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cfSupportScript.sml
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cfSupportScript.sml
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(**
Support lemmas for CF proofs in the end-to-end correctness theorems
**)
open basis_ffiTheory cfHeapsBaseTheory basis;
open cfTacticsLib ml_translatorLib;
open source_to_source2Theory CakeMLtoFloVerTheory CakeMLtoFloVerProofsTheory;
open preamble;
val _ = new_theory "cfSupport";
val _ = translation_extends "basisProg";
Theorem IMP_SPLIT:
(P ⇒ (Q1 ∧ Q2)) ⇔ ((P ⇒ Q1) ∧ (P ⇒ Q2))
Proof
EQ_TAC \\ rpt strip_tac \\ fs[]
QED
Definition getDeclLetParts_def:
getDeclLetParts [Dlet loc (Pvar fname) e] =
let (vars, body) = stripFuns e in
(fname, vars, body)
End
Definition real_spec_prog_def:
real_spec_prog body env fvars vs =
case
evaluate
(empty_state with fp_state := empty_state.fp_state with <| canOpt := FPScope NoOpt; real_sem := T|>)
(env with v :=
toRspace (extend_env_with_vars (REVERSE fvars) (REVERSE vs) env.v))
[realify body] of
| (st, Rval [Real r]) => r
End
(**
fun reader1 u =
let
val cl = CommandLine.arguments ();
val cst1 = List.hd cl;
in (cst1) end;
**)
Definition reader1_def:
reader1 =
[Dletrec
unknown_loc
[("reader1","u",
Let (SOME "a") (Con NONE [])
(Let (SOME "cl")
(App Opapp
[Var (Long "CommandLine" (Short "arguments"));
Var (Short "a")])
(Let (SOME "cst1")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "cl")])
(Var (Short "cst1")))))]]
End
val _ = append_prog (reader1_def |> concl |> rhs);
(**
process_topdecs ‘fun reader2 u =
let
val cl = CommandLine.arguments ();
val cst1 = List.hd cl;
val cst2 = List.hd (List.tl cl);
in (cst1, cst2) end;’
**)
Definition reader2_def:
reader2 =
[Dletrec
unknown_loc
[("reader2","u",
Let (SOME "a") (Con NONE [])
(Let (SOME "cl")
(App Opapp
[Var (Long "CommandLine" (Short "arguments"));
Var (Short "a")])
(Let (SOME "cst1")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "cl")])
(Let (SOME "b")
(App Opapp
[Var (Long "List" (Short "tl")); Var (Short "cl")])
(Let (SOME "cst2")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "b")])
(Con NONE [Var (Short "cst1"); Var (Short "cst2")]))))))]]
End
val _ = append_prog (reader2_def |> concl |> rhs);
(**
fun reader3 u =
let
val cl = CommandLine.arguments ();
val cst1 = List.hd cl;
val cst2 = List.hd (List.tl cl);
val cst3 = List.hd (List.tl (List.tl cl));
in (cst1, (cst2, cst3)) end;
**)
Definition reader3_def:
reader3 =
[Dletrec
unknown_loc
[("reader3","u",
Let (SOME "a") (Con NONE [])
(Let (SOME "cl")
(App Opapp
[Var (Long "CommandLine" (Short "arguments"));
Var (Short "a")])
(Let (SOME "cst1")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "cl")])
(Let (SOME "b")
(App Opapp
[Var (Long "List" (Short "tl")); Var (Short "cl")])
(Let (SOME "cst2")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "b")])
(Let (SOME "c")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "cl")])
(Let (SOME "d")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "c")])
(Let (SOME "cst3")
(App Opapp
[Var (Long "List" (Short "hd"));
Var (Short "d")])
(Let (SOME "e")
(Con NONE
[Var (Short "cst2");
Var (Short "cst3")])
(Con NONE
[Var (Short "cst1"); Var (Short "e")]))))))))))]]
End
val _ = append_prog (reader3_def |> concl |> rhs);
(**
fun reader4 u =
let
val cl = CommandLine.arguments ();
val cst1 = List.hd cl;
val cst2 = List.hd (List.tl cl);
val cst3 = List.hd (List.tl (List.tl cl));
val cst4 = List.hd (List.tl (List.tl (List.tl cl)));
in (cst1, (cst2, (cst3, cst4))) end;
**)
Definition reader4_def:
reader4 =
[Dletrec unknown_loc
[("reader4","u",
Let (SOME "a") (Con NONE [])
(Let (SOME "cl")
(App Opapp
[Var (Long "CommandLine" (Short "arguments"));
Var (Short "a")])
(Let (SOME "cst1")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "cl")])
(Let (SOME "b")
(App Opapp
[Var (Long "List" (Short "tl")); Var (Short "cl")])
(Let (SOME "cst2")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "b")])
(Let (SOME "c")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "cl")])
(Let (SOME "d")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "c")])
(Let (SOME "cst3")
(App Opapp
[Var (Long "List" (Short "hd"));
Var (Short "d")])
(Let (SOME "e")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "cl")])
(Let (SOME "f")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "e")])
(Let (SOME "g")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "f")])
(Let (SOME "cst4")
(App Opapp
[Var
(Long "List" (Short "hd"));
Var (Short "g")])
(Let (SOME "h")
(Con NONE
[Var (Short "cst3");
Var (Short "cst4")])
(Let (SOME "i")
(Con NONE
[Var (Short "cst2");
Var (Short "h")])
(Con NONE
[Var (Short "cst1");
Var (Short "i")])))))))))))))))]]
End
val _ = append_prog (reader4_def |> concl |> rhs);
(**
fun reader6 u =
let
val cl = CommandLine.arguments ();
val cst1 = List.hd cl;
val cst2 = List.hd (List.tl cl);
val cst3 = List.hd (List.tl (List.tl cl));
val cst4 = List.hd (List.tl (List.tl (List.tl cl)));
val cst5 = List.hd (List.tl (List.tl (List.tl (List.tl cl))));
val cst6 = List.hd (List.tl (List.tl (List.tl (List.tl (List.tl cl)))));
in (cst1, (cst2, (cst3, (cst4, (cst5, cst6))))) end;
**)
Definition reader6_def:
reader6 =
[Dletrec unknown_loc
[("reader6","u",
Let (SOME "a") (Con NONE [])
(Let (SOME "cl")
(App Opapp
[Var (Long "CommandLine" (Short "arguments"));
Var (Short "a")])
(Let (SOME "cst1")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "cl")])
(Let (SOME "b")
(App Opapp
[Var (Long "List" (Short "tl")); Var (Short "cl")])
(Let (SOME "cst2")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "b")])
(Let (SOME "c")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "cl")])
(Let (SOME "d")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "c")])
(Let (SOME "cst3")
(App Opapp
[Var (Long "List" (Short "hd"));
Var (Short "d")])
(Let (SOME "e")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "cl")])
(Let (SOME "f")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "e")])
(Let (SOME "g")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "f")])
(Let (SOME "cst4")
(App Opapp
[Var
(Long "List" (Short "hd"));
Var (Short "g")])
(Let (SOME "h")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "cl")])
(Let (SOME "i")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "h")])
(Let (SOME "j")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "i")])
(Let (SOME "k")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "j")])
(Let (SOME "cst5")
(App Opapp
[Var
(Long "List"
(Short
"hd"));
Var
(Short "k")])
(Let (SOME "l")
(App Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"cl")])
(Let (SOME "m")
(App Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"l")])
(Let
(SOME "n")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"m")])
(Let
(SOME
"o")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"n")])
(Let
(SOME
"p")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"o")])
(Let
(SOME
"cst6")
(App
Opapp
[Var
(Long
"List"
(Short
"hd"));
Var
(Short
"p")])
(Let
(SOME
"q")
(Con
NONE
[Var
(Short
"cst5");
Var
(Short
"cst6")])
(Let
(SOME
"r")
(Con
NONE
[Var
(Short
"cst4");
Var
(Short
"q")])
(Let
(SOME
"s")
(Con
NONE
[Var
(Short
"cst3");
Var
(Short
"r")])
(Let
(SOME
"t")
(Con
NONE
[Var
(Short
"cst2");
Var
(Short
"s")])
(Con
NONE
[Var
(Short
"cst1");
Var
(Short
"t")]))))))))))))))))))))))))))))]]
End
val _ = append_prog (reader6_def |> concl |> rhs);
(**
fun reader8 u =
let
val cl = CommandLine.arguments ();
val cst1 = List.hd cl;
val cst2 = List.hd (List.tl cl);
val cst3 = List.hd (List.tl (List.tl cl));
val cst4 = List.hd (List.tl (List.tl (List.tl cl)));
val cst5 = List.hd (List.tl (List.tl (List.tl (List.tl cl))));
val cst6 = List.hd (List.tl (List.tl (List.tl (List.tl (List.tl cl)))));
val cst7 = List.hd (List.tl (List.tl (List.tl (List.tl (List.tl (List.tl cl))))));
val cst8 = List.hd (List.tl (List.tl (List.tl (List.tl (List.tl (List.tl (List.tl cl)))))));
in (cst1, (cst2, (cst3, (cst4, (cst5, (cst6, (cst7, cst8))))))) end;
**)
Definition reader8_def:
reader8 =
[Dletrec unknown_loc
[("reader8","u",
Let (SOME "a") (Con NONE [])
(Let (SOME "cl")
(App Opapp
[Var (Long "CommandLine" (Short "arguments"));
Var (Short "a")])
(Let (SOME "cst1")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "cl")])
(Let (SOME "b")
(App Opapp
[Var (Long "List" (Short "tl")); Var (Short "cl")])
(Let (SOME "cst2")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "b")])
(Let (SOME "c")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "cl")])
(Let (SOME "d")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "c")])
(Let (SOME "cst3")
(App Opapp
[Var (Long "List" (Short "hd"));
Var (Short "d")])
(Let (SOME "e")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "cl")])
(Let (SOME "f")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "e")])
(Let (SOME "g")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "f")])
(Let (SOME "cst4")
(App Opapp
[Var
(Long "List" (Short "hd"));
Var (Short "g")])
(Let (SOME "h")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "cl")])
(Let (SOME "i")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "h")])
(Let (SOME "j")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "i")])
(Let (SOME "k")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "j")])
(Let (SOME "cst5")
(App Opapp
[Var
(Long "List"
(Short
"hd"));
Var
(Short "k")])
(Let (SOME "l")
(App Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"cl")])
(Let (SOME "m")
(App Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"l")])
(Let
(SOME "n")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"m")])
(Let
(SOME
"o")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"n")])
(Let
(SOME
"p")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"o")])
(Let
(SOME
"cst6")
(App
Opapp
[Var
(Long
"List"
(Short
"hd"));
Var
(Short
"p")])
(Let
(SOME
"q")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"cl")])
(Let
(SOME
"r")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"q")])
(Let
(SOME
"s")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"r")])
(Let
(SOME
"t")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"s")])
(Let
(SOME
"v")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"t")])
(Let
(SOME
"w")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"v")])
(Let
(SOME
"cst7")
(App
Opapp
[Var
(Long
"List"
(Short
"hd"));
Var
(Short
"w")])
(Let
(SOME
"x")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"cl")])
(Let
(SOME
"y")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"x")])
(Let
(SOME
"z")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"y")])
(Let
(SOME
"t0")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"z")])
(Let
(SOME
"t1")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"t0")])
(Let
(SOME
"t2")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"t1")])
(Let
(SOME
"t3")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"t2")])
(Let
(SOME
"cst8")
(App
Opapp
[Var
(Long
"List"
(Short
"hd"));
Var
(Short
"t3")])
(Let
(SOME
"t4")
(Con
NONE
[Var
(Short
"cst7");
Var
(Short
"cst8")])
(Let
(SOME
"t5")
(Con
NONE
[Var
(Short
"cst6");
Var
(Short
"t4")])
(Let
(SOME
"t6")
(Con
NONE
[Var
(Short
"cst5");
Var
(Short
"t5")])
(Let
(SOME
"t7")
(Con
NONE
[Var
(Short
"cst4");
Var
(Short
"t6")])
(Let
(SOME
"t8")
(Con
NONE
[Var
(Short
"cst3");
Var
(Short
"t7")])
(Let
(SOME
"t9")
(Con
NONE
[Var
(Short
"cst2");
Var
(Short
"t8")])
(Con
NONE
[Var
(Short
"cst1");
Var
(Short
"t9")])))))))))))))))))))))))))))))))))))))))))))))]]
End
val _ = append_prog (reader8_def |> concl |> rhs);
(**
fun reader8 u =
let
val cl = CommandLine.arguments ();
val cst1 = List.hd cl;
val cst2 = List.hd (List.tl cl);
val cst3 = List.hd (List.tl (List.tl cl));
val cst4 = List.hd (List.tl (List.tl (List.tl cl)));
val cst5 = List.hd (List.tl (List.tl (List.tl (List.tl cl))));
val cst6 = List.hd (List.tl (List.tl (List.tl (List.tl (List.tl cl)))));
val cst7 = List.hd (List.tl (List.tl (List.tl (List.tl (List.tl (List.tl cl))))));
val cst8 = List.hd (List.tl (List.tl (List.tl (List.tl (List.tl (List.tl (List.tl cl)))))));
val cst9 = List.hd (List.tl (List.tl (List.tl (List.tl (List.tl (List.tl (List.tl (List.tl cl))))))));
in (cst1, (cst2, (cst3, (cst4, (cst5, (cst6, (cst7, (cst8, cst9)))))))) end;
**)
Definition reader9_def:
reader9 =
[Dletrec unknown_loc
[("reader9","u",
Let (SOME "a") (Con NONE [])
(Let (SOME "cl")
(App Opapp
[Var (Long "CommandLine" (Short "arguments"));
Var (Short "a")])
(Let (SOME "cst1")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "cl")])
(Let (SOME "b")
(App Opapp
[Var (Long "List" (Short "tl")); Var (Short "cl")])
(Let (SOME "cst2")
(App Opapp
[Var (Long "List" (Short "hd")); Var (Short "b")])
(Let (SOME "c")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "cl")])
(Let (SOME "d")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "c")])
(Let (SOME "cst3")
(App Opapp
[Var (Long "List" (Short "hd"));
Var (Short "d")])
(Let (SOME "e")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "cl")])
(Let (SOME "f")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "e")])
(Let (SOME "g")
(App Opapp
[Var (Long "List" (Short "tl"));
Var (Short "f")])
(Let (SOME "cst4")
(App Opapp
[Var
(Long "List" (Short "hd"));
Var (Short "g")])
(Let (SOME "h")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "cl")])
(Let (SOME "i")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "h")])
(Let (SOME "j")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "i")])
(Let (SOME "k")
(App Opapp
[Var
(Long "List"
(Short "tl"));
Var (Short "j")])
(Let (SOME "cst5")
(App Opapp
[Var
(Long "List"
(Short
"hd"));
Var
(Short "k")])
(Let (SOME "l")
(App Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"cl")])
(Let (SOME "m")
(App Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"l")])
(Let
(SOME "n")
(App
Opapp
[Var
(Long
"List"
(Short
"tl"));
Var
(Short
"m")])
(Let
(SOME
"o")
(App
Opapp