_0", C ((V ("x_0"), V ("x_1"))))) => false;
P (("x_1", C ((P (("x_0", C ((V ("x_0"), V ("x_1"))))), V ("x_1"))))) => true;
C ((P (("x", V ("x"))), C ((V ("x"), P (("x", V ("x"))))))) => false;
C ((C ((V ("x"), P (("x", V ("x"))))), P (("x", V ("x"))))) => false;
}
12 changes: 12 additions & 0 deletions OCaml/lambda-100/metadata.json
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{
"language": "ocaml",
"id": "lambda-100",

"buggyPath": "buggy",
"referencePath": null,

"buildCommand": "ocamlc src.ml",
"testCommand": null,

"categories": ["functional"]
}
2 changes: 2 additions & 0 deletions OCaml/lambda-11/.dockerignore
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.dockerignore
Dockerfile
6 changes: 6 additions & 0 deletions OCaml/lambda-11/Dockerfile
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FROM ghcr.io/sambyeol/ocaml-devcontainer:4.14.1-debian-root

USER root
RUN mkdir -p /workspace
WORKDIR /workspace
COPY . /workspace
0 functional/OCaml/lambda/bugs/bug_11/bug.ml → OCaml/lambda-11/buggy/src.ml
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35 changes: 35 additions & 0 deletions OCaml/lambda-11/buggy/testcases
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{
V ("X") => false;
(C (P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))), V "z")) => false;
(C (V "h", C (C (V "f", V "f"), V "y"))) => false;
(P ("y", P ("g", C (V "f", V "f")))) => false;
(C (C (V "b", P ("c", V "c")), P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(C (V "h", V "y")) => false;
(P ("g", P ("x", V "y"))) => false;
(C (P ("y", P ("c", C (C (V "f", V "f"), V "c"))), C (C (V "f", V "f"), V "y"))) => false;
(C (P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))), P ("b", C (V "f", V "f")))) => false;
(C (C (C (V "z", P ("x", V "y")), P ("y", P ("c", C (C (V "f", V "f"), V "c")))), C (V "x", V "h"))) => false;
(P ("h", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(P ("c", V "c")) => true;
(P ("h", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("h", P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("g", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("x", P ("c", V "c"))) => true;
(P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => true;
(P ("h", C (P ("x", P ("c", V "c")), V "h"))) => true;
(P ("a", P ("b", C(V "a", V "b")))) => true;
C ((P (("x", V ("x"))), P (("x", V ("x"))))) => true;
C ((P (("x", V ("x"))), V ("x"))) => false;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_0"))))))) => false;
P (("x_1", P (("x_0", C ((V ("x_1"), V ("x_1"))))))) => true;
P (("x_0", P (("x_1", P (("x_2", C ((V ("x_0"), V ("x_1"))))))))) => true;
P (("x", P (("x", P (("x", V ("x"))))))) => true;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_1"))))))) => false;
P (("x_0", C ((P (("x_1", V ("x_1"))), V ("x_1"))))) => false;
P (("x_0", C ((V ("x_0"), V ("x_1"))))) => false;
P (("x_1", C ((P (("x_0", C ((V ("x_0"), V ("x_1"))))), V ("x_1"))))) => true;
C ((P (("x", V ("x"))), C ((V ("x"), P (("x", V ("x"))))))) => false;
C ((C ((V ("x"), P (("x", V ("x"))))), P (("x", V ("x"))))) => false;
}
12 changes: 12 additions & 0 deletions OCaml/lambda-11/metadata.json
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{
"language": "ocaml",
"id": "lambda-11",

"buggyPath": "buggy",
"referencePath": null,

"buildCommand": "ocamlc src.ml",
"testCommand": null,

"categories": ["functional"]
}
2 changes: 2 additions & 0 deletions OCaml/lambda-12/.dockerignore
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.dockerignore
Dockerfile
6 changes: 6 additions & 0 deletions OCaml/lambda-12/Dockerfile
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FROM ghcr.io/sambyeol/ocaml-devcontainer:4.14.1-debian-root

USER root
RUN mkdir -p /workspace
WORKDIR /workspace
COPY . /workspace
2 changes: 1 addition & 1 deletion functional/OCaml/lambda/bugs/bug_12/bug.ml → OCaml/lambda-12/buggy/src.ml
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Expand Up @@ -18,4 +18,4 @@ let rec check (m : lambda) : bool =
| C (m0, m1) -> check_sub (m0, l) && check_sub (m1, l)
in

match m with V s -> raise Invalid_input "V only" | _ -> check_sub (m, [])
match m with V s -> raise (Invalid_input "V only") | _ -> check_sub (m, [])
35 changes: 35 additions & 0 deletions OCaml/lambda-12/buggy/testcases
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{
V ("X") => false;
(C (P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))), V "z")) => false;
(C (V "h", C (C (V "f", V "f"), V "y"))) => false;
(P ("y", P ("g", C (V "f", V "f")))) => false;
(C (C (V "b", P ("c", V "c")), P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(C (V "h", V "y")) => false;
(P ("g", P ("x", V "y"))) => false;
(C (P ("y", P ("c", C (C (V "f", V "f"), V "c"))), C (C (V "f", V "f"), V "y"))) => false;
(C (P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))), P ("b", C (V "f", V "f")))) => false;
(C (C (C (V "z", P ("x", V "y")), P ("y", P ("c", C (C (V "f", V "f"), V "c")))), C (V "x", V "h"))) => false;
(P ("h", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(P ("c", V "c")) => true;
(P ("h", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("h", P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("g", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("x", P ("c", V "c"))) => true;
(P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => true;
(P ("h", C (P ("x", P ("c", V "c")), V "h"))) => true;
(P ("a", P ("b", C(V "a", V "b")))) => true;
C ((P (("x", V ("x"))), P (("x", V ("x"))))) => true;
C ((P (("x", V ("x"))), V ("x"))) => false;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_0"))))))) => false;
P (("x_1", P (("x_0", C ((V ("x_1"), V ("x_1"))))))) => true;
P (("x_0", P (("x_1", P (("x_2", C ((V ("x_0"), V ("x_1"))))))))) => true;
P (("x", P (("x", P (("x", V ("x"))))))) => true;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_1"))))))) => false;
P (("x_0", C ((P (("x_1", V ("x_1"))), V ("x_1"))))) => false;
P (("x_0", C ((V ("x_0"), V ("x_1"))))) => false;
P (("x_1", C ((P (("x_0", C ((V ("x_0"), V ("x_1"))))), V ("x_1"))))) => true;
C ((P (("x", V ("x"))), C ((V ("x"), P (("x", V ("x"))))))) => false;
C ((C ((V ("x"), P (("x", V ("x"))))), P (("x", V ("x"))))) => false;
}
12 changes: 12 additions & 0 deletions OCaml/lambda-12/metadata.json
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{
"language": "ocaml",
"id": "lambda-12",

"buggyPath": "buggy",
"referencePath": null,

"buildCommand": "ocamlc src.ml",
"testCommand": null,

"categories": ["functional"]
}
2 changes: 2 additions & 0 deletions OCaml/lambda-13/.dockerignore
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.dockerignore
Dockerfile
6 changes: 6 additions & 0 deletions OCaml/lambda-13/Dockerfile
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FROM ghcr.io/sambyeol/ocaml-devcontainer:4.14.1-debian-root

USER root
RUN mkdir -p /workspace
WORKDIR /workspace
COPY . /workspace
4 changes: 2 additions & 2 deletions functional/OCaml/lambda/bugs/bug_13/bug.ml → OCaml/lambda-13/buggy/src.ml
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Expand Up @@ -4,8 +4,8 @@ and var = string

let rec check (a : lambda) : bool =
match a with
| V _ -> raise Invalid_argument "check"
| C (a, b) -> raise Invalid_argument "check"
| V _ -> raise (Invalid_argument "check")
| C (a, b) -> raise (Invalid_argument "check")
| P (a, V b) -> if a = b then true else false
| P (a, C (V b, V c)) -> if a = b || a = c then true else false
| P (a, C (P (b, V c), V d)) -> if a = c || a = d then true else false
Expand Down
35 changes: 35 additions & 0 deletions OCaml/lambda-13/buggy/testcases
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{
V ("X") => false;
(C (P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))), V "z")) => false;
(C (V "h", C (C (V "f", V "f"), V "y"))) => false;
(P ("y", P ("g", C (V "f", V "f")))) => false;
(C (C (V "b", P ("c", V "c")), P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(C (V "h", V "y")) => false;
(P ("g", P ("x", V "y"))) => false;
(C (P ("y", P ("c", C (C (V "f", V "f"), V "c"))), C (C (V "f", V "f"), V "y"))) => false;
(C (P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))), P ("b", C (V "f", V "f")))) => false;
(C (C (C (V "z", P ("x", V "y")), P ("y", P ("c", C (C (V "f", V "f"), V "c")))), C (V "x", V "h"))) => false;
(P ("h", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(P ("c", V "c")) => true;
(P ("h", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("h", P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("g", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("x", P ("c", V "c"))) => true;
(P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => true;
(P ("h", C (P ("x", P ("c", V "c")), V "h"))) => true;
(P ("a", P ("b", C(V "a", V "b")))) => true;
C ((P (("x", V ("x"))), P (("x", V ("x"))))) => true;
C ((P (("x", V ("x"))), V ("x"))) => false;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_0"))))))) => false;
P (("x_1", P (("x_0", C ((V ("x_1"), V ("x_1"))))))) => true;
P (("x_0", P (("x_1", P (("x_2", C ((V ("x_0"), V ("x_1"))))))))) => true;
P (("x", P (("x", P (("x", V ("x"))))))) => true;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_1"))))))) => false;
P (("x_0", C ((P (("x_1", V ("x_1"))), V ("x_1"))))) => false;
P (("x_0", C ((V ("x_0"), V ("x_1"))))) => false;
P (("x_1", C ((P (("x_0", C ((V ("x_0"), V ("x_1"))))), V ("x_1"))))) => true;
C ((P (("x", V ("x"))), C ((V ("x"), P (("x", V ("x"))))))) => false;
C ((C ((V ("x"), P (("x", V ("x"))))), P (("x", V ("x"))))) => false;
}
12 changes: 12 additions & 0 deletions OCaml/lambda-13/metadata.json
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{
"language": "ocaml",
"id": "lambda-13",

"buggyPath": "buggy",
"referencePath": null,

"buildCommand": "ocamlc src.ml",
"testCommand": null,

"categories": ["functional"]
}
2 changes: 2 additions & 0 deletions OCaml/lambda-14/.dockerignore
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.dockerignore
Dockerfile
6 changes: 6 additions & 0 deletions OCaml/lambda-14/Dockerfile
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FROM ghcr.io/sambyeol/ocaml-devcontainer:4.14.1-debian-root

USER root
RUN mkdir -p /workspace
WORKDIR /workspace
COPY . /workspace
4 changes: 2 additions & 2 deletions functional/OCaml/lambda/bugs/bug_14/bug.ml → OCaml/lambda-14/buggy/src.ml
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Expand Up @@ -4,8 +4,8 @@ and var = string

let rec check (a : lambda) : bool =
match a with
| V _ -> raise Invalid_argument "check"
| C (a, b) -> raise Invalid_argument "check"
| V _ -> raise (Invalid_argument "check")
| C (a, b) -> raise (Invalid_argument "check")
| P (a, V b) -> if a = b then true else false
| P (a, C (V b, V c)) -> if a = b || a = c then true else false
| P (a, C (P (b, V c), V d)) -> if a = c && a = d then true else false
Expand Down
35 changes: 35 additions & 0 deletions OCaml/lambda-14/buggy/testcases
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{
V ("X") => false;
(C (P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))), V "z")) => false;
(C (V "h", C (C (V "f", V "f"), V "y"))) => false;
(P ("y", P ("g", C (V "f", V "f")))) => false;
(C (C (V "b", P ("c", V "c")), P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(C (V "h", V "y")) => false;
(P ("g", P ("x", V "y"))) => false;
(C (P ("y", P ("c", C (C (V "f", V "f"), V "c"))), C (C (V "f", V "f"), V "y"))) => false;
(C (P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))), P ("b", C (V "f", V "f")))) => false;
(C (C (C (V "z", P ("x", V "y")), P ("y", P ("c", C (C (V "f", V "f"), V "c")))), C (V "x", V "h"))) => false;
(P ("h", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => false;
(P ("c", V "c")) => true;
(P ("h", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("h", P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("g", P ("h", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))))) => true;
(P ("x", P ("c", V "c"))) => true;
(P ("b", P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c")))))) => true;
(P ("f", P ("y", P ("c", C (C (V "f", V "f"), V "c"))))) => true;
(P ("h", C (P ("x", P ("c", V "c")), V "h"))) => true;
(P ("a", P ("b", C(V "a", V "b")))) => true;
C ((P (("x", V ("x"))), P (("x", V ("x"))))) => true;
C ((P (("x", V ("x"))), V ("x"))) => false;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_0"))))))) => false;
P (("x_1", P (("x_0", C ((V ("x_1"), V ("x_1"))))))) => true;
P (("x_0", P (("x_1", P (("x_2", C ((V ("x_0"), V ("x_1"))))))))) => true;
P (("x", P (("x", P (("x", V ("x"))))))) => true;
P (("x_0", C ((V ("x_1"), P (("x_1", V ("x_1"))))))) => false;
P (("x_0", C ((P (("x_1", V ("x_1"))), V ("x_1"))))) => false;
P (("x_0", C ((V ("x_0"), V ("x_1"))))) => false;
P (("x_1", C ((P (("x_0", C ((V ("x_0"), V ("x_1"))))), V ("x_1"))))) => true;
C ((P (("x", V ("x"))), C ((V ("x"), P (("x", V ("x"))))))) => false;
C ((C ((V ("x"), P (("x", V ("x"))))), P (("x", V ("x"))))) => false;
}
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