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GenTestFiles.hs
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GenTestFiles.hs
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{-|
Generating test files with code copied & renamed multiple times.
-}
module GenTestFiles where
replace :: String -> String -> String
replace x =
foldr (\c s -> case c of '%' -> x ++ s; _ -> c:s) []
render :: [String] -> Int -> String
render ls n = replace (if n == 0 then "" else show n) $ unlines ls
times :: Int -> (Int -> String) -> String
times n f = concatMap f [0..n-1]
-- todo: genEverything function
smallttStlc10k = writeFile "bench/stlc10k.stt" $ times 80 smallttStlc
smallttStlc5k = writeFile "bench/stlc5k.stt" $ times 40 smallttStlc
smallttStlcLessImpl10k = writeFile "bench/stlc_lessimpl10k.stt" $ times 80 smallttStlcLessImpl
smallttStlcLessImpl5k = writeFile "bench/stlc_lessimpl5k.stt" $ times 40 smallttStlcLessImpl
smallttStlc100k = writeFile "bench/stlc100k.stt" $ times 800 smallttStlc
leanStlc1k = writeFile "bench/stlc1k.lean" $ times 8 leanStlc
leanStlc5k = writeFile "bench/stlc5k.lean" $ times 40 leanStlc
leanStlc10k = writeFile "bench/stlc10k.lean" $ times 80 leanStlc
leanStlcLessImpl10k = writeFile "bench/stlc_lessimpl10k.lean" $ times 80 leanStlcLessImpl
leanStlcLessImpl5k = writeFile "bench/stlc_lessimpl5k.lean" $ times 40 leanStlcLessImpl
leanStlc100k = writeFile "bench/stlc100k.lean" $ times 800 leanStlc
agdaStlcLessImpl10k = writeFile "bench/stlc_lessimpl10k.agda" $ times 80 agdaStlcLessImpl
agdaStlcLessImpl5k = writeFile "bench/stlc_lessimpl5k.agda" $ times 40 agdaStlcLessImpl
agdaStlc1k = writeFile "bench/stlc1k.agda" $ times 8 agdaStlc
agdaStlc5k = writeFile "bench/stlc5k.agda" $ times 40 agdaStlc
agdaStlc10k = writeFile "bench/stlc10k.agda" $ times 80 agdaStlc
agdaStlc100k = writeFile "bench/stlc100k.agda" $ times 800 agdaStlc
idrisStlc1k = writeFile "bench/stlc1k.idr" $ times 8 idrisStlc
idrisStlc5k = writeFile "bench/stlc5k.idr" $ times 40 idrisStlc
idrisStlc10k = writeFile "bench/stlc10k.idr" $ times 80 idrisStlc
coqStlcLessImpl10k = writeFile "bench/stlc_lessimpl10k.v" $ times 80 coqStlcLessImpl
coqStlcLessImpl5k = writeFile "bench/stlc_lessimpl5k.v" $ times 40 coqStlcLessImpl
idrisStlcLessImpl10k = writeFile "bench/stlc_lessimpl10k.idr" $ times 80 idrisStlcLessImpl
idrisStlcLessImpl5k = writeFile "bench/stlc_lessimpl5k.idr" $ times 40 idrisStlcLessImpl
smallttStlcSmall10k = writeFile "bench/stlc_small10k.stt" $ times 192 smallttStlcSmall
smallttStlcSmall5k = writeFile "bench/stlc_small5k.stt" $ times 96 smallttStlcSmall
agdaStlcSmall10k = writeFile "bench/stlc_small10k.agda" $ times 192 agdaStlcSmall
agdaStlcSmall5k = writeFile "bench/stlc_small5k.agda" $ times 96 agdaStlcSmall
coqStlcSmall10k = writeFile "bench/stlc_small10k.v" $ times 192 coqStlcSmall
coqStlcSmall5k = writeFile "bench/stlc_small5k.v" $ times 96 coqStlcSmall
leanStlcSmall10k = writeFile "bench/stlc_small10k.lean" $ times 192 leanStlcSmall
leanStlcSmall5k = writeFile "bench/stlc_small5k.lean" $ times 96 leanStlcSmall
idrisStlcSmall10k = writeFile "bench/stlc_small10k.idr" $ times 192 idrisStlcSmall
idrisStlcSmall5k = writeFile "bench/stlc_small5k.idr" $ times 96 idrisStlcSmall
idrisStlcSmall1k = writeFile "bench/stlc_small1k.idr" $ times 19 idrisStlcSmall
idrisStlcSmall2k = writeFile "bench/stlc_small2k.idr" $ times 38 idrisStlcSmall
agdaStlcSmall1M = writeFile "bench/stlc_small1M.agda" $ times 19200 agdaStlcSmall
coqStlcSmall1M = writeFile "bench/stlc_small1M.v" $ times 19200 coqStlcSmall
leanStlcSmall1M = writeFile "bench/stlc_small1M.lean" $ times 19200 leanStlcSmall
smallttStlcSmall1M = writeFile "bench/stlc_small1M.stt" $ times 19200 smallttStlcSmall
idrisStlcSmall1M = writeFile "bench/stlc_small1M.idr" $ times 19200 idrisStlcSmall
test1 :: Int -> String
test1 = render [
"id% : {A} → A → A",
" = λ x. x",
"",
"id%Test : {A} → A → A",
" = id% id% id% id% id% id% id% id% id% id% id% id% id% id% id% id% id% id% id% id%",
" id% id% id% id% id% id% id% id% id% id% id% id% id% id% id% id% id% id% id% id%",
"",
"Nat% : U",
" = (n : U) → (n → n) → n → n",
"",
"zero% : Nat%",
" = λ n s z. z",
"",
"suc% : Nat% → Nat%",
" = λ a n s z. s (a n s z)",
"",
"add% : Nat% → Nat% → Nat%",
" = λ a b n s z. a n s (b n s z)",
"",
"mul% : Nat% → Nat% → Nat%",
" = λ a b n s. a n (b n s)",
"",
"Eq% : {A} → A → A → U",
" = λ {A} x y. (P : A → U) → P x → P y",
"",
"refl% : {A}{x : A} → Eq% x x",
" = λ P px. px",
"",
"two% : Nat% = λ N s z. s (s z)",
"five% : Nat% = λ N s z. s (s (s (s (s z))))",
"n10% = mul% two% five%",
"n10b% = mul% five% two%",
"n20% = mul% two% n10%",
"n20b% = mul% two% n10b%",
"n21% = suc% n20%",
"n21b% = suc% n20b%",
"n22% = suc% n21%",
"n22b% = suc% n21b%",
"n100% = mul% n10% n10%",
"n100b% = mul% n10b% n10b%",
"n10k% = mul% n100% n100%",
"n10kb% = mul% n100b% n100b%",
"n100k% = mul% n10k% n10%",
"n100kb% = mul% n10kb% n10b%",
"n1M% = mul% n10k% n100%",
"n1Mb% = mul% n10kb% n100b%",
"n5M% = mul% n1M% five%",
"n5Mb% = mul% n1Mb% five%",
"n10M% = mul% n5M% two%",
"n10Mb% = mul% n5Mb% two%",
"",
"",
"Vec% : U → Nat% → U",
" = λ a n. (V : Nat% → U) → V zero% → ({n} → a → V n → V (suc% n)) → V n",
"",
"vnil% : {a} → Vec% a zero%",
" = λ V n c. n",
"",
"vcons% : {a n} → a → Vec% a n → Vec% a (suc% n)",
" = λ a as V n c. c a (as V n c)",
"",
"vec1% = (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero%",
" (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero%",
" (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero%",
" (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero%",
" (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero% (vcons% zero%",
" (vcons% zero% (vcons% zero% vnil%))))))))))))))))))))))))))))))))",
"",
"Pair% : U → U → U",
" = λ A B. (Pair% : U)(pair : A → B → Pair%) → Pair%",
"",
"pair% : {A B} → A → B → Pair% A B",
" = λ a b Pair% pair. pair a b",
"",
"proj1% : {A B} → Pair% A B → A",
" = λ p. p _ (λ x y. x)",
"",
"proj2% : {A B} → Pair% A B → B",
" = λ p. p _ (λ x y. y)",
"",
"Top% : U",
" = (Top : U)(tt : Top) → Top",
"",
"tt% : Top%",
" = λ Top tt. tt",
"",
"Bot% : U",
" = (Bot : U) → Bot",
"",
"Ty% : U",
" = (Ty : U)",
" (ι : Ty)",
" (fun : Ty → Ty → Ty)",
" → Ty",
"",
"ι% : Ty%",
" = λ _ ι _. ι",
"",
"fun% : Ty% → Ty% → Ty%",
" = λ A B Ty ι fun. fun (A Ty ι fun) (B Ty ι fun)",
"",
"Con% : U",
" = (Con : U)",
" (nil : Con)",
" (cons : Con → Ty% → Con)",
" → Con",
"",
"nil% : Con%",
" = λ Con nil cons. nil",
"",
"cons% : Con% → Ty% → Con%",
" = λ Γ A Con nil cons. cons (Γ Con nil cons) A",
"",
"Var% : Con% → Ty% → U",
" = λ Γ A.",
" (Var : Con% → Ty% → U)",
" (vz : {Γ A} → Var (cons% Γ A) A)",
" (vs : {Γ B A} → Var Γ A → Var (cons% Γ B) A)",
" → Var Γ A",
"",
"vz% : {Γ A} → Var% (cons% Γ A) A",
" = λ Var vz vs. vz",
"",
"vs% : {Γ B A} → Var% Γ A → Var% (cons% Γ B) A",
" = λ x Var vz vs. vs (x Var vz vs)",
"",
"Tm% : Con% → Ty% → U",
" = λ Γ A.",
" (Tm : Con% → Ty% → U)",
" (var : {Γ A} → Var% Γ A → Tm Γ A)",
" (lam : {Γ A B} → Tm (cons% Γ A) B → Tm Γ (fun% A B))",
" (app : {Γ A B} → Tm Γ (fun% A B) → Tm Γ A → Tm Γ B)",
" → Tm Γ A",
"",
"var% : {Γ A} → Var% Γ A → Tm% Γ A",
" = λ x Tm var lam app. var x",
"",
"lam% : {Γ A B} → Tm% (cons% Γ A) B → Tm% Γ (fun% A B)",
" = λ t Tm var lam app. lam (t Tm var lam app)",
"",
"app% : {Γ A B} → Tm% Γ (fun% A B) → Tm% Γ A → Tm% Γ B",
" = λ t u Tm var lam app. app (t Tm var lam app) (u Tm var lam app)",
"",
"EvalTy% : Ty% → U",
" = λ A. A _ Bot% (λ A B. A → B)",
"",
"EvalCon% : Con% → U",
" = λ Γ. Γ _ Top% (λ Δ A. Pair% Δ (EvalTy% A))",
"",
"EvalVar% : {Γ A} → Var% Γ A → EvalCon% Γ → EvalTy% A",
" = λ x. x (λ Γ A. EvalCon% Γ → EvalTy% A)",
" (λ env. proj2% env)",
" (λ rec env. rec (proj1% env))",
"",
"EvalTm% : {Γ A} → Tm% Γ A → EvalCon% Γ → EvalTy% A",
" = λ t. t _",
" EvalVar%",
" (λ t env α. t (pair% env α))",
" (λ t u env. t env (u env))",
"",
"test% : Tm% nil% (fun% (fun% ι% ι%) (fun% ι% ι%))",
" = lam% (lam% (app% (var% (vs% vz%)) (app% (var% (vs% vz%))",
" (app% (var% (vs% vz%)) (app% (var% (vs% vz%))",
" (app% (var% (vs% vz%)) (app% (var% (vs% vz%)) (var% vz%))))))))"
]
smallttStlc :: Int -> String
smallttStlc = render [
"Ty% : U",
" = (Ty% : U)",
" (nat top bot : Ty%)",
" (arr prod sum : Ty% → Ty% → Ty%)",
" → Ty%",
"",
"nat% : Ty% = λ _ nat% _ _ _ _ _. nat%",
"top% : Ty% = λ _ _ top% _ _ _ _. top%",
"bot% : Ty% = λ _ _ _ bot% _ _ _. bot%",
"",
"arr% : Ty% → Ty% → Ty%",
" = λ A B Ty% nat% top% bot% arr% prod sum.",
" arr% (A Ty% nat% top% bot% arr% prod sum) (B Ty% nat% top% bot% arr% prod sum)",
"",
"prod% : Ty% → Ty% → Ty%",
" = λ A B Ty% nat% top% bot% arr% prod% sum.",
" prod% (A Ty% nat% top% bot% arr% prod% sum) (B Ty% nat% top% bot% arr% prod% sum)",
"",
"sum% : Ty% → Ty% → Ty%",
" = λ A B Ty% nat% top% bot% arr% prod% sum%.",
" sum% (A Ty% nat% top% bot% arr% prod% sum%) (B Ty% nat% top% bot% arr% prod% sum%)",
"",
"Con% : U",
" = (Con% : U)",
" (nil : Con%)",
" (snoc : Con% → Ty% → Con%)",
" → Con%",
"",
"nil% : Con%",
" = λ Con% nil% snoc. nil%",
"",
"snoc% : Con% → Ty% → Con%",
" = λ Γ A Con% nil% snoc%. snoc% (Γ Con% nil% snoc%) A",
"",
"Var% : Con% → Ty% → U",
" = λ Γ A.",
" (Var% : Con% → Ty% → U)",
" (vz : {Γ A} → Var% (snoc% Γ A) A)",
" (vs : {Γ B A} → Var% Γ A → Var% (snoc% Γ B) A)",
" → Var% Γ A",
"",
"vz% : {Γ A} → Var% (snoc% Γ A) A",
" = λ Var% vz% vs. vz%",
"",
"vs% : {Γ B A} → Var% Γ A → Var% (snoc% Γ B) A",
" = λ x Var% vz% vs%. vs% (x Var% vz% vs%)",
"",
"Tm% : Con% → Ty% → U",
" = λ Γ A.",
" (Tm% : Con% → Ty% → U)",
" (var : {Γ A} → Var% Γ A → Tm% Γ A)",
" (lam : {Γ A B} → Tm% (snoc% Γ A) B → Tm% Γ (arr% A B))",
" (app : {Γ A B} → Tm% Γ (arr% A B) → Tm% Γ A → Tm% Γ B)",
" (tt : {Γ} → Tm% Γ top%)",
" (pair : {Γ A B} → Tm% Γ A → Tm% Γ B → Tm% Γ (prod% A B))",
" (fst : {Γ A B} → Tm% Γ (prod% A B) → Tm% Γ A)",
" (snd : {Γ A B} → Tm% Γ (prod% A B) → Tm% Γ B)",
" (left : {Γ A B} → Tm% Γ A → Tm% Γ (sum% A B))",
" (right : {Γ A B} → Tm% Γ B → Tm% Γ (sum% A B))",
" (case : {Γ A B C} → Tm% Γ (sum% A B) → Tm% Γ (arr% A C) → Tm% Γ (arr% B C) → Tm% Γ C)",
" (zero : {Γ} → Tm% Γ nat%)",
" (suc : {Γ} → Tm% Γ nat% → Tm% Γ nat%)",
" (rec : {Γ A} → Tm% Γ nat% → Tm% Γ (arr% nat% (arr% A A)) → Tm% Γ A → Tm% Γ A)",
" → Tm% Γ A",
"",
"var% : {Γ A} → Var% Γ A → Tm% Γ A",
" = λ x Tm% var% lam app tt pair fst snd left right case zero suc rec.",
" var% x",
"",
"lam% : {Γ A B} → Tm% (snoc% Γ A) B → Tm% Γ (arr% A B)",
" = λ t Tm% var% lam% app tt pair fst snd left right case zero suc rec.",
" lam% (t Tm% var% lam% app tt pair fst snd left right case zero suc rec)",
"",
"app% : {Γ A B} → Tm% Γ (arr% A B) → Tm% Γ A → Tm% Γ B",
" = λ t u Tm% var% lam% app% tt pair fst snd left right case zero suc rec.",
" app% (t Tm% var% lam% app% tt pair fst snd left right case zero suc rec)",
" (u Tm% var% lam% app% tt pair fst snd left right case zero suc rec)",
"",
"tt% : {Γ} → Tm% Γ top%",
" = λ Tm% var% lam% app% tt% pair fst snd left right case zero suc rec. tt%",
"",
"pair% : {Γ A B} → Tm% Γ A → Tm% Γ B → Tm% Γ (prod% A B)",
" = λ t u Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec.",
" pair% (t Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec)",
" (u Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec)",
"",
"fst% : {Γ A B} → Tm% Γ (prod% A B) → Tm% Γ A",
" = λ t Tm% var% lam% app% tt% pair% fst% snd left right case zero suc rec.",
" fst% (t Tm% var% lam% app% tt% pair% fst% snd left right case zero suc rec)",
"",
"snd% : {Γ A B} → Tm% Γ (prod% A B) → Tm% Γ B",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left right case zero suc rec.",
" snd% (t Tm% var% lam% app% tt% pair% fst% snd% left right case zero suc rec)",
"",
"left% : {Γ A B} → Tm% Γ A → Tm% Γ (sum% A B)",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left% right case zero suc rec.",
" left% (t Tm% var% lam% app% tt% pair% fst% snd% left% right case zero suc rec)",
"",
"right% : {Γ A B} → Tm% Γ B → Tm% Γ (sum% A B)",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left% right% case zero suc rec.",
" right% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case zero suc rec)",
"",
"case% : {Γ A B C} → Tm% Γ (sum% A B) → Tm% Γ (arr% A C) → Tm% Γ (arr% B C) → Tm% Γ C",
" = λ t u v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec.",
" case% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
" (u Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
" (v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
"",
"zero% : {Γ} → Tm% Γ nat%",
" = λ Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc rec. zero%",
"",
"suc% : {Γ} → Tm% Γ nat% → Tm% Γ nat%",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec.",
" suc% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec)",
"",
"rec% : {Γ A} → Tm% Γ nat% → Tm% Γ (arr% nat% (arr% A A)) → Tm% Γ A → Tm% Γ A",
" = λ t u v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%.",
" rec% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
" (u Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
" (v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
"",
"v0% : {Γ A} → Tm% (snoc% Γ A) A",
" = var% vz%",
"",
"v1% : {Γ A B} → Tm% (snoc% (snoc% Γ A) B) A",
" = var% (vs% vz%)",
"",
"v2% : {Γ A B C} → Tm% (snoc% (snoc% (snoc% Γ A) B) C) A",
" = var% (vs% (vs% vz%))",
"",
"v3% : {Γ A B C D} → Tm% (snoc% (snoc% (snoc% (snoc% Γ A) B) C) D) A",
" = var% (vs% (vs% (vs% vz%)))",
"",
"tbool% : Ty%",
" = sum% top% top%",
"",
"true% : {Γ} → Tm% Γ tbool%",
" = left% tt%",
"",
"tfalse% : {Γ} → Tm% Γ tbool%",
" = right% tt%",
"",
"ifthenelse% : {Γ A} → Tm% Γ (arr% tbool% (arr% A (arr% A A)))",
" = lam% (lam% (lam% (case% v2% (lam% v2%) (lam% v1%))))",
"",
"times4% : {Γ A} → Tm% Γ (arr% (arr% A A) (arr% A A))",
" = lam% (lam% (app% v1% (app% v1% (app% v1% (app% v1% v0%)))))",
"",
"add% : {Γ} → Tm% Γ (arr% nat% (arr% nat% nat%))",
" = lam% (rec% v0%",
" (lam% (lam% (lam% (suc% (app% v1% v0%)))))",
" (lam% v0%))",
"",
"mul% : {Γ} → Tm% Γ (arr% nat% (arr% nat% nat%))",
" = lam% (rec% v0%",
" (lam% (lam% (lam% (app% (app% add% (app% v1% v0%)) v0%))))",
" (lam% zero%))",
"",
"fact% : {Γ} → Tm% Γ (arr% nat% nat%)",
" = lam% (rec% v0% (lam% (lam% (app% (app% mul% (suc% v1%)) v0%)))",
" (suc% zero%))"
]
leanStlc :: Int -> String
leanStlc = render [
"def Ty% : Type 1",
" := ∀ (Ty% : Type)",
" (nat top bot : Ty%)",
" (arr prod sum : Ty% → Ty% → Ty%)",
" , Ty%",
"",
"def nat% : Ty% := λ _ nat% _ _ _ _ _ => nat%",
"def top% : Ty% := λ _ _ top% _ _ _ _ => top%",
"def bot% : Ty% := λ _ _ _ bot% _ _ _ => bot%",
"",
"def arr% : Ty% → Ty% → Ty%",
" := λ A B Ty% nat% top% bot% arr% prod sum =>",
" arr% (A Ty% nat% top% bot% arr% prod sum) (B Ty% nat% top% bot% arr% prod sum)",
"",
"def prod% : Ty% → Ty% → Ty%",
" := λ A B Ty% nat% top% bot% arr% prod% sum =>",
" prod% (A Ty% nat% top% bot% arr% prod% sum) (B Ty% nat% top% bot% arr% prod% sum)",
"",
"def sum% : Ty% → Ty% → Ty%",
" := λ A B Ty% nat% top% bot% arr% prod% sum% =>",
" sum% (A Ty% nat% top% bot% arr% prod% sum%) (B Ty% nat% top% bot% arr% prod% sum%)",
"",
"def Con% : Type 1",
" := ∀ (Con% : Type)",
" (nil : Con%)",
" (snoc : Con% → Ty% → Con%)",
" , Con%",
"",
"def nil% : Con%",
" := λ Con% nil% snoc => nil%",
"",
"def snoc% : Con% → Ty% → Con%",
" := λ Γ A Con% nil% snoc% => snoc% (Γ Con% nil% snoc%) A",
"",
"def Var% : Con% → Ty% → Type 1",
" := λ Γ A =>",
" ∀ (Var% : Con% → Ty% → Type)",
" (vz : ∀{Γ A}, Var% (snoc% Γ A) A)",
" (vs : ∀{Γ B A}, Var% Γ A → Var% (snoc% Γ B) A)",
" , Var% Γ A",
"",
"def vz% : ∀ {Γ A}, Var% (snoc% Γ A) A",
" := λ Var% vz% vs => vz%",
"",
"def vs% : ∀ {Γ B A}, Var% Γ A → Var% (snoc% Γ B) A",
" := λ x Var% vz% vs% => vs% (x Var% vz% vs%)",
"",
"def Tm% : Con% → Ty% → Type 1",
" := λ Γ A =>",
" ∀ (Tm% : Con% → Ty% → Type)",
" (var : ∀ {Γ A}, Var% Γ A → Tm% Γ A)",
" (lam : ∀ {Γ A B}, (Tm% (snoc% Γ A) B → Tm% Γ (arr% A B)))",
" (app : ∀ {Γ A B} , Tm% Γ (arr% A B) → Tm% Γ A → Tm% Γ B)",
" (tt : ∀ {Γ} , Tm% Γ top%)",
" (pair : ∀ {Γ A B} , Tm% Γ A → Tm% Γ B → Tm% Γ (prod% A B))",
" (fst : ∀ {Γ A B} , Tm% Γ (prod% A B) → Tm% Γ A)",
" (snd : ∀ {Γ A B} , Tm% Γ (prod% A B) → Tm% Γ B)",
" (left : ∀ {Γ A B} , Tm% Γ A → Tm% Γ (sum% A B))",
" (right : ∀ {Γ A B} , Tm% Γ B → Tm% Γ (sum% A B))",
" (case : ∀ {Γ A B C} , Tm% Γ (sum% A B) → Tm% Γ (arr% A C) → Tm% Γ (arr% B C) → Tm% Γ C)",
" (zero : ∀ {Γ} , Tm% Γ nat%)",
" (suc : ∀ {Γ} , Tm% Γ nat% → Tm% Γ nat%)",
" (rec : ∀ {Γ A} , Tm% Γ nat% → Tm% Γ (arr% nat% (arr% A A)) → Tm% Γ A → Tm% Γ A)",
" , Tm% Γ A",
"",
"def var% : ∀ {Γ A}, Var% Γ A → Tm% Γ A",
" := λ x Tm% var% lam app tt pair fst snd left right case zero suc rec =>",
" var% x",
"",
"def lam% : ∀ {Γ A B} , Tm% (snoc% Γ A) B → Tm% Γ (arr% A B)",
" := λ t Tm% var% lam% app tt pair fst snd left right case zero suc rec =>",
" lam% (t Tm% var% lam% app tt pair fst snd left right case zero suc rec)",
"",
"def app% : ∀ {Γ A B} , Tm% Γ (arr% A B) → Tm% Γ A → Tm% Γ B",
" := λ t u Tm% var% lam% app% tt pair fst snd left right case zero suc rec =>",
" app% (t Tm% var% lam% app% tt pair fst snd left right case zero suc rec)",
" (u Tm% var% lam% app% tt pair fst snd left right case zero suc rec)",
"",
"def tt% : ∀ {Γ} , Tm% Γ top%",
" := λ Tm% var% lam% app% tt% pair fst snd left right case zero suc rec => tt%",
"",
"def pair% : ∀ {Γ A B} , Tm% Γ A → Tm% Γ B → Tm% Γ (prod% A B)",
" := λ t u Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec =>",
" pair% (t Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec)",
" (u Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec)",
"",
"def fst% : ∀ {Γ A B} , Tm% Γ (prod% A B) → Tm% Γ A",
" := λ t Tm% var% lam% app% tt% pair% fst% snd left right case zero suc rec =>",
" fst% (t Tm% var% lam% app% tt% pair% fst% snd left right case zero suc rec)",
"",
"def snd% : ∀ {Γ A B} , Tm% Γ (prod% A B) → Tm% Γ B",
" := λ t Tm% var% lam% app% tt% pair% fst% snd% left right case zero suc rec =>",
" snd% (t Tm% var% lam% app% tt% pair% fst% snd% left right case zero suc rec)",
"",
"def left% : ∀ {Γ A B} , Tm% Γ A → Tm% Γ (sum% A B)",
" := λ t Tm% var% lam% app% tt% pair% fst% snd% left% right case zero suc rec =>",
" left% (t Tm% var% lam% app% tt% pair% fst% snd% left% right case zero suc rec)",
"",
"def right% : ∀ {Γ A B} , Tm% Γ B → Tm% Γ (sum% A B)",
" := λ t Tm% var% lam% app% tt% pair% fst% snd% left% right% case zero suc rec =>",
" right% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case zero suc rec)",
"",
"def case% : ∀ {Γ A B C} , Tm% Γ (sum% A B) → Tm% Γ (arr% A C) → Tm% Γ (arr% B C) → Tm% Γ C",
" := λ t u v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec =>",
" case% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
" (u Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
" (v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
"",
"def zero% : ∀ {Γ} , Tm% Γ nat%",
" := λ Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc rec => zero%",
"",
"def suc% : ∀ {Γ} , Tm% Γ nat% → Tm% Γ nat%",
" := λ t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec =>",
" suc% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec)",
"",
"def rec% : ∀ {Γ A} , Tm% Γ nat% → Tm% Γ (arr% nat% (arr% A A)) → Tm% Γ A → Tm% Γ A",
" := λ t u v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec% =>",
" rec% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
" (u Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
" (v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
"",
"def v0% : ∀ {Γ A}, Tm% (snoc% Γ A) A",
" := var% vz%",
"",
"def v1% : ∀ {Γ A B}, Tm% (snoc% (snoc% Γ A) B) A",
" := var% (vs% vz%)",
"",
"def v2% : ∀ {Γ A B C}, Tm% (snoc% (snoc% (snoc% Γ A) B) C) A",
" := var% (vs% (vs% vz%))",
"",
"def v3% : ∀ {Γ A B C D}, Tm% (snoc% (snoc% (snoc% (snoc% Γ A) B) C) D) A",
" := var% (vs% (vs% (vs% vz%)))",
"",
"def tbool% : Ty%",
" := sum% top% top%",
"",
"def ttrue% : ∀ {Γ}, Tm% Γ tbool%",
" := left% tt%",
"",
"def tfalse% : ∀ {Γ}, Tm% Γ tbool%",
" := right% tt%",
"",
"def ifthenelse% : ∀ {Γ A}, Tm% Γ (arr% tbool% (arr% A (arr% A A)))",
" := lam% (lam% (lam% (case% v2% (lam% v2%) (lam% v1%))))",
"",
"def times4% : ∀ {Γ A}, Tm% Γ (arr% (arr% A A) (arr% A A))",
" := lam% (lam% (app% v1% (app% v1% (app% v1% (app% v1% v0%)))))",
"",
"def add% : ∀ {Γ}, Tm% Γ (arr% nat% (arr% nat% nat%))",
" := lam% (rec% v0%",
" (lam% (lam% (lam% (suc% (app% v1% v0%)))))",
" (lam% v0%))",
"",
"def mul% : ∀ {Γ}, Tm% Γ (arr% nat% (arr% nat% nat%))",
" := lam% (rec% v0%",
" (lam% (lam% (lam% (app% (app% add% (app% v1% v0%)) v0%))))",
" (lam% zero%))",
"",
"def fact% : ∀ {Γ}, Tm% Γ (arr% nat% nat%)",
" := lam% (rec% v0% (lam% (lam% (app% (app% mul% (suc% v1%)) v0%)))",
" (suc% zero%))"
]
agdaStlc :: Int -> String
agdaStlc = render [
"{-# OPTIONS --type-in-type #-}",
"",
"Ty% : Set",
"Ty% =",
" (Ty% : Set)",
" (nat top bot : Ty%)",
" (arr prod sum : Ty% → Ty% → Ty%)",
" → Ty%",
"",
"nat% : Ty%; nat% = λ _ nat% _ _ _ _ _ → nat%",
"top% : Ty%; top% = λ _ _ top% _ _ _ _ → top%",
"bot% : Ty%; bot% = λ _ _ _ bot% _ _ _ → bot%",
"",
"arr% : Ty% → Ty% → Ty%; arr%",
" = λ A B Ty% nat% top% bot% arr% prod sum →",
" arr% (A Ty% nat% top% bot% arr% prod sum) (B Ty% nat% top% bot% arr% prod sum)",
"",
"prod% : Ty% → Ty% → Ty%; prod%",
" = λ A B Ty% nat% top% bot% arr% prod% sum →",
" prod% (A Ty% nat% top% bot% arr% prod% sum) (B Ty% nat% top% bot% arr% prod% sum)",
"",
"sum% : Ty% → Ty% → Ty%; sum%",
" = λ A B Ty% nat% top% bot% arr% prod% sum% →",
" sum% (A Ty% nat% top% bot% arr% prod% sum%) (B Ty% nat% top% bot% arr% prod% sum%)",
"",
"Con% : Set; Con%",
" = (Con% : Set)",
" (nil : Con%)",
" (snoc : Con% → Ty% → Con%)",
" → Con%",
"",
"nil% : Con%; nil%",
" = λ Con% nil% snoc → nil%",
"",
"snoc% : Con% → Ty% → Con%; snoc%",
" = λ Γ A Con% nil% snoc% → snoc% (Γ Con% nil% snoc%) A",
"",
"Var% : Con% → Ty% → Set; Var%",
" = λ Γ A →",
" (Var% : Con% → Ty% → Set)",
" (vz : ∀{Γ A} → Var% (snoc% Γ A) A)",
" (vs : ∀{Γ B A} → Var% Γ A → Var% (snoc% Γ B) A)",
" → Var% Γ A",
"",
"vz% : ∀{Γ A} → Var% (snoc% Γ A) A; vz%",
" = λ Var% vz% vs → vz%",
"",
"vs% : ∀{Γ B A} → Var% Γ A → Var% (snoc% Γ B) A; vs%",
" = λ x Var% vz% vs% → vs% (x Var% vz% vs%)",
"",
"Tm% : Con% → Ty% → Set; Tm%",
" = λ Γ A →",
" (Tm% : Con% → Ty% → Set)",
" (var : ∀{Γ A} → Var% Γ A → Tm% Γ A)",
" (lam : ∀{Γ A B} → Tm% (snoc% Γ A) B → Tm% Γ (arr% A B))",
" (app : ∀{Γ A B} → Tm% Γ (arr% A B) → Tm% Γ A → Tm% Γ B)",
" (tt : ∀{Γ} → Tm% Γ top%)",
" (pair : ∀{Γ A B} → Tm% Γ A → Tm% Γ B → Tm% Γ (prod% A B))",
" (fst : ∀{Γ A B} → Tm% Γ (prod% A B) → Tm% Γ A)",
" (snd : ∀{Γ A B} → Tm% Γ (prod% A B) → Tm% Γ B)",
" (left : ∀{Γ A B} → Tm% Γ A → Tm% Γ (sum% A B))",
" (right : ∀{Γ A B} → Tm% Γ B → Tm% Γ (sum% A B))",
" (case : ∀{Γ A B C} → Tm% Γ (sum% A B) → Tm% Γ (arr% A C) → Tm% Γ (arr% B C) → Tm% Γ C)",
" (zero : ∀{Γ} → Tm% Γ nat%)",
" (suc : ∀{Γ} → Tm% Γ nat% → Tm% Γ nat%)",
" (rec : ∀{Γ A} → Tm% Γ nat% → Tm% Γ (arr% nat% (arr% A A)) → Tm% Γ A → Tm% Γ A)",
" → Tm% Γ A",
"",
"var% : ∀{Γ A} → Var% Γ A → Tm% Γ A; var%",
" = λ x Tm% var% lam app tt pair fst snd left right case zero suc rec →",
" var% x",
"",
"lam% : ∀{Γ A B} → Tm% (snoc% Γ A) B → Tm% Γ (arr% A B); lam%",
" = λ t Tm% var% lam% app tt pair fst snd left right case zero suc rec →",
" lam% (t Tm% var% lam% app tt pair fst snd left right case zero suc rec)",
"",
"app% : ∀{Γ A B} → Tm% Γ (arr% A B) → Tm% Γ A → Tm% Γ B; app%",
" = λ t u Tm% var% lam% app% tt pair fst snd left right case zero suc rec →",
" app% (t Tm% var% lam% app% tt pair fst snd left right case zero suc rec)",
" (u Tm% var% lam% app% tt pair fst snd left right case zero suc rec)",
"",
"tt% : ∀{Γ} → Tm% Γ top%; tt%",
" = λ Tm% var% lam% app% tt% pair fst snd left right case zero suc rec → tt%",
"",
"pair% : ∀{Γ A B} → Tm% Γ A → Tm% Γ B → Tm% Γ (prod% A B); pair%",
" = λ t u Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec →",
" pair% (t Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec)",
" (u Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec)",
"",
"fst% : ∀{Γ A B} → Tm% Γ (prod% A B) → Tm% Γ A; fst%",
" = λ t Tm% var% lam% app% tt% pair% fst% snd left right case zero suc rec →",
" fst% (t Tm% var% lam% app% tt% pair% fst% snd left right case zero suc rec)",
"",
"snd% : ∀{Γ A B} → Tm% Γ (prod% A B) → Tm% Γ B; snd%",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left right case zero suc rec →",
" snd% (t Tm% var% lam% app% tt% pair% fst% snd% left right case zero suc rec)",
"",
"left% : ∀{Γ A B} → Tm% Γ A → Tm% Γ (sum% A B); left%",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left% right case zero suc rec →",
" left% (t Tm% var% lam% app% tt% pair% fst% snd% left% right case zero suc rec)",
"",
"right% : ∀{Γ A B} → Tm% Γ B → Tm% Γ (sum% A B); right%",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left% right% case zero suc rec →",
" right% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case zero suc rec)",
"",
"case% : ∀{Γ A B C} → Tm% Γ (sum% A B) → Tm% Γ (arr% A C) → Tm% Γ (arr% B C) → Tm% Γ C; case%",
" = λ t u v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec →",
" case% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
" (u Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
" (v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
"",
"zero% : ∀{Γ} → Tm% Γ nat%; zero%",
" = λ Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc rec → zero%",
"",
"suc% : ∀{Γ} → Tm% Γ nat% → Tm% Γ nat%; suc%",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec →",
" suc% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec)",
"",
"rec% : ∀{Γ A} → Tm% Γ nat% → Tm% Γ (arr% nat% (arr% A A)) → Tm% Γ A → Tm% Γ A; rec%",
" = λ t u v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec% →",
" rec% (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
" (u Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
" (v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
"",
"v0% : ∀{Γ A} → Tm% (snoc% Γ A) A; v0%",
" = var% vz%",
"",
"v1% : ∀{Γ A B} → Tm% (snoc% (snoc% Γ A) B) A; v1%",
" = var% (vs% vz%)",
"",
"v2% : ∀{Γ A B C} → Tm% (snoc% (snoc% (snoc% Γ A) B) C) A; v2%",
" = var% (vs% (vs% vz%))",
"",
"v3% : ∀{Γ A B C D} → Tm% (snoc% (snoc% (snoc% (snoc% Γ A) B) C) D) A; v3%",
" = var% (vs% (vs% (vs% vz%)))",
"",
"tbool% : Ty%; tbool%",
" = sum% top% top%",
"",
"true% : ∀{Γ} → Tm% Γ tbool%; true%",
" = left% tt%",
"",
"tfalse% : ∀{Γ} → Tm% Γ tbool%; tfalse%",
" = right% tt%",
"",
"ifthenelse% : ∀{Γ A} → Tm% Γ (arr% tbool% (arr% A (arr% A A))); ifthenelse%",
" = lam% (lam% (lam% (case% v2% (lam% v2%) (lam% v1%))))",
"",
"times4% : ∀{Γ A} → Tm% Γ (arr% (arr% A A) (arr% A A)); times4%",
" = lam% (lam% (app% v1% (app% v1% (app% v1% (app% v1% v0%)))))",
"",
"add% : ∀{Γ} → Tm% Γ (arr% nat% (arr% nat% nat%)); add%",
" = lam% (rec% v0%",
" (lam% (lam% (lam% (suc% (app% v1% v0%)))))",
" (lam% v0%))",
"",
"mul% : ∀{Γ} → Tm% Γ (arr% nat% (arr% nat% nat%)); mul%",
" = lam% (rec% v0%",
" (lam% (lam% (lam% (app% (app% add% (app% v1% v0%)) v0%))))",
" (lam% zero%))",
"",
"fact% : ∀{Γ} → Tm% Γ (arr% nat% nat%); fact%",
" = lam% (rec% v0% (lam% (lam% (app% (app% mul% (suc% v1%)) v0%)))",
" (suc% zero%))"
]
smallttStlcLessImpl :: Int -> String
smallttStlcLessImpl = render [
"",
"Ty% : U",
" = (Ty% : U)",
" (nat top bot : Ty%)",
" (arr prod sum : Ty% → Ty% → Ty%)",
" → Ty%",
"",
"nat% : Ty% = λ _ nat% _ _ _ _ _. nat%",
"top% : Ty% = λ _ _ top% _ _ _ _. top%",
"bot% : Ty% = λ _ _ _ bot% _ _ _. bot%",
"",
"arr% : Ty% → Ty% → Ty%",
" = λ A B Ty% nat% top% bot% arr% prod sum.",
" arr% (A Ty% nat% top% bot% arr% prod sum) (B Ty% nat% top% bot% arr% prod sum)",
"",
"prod% : Ty% → Ty% → Ty%",
" = λ A B Ty% nat% top% bot% arr% prod% sum.",
" prod% (A Ty% nat% top% bot% arr% prod% sum) (B Ty% nat% top% bot% arr% prod% sum)",
"",
"sum% : Ty% → Ty% → Ty%",
" = λ A B Ty% nat% top% bot% arr% prod% sum%.",
" sum% (A Ty% nat% top% bot% arr% prod% sum%) (B Ty% nat% top% bot% arr% prod% sum%)",
"",
"Con% : U",
" = (Con% : U)",
" (nil : Con%)",
" (snoc : Con% → Ty% → Con%)",
" → Con%",
"",
"nil% : Con%",
" = λ Con% nil% snoc. nil%",
"",
"snoc% : Con% → Ty% → Con%",
" = λ Γ A Con% nil% snoc%. snoc% (Γ Con% nil% snoc%) A",
"",
"Var% : Con% → Ty% → U",
" = λ Γ A.",
" (Var% : Con% → Ty% → U)",
" (vz : (Γ : _)(A : _) → Var% (snoc% Γ A) A)",
" (vs : (Γ : _)(B A : _) → Var% Γ A → Var% (snoc% Γ B) A)",
" → Var% Γ A",
"",
"vz% : {Γ A} → Var% (snoc% Γ A) A",
" = λ Var% vz% vs. vz% _ _",
"",
"vs% : {Γ B A} → Var% Γ A → Var% (snoc% Γ B) A",
" = λ x Var% vz% vs%. vs% _ _ _ (x Var% vz% vs%)",
"",
"Tm% : Con% → Ty% → U",
" = λ Γ A.",
" (Tm% : Con% → Ty% → U)",
" (var : (Γ : _) (A : _) → Var% Γ A → Tm% Γ A)",
" (lam : (Γ : _) (A B : _) → Tm% (snoc% Γ A) B → Tm% Γ (arr% A B))",
" (app : (Γ : _) (A B : _) → Tm% Γ (arr% A B) → Tm% Γ A → Tm% Γ B)",
" (tt : (Γ : _) → Tm% Γ top%)",
" (pair : (Γ : _)(A B : _) → Tm% Γ A → Tm% Γ B → Tm% Γ (prod% A B))",
" (fst : (Γ : _)(A B : _) → Tm% Γ (prod% A B) → Tm% Γ A)",
" (snd : (Γ : _)(A B : _) → Tm% Γ (prod% A B) → Tm% Γ B)",
" (left : (Γ : _)(A B : _) → Tm% Γ A → Tm% Γ (sum% A B))",
" (right : (Γ : _)(A B : _) → Tm% Γ B → Tm% Γ (sum% A B))",
" (case : (Γ : _)(A B C : _) → Tm% Γ (sum% A B) → Tm% Γ (arr% A C) → Tm% Γ (arr% B C) → Tm% Γ C)",
" (zero : (Γ : _) → Tm% Γ nat%)",
" (suc : (Γ : _) → Tm% Γ nat% → Tm% Γ nat%)",
" (rec : (Γ : _)(A : _) → Tm% Γ nat% → Tm% Γ (arr% nat% (arr% A A)) → Tm% Γ A → Tm% Γ A)",
" → Tm% Γ A",
"",
"var% : {Γ A} → Var% Γ A → Tm% Γ A",
" = λ x Tm% var% lam app tt pair fst snd left right case zero suc rec.",
" var% _ _ x",
"",
"lam% : {Γ A B} → Tm% (snoc% Γ A) B → Tm% Γ (arr% A B)",
" = λ t Tm% var% lam% app tt pair fst snd left right case zero suc rec.",
" lam% _ _ _ (t Tm% var% lam% app tt pair fst snd left right case zero suc rec)",
"",
"app% : {Γ A B} → Tm% Γ (arr% A B) → Tm% Γ A → Tm% Γ B",
" = λ t u Tm% var% lam% app% tt pair fst snd left right case zero suc rec.",
" app% _ _ _ (t Tm% var% lam% app% tt pair fst snd left right case zero suc rec)",
" (u Tm% var% lam% app% tt pair fst snd left right case zero suc rec)",
"",
"tt% : {Γ} → Tm% Γ top%",
" = λ Tm% var% lam% app% tt% pair fst snd left right case zero suc rec. tt% _",
"",
"pair% : {Γ A B} → Tm% Γ A → Tm% Γ B → Tm% Γ (prod% A B)",
" = λ t u Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec.",
" pair% _ _ _ (t Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec)",
" (u Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec)",
"",
"fst% : {Γ A B} → Tm% Γ (prod% A B) → Tm% Γ A",
" = λ t Tm% var% lam% app% tt% pair% fst% snd left right case zero suc rec.",
" fst% _ _ _ (t Tm% var% lam% app% tt% pair% fst% snd left right case zero suc rec)",
"",
"snd% : {Γ A B} → Tm% Γ (prod% A B) → Tm% Γ B",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left right case zero suc rec.",
" snd% _ _ _ (t Tm% var% lam% app% tt% pair% fst% snd% left right case zero suc rec)",
"",
"left% : {Γ A B} → Tm% Γ A → Tm% Γ (sum% A B)",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left% right case zero suc rec.",
" left% _ _ _ (t Tm% var% lam% app% tt% pair% fst% snd% left% right case zero suc rec)",
"",
"right% : {Γ A B} → Tm% Γ B → Tm% Γ (sum% A B)",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left% right% case zero suc rec.",
" right% _ _ _ (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case zero suc rec)",
"",
"case% : {Γ A B C} → Tm% Γ (sum% A B) → Tm% Γ (arr% A C) → Tm% Γ (arr% B C) → Tm% Γ C",
" = λ t u v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec.",
" case% _ _ _ _",
" (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
" (u Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
" (v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero suc rec)",
"",
"zero% : {Γ} → Tm% Γ nat%",
" = λ Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc rec. zero% _",
"",
"suc% : {Γ} → Tm% Γ nat% → Tm% Γ nat%",
" = λ t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec.",
" suc% _ (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec)",
"",
"rec% : {Γ A} → Tm% Γ nat% → Tm% Γ (arr% nat% (arr% A A)) → Tm% Γ A → Tm% Γ A",
" = λ t u v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%.",
" rec% _ _",
" (t Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
" (u Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
" (v Tm% var% lam% app% tt% pair% fst% snd% left% right% case% zero% suc% rec%)",
"",
"v0% : {Γ A} → Tm% (snoc% Γ A) A",
" = var% vz%",
"",
"v1% : {Γ A B} → Tm% (snoc% (snoc% Γ A) B) A",
" = var% (vs% vz%)",
"",
"v2% : {Γ A B C} → Tm% (snoc% (snoc% (snoc% Γ A) B) C) A",
" = var% (vs% (vs% vz%))",
"",
"v3% : {Γ A B C D} → Tm% (snoc% (snoc% (snoc% (snoc% Γ A) B) C) D) A",
" = var% (vs% (vs% (vs% vz%)))",
"",
"tbool% : Ty%",
" = sum% top% top%",
"",
"true% : {Γ} → Tm% Γ tbool%",
" = left% tt%",
"",
"tfalse% : {Γ} → Tm% Γ tbool%",
" = right% tt%",
"",
"ifthenelse% : {Γ A} → Tm% Γ (arr% tbool% (arr% A (arr% A A)))",
" = lam% (lam% (lam% (case% v2% (lam% v2%) (lam% v1%))))",
"",
"times4% : {Γ A} → Tm% Γ (arr% (arr% A A) (arr% A A))",
" = lam% (lam% (app% v1% (app% v1% (app% v1% (app% v1% v0%)))))",
"",
"add% : {Γ} → Tm% Γ (arr% nat% (arr% nat% nat%))",
" = lam% (rec% v0%",
" (lam% (lam% (lam% (suc% (app% v1% v0%)))))",
" (lam% v0%))",
"",
"mul% : {Γ} → Tm% Γ (arr% nat% (arr% nat% nat%))",
" = lam% (rec% v0%",
" (lam% (lam% (lam% (app% (app% add% (app% v1% v0%)) v0%))))",
" (lam% zero%))",
"",
"fact% : {Γ} → Tm% Γ (arr% nat% nat%)",
" = lam% (rec% v0% (lam% (lam% (app% (app% mul% (suc% v1%)) v0%)))",
" (suc% zero%))"
]
leanStlcLessImpl = render [
"def Ty% : Type 1",
" := ∀ (Ty% : Type)",
" (nat top bot : Ty%)",
" (arr prod sum : Ty% → Ty% → Ty%)",
" , Ty%",
"",
"def nat% : Ty% := λ _ nat% _ _ _ _ _ => nat%",
"def top% : Ty% := λ _ _ top% _ _ _ _ => top%",
"def bot% : Ty% := λ _ _ _ bot% _ _ _ => bot%",
"",
"def arr% : Ty% → Ty% → Ty%",
" := λ A B Ty% nat% top% bot% arr% prod sum =>",
" arr% (A Ty% nat% top% bot% arr% prod sum) (B Ty% nat% top% bot% arr% prod sum)",
"",
"def prod% : Ty% → Ty% → Ty%",
" := λ A B Ty% nat% top% bot% arr% prod% sum =>",
" prod% (A Ty% nat% top% bot% arr% prod% sum) (B Ty% nat% top% bot% arr% prod% sum)",
"",
"def sum% : Ty% → Ty% → Ty%",
" := λ A B Ty% nat% top% bot% arr% prod% sum% =>",
" sum% (A Ty% nat% top% bot% arr% prod% sum%) (B Ty% nat% top% bot% arr% prod% sum%)",
"",
"def Con% : Type 1",
" := ∀ (Con% : Type)",
" (nil : Con%)",
" (snoc : Con% → Ty% → Con%)",
" , Con%",
"",
"def nil% : Con%",
" := λ Con% nil% snoc => nil%",
"",
"def snoc% : Con% → Ty% → Con%",
" := λ Γ A Con% nil% snoc% => snoc% (Γ Con% nil% snoc%) A",
"",
"def Var% : Con% → Ty% → Type 1",
" := λ Γ A =>",
" ∀ (Var% : Con% → Ty% → Type)",
" (vz : ∀ Γ A, Var% (snoc% Γ A) A)",
" (vs : ∀ Γ B A, Var% Γ A → Var% (snoc% Γ B) A)",
" , Var% Γ A",
"",
"def vz% : ∀ {Γ A}, Var% (snoc% Γ A) A",
" := λ Var% vz% vs => vz% _ _",
"",
"def vs% : ∀ {Γ B A}, Var% Γ A → Var% (snoc% Γ B) A",
" := λ x Var% vz% vs% => vs% _ _ _ (x Var% vz% vs%)",
"",
"def Tm% : Con% → Ty% → Type 1",
" := λ Γ A =>",
" ∀ (Tm% : Con% → Ty% → Type)",
" (var : ∀ Γ A , Var% Γ A → Tm% Γ A)",
" (lam : ∀ Γ A B , Tm% (snoc% Γ A) B → Tm% Γ (arr% A B))",
" (app : ∀ Γ A B , Tm% Γ (arr% A B) → Tm% Γ A → Tm% Γ B)",
" (tt : ∀ Γ , Tm% Γ top%)",
" (pair : ∀ Γ A B , Tm% Γ A → Tm% Γ B → Tm% Γ (prod% A B))",
" (fst : ∀ Γ A B , Tm% Γ (prod% A B) → Tm% Γ A)",
" (snd : ∀ Γ A B , Tm% Γ (prod% A B) → Tm% Γ B)",
" (left : ∀ Γ A B , Tm% Γ A → Tm% Γ (sum% A B))",
" (right : ∀ Γ A B , Tm% Γ B → Tm% Γ (sum% A B))",
" (case : ∀ Γ A B C , Tm% Γ (sum% A B) → Tm% Γ (arr% A C) → Tm% Γ (arr% B C) → Tm% Γ C)",
" (zero : ∀ Γ , Tm% Γ nat%)",
" (suc : ∀ Γ , Tm% Γ nat% → Tm% Γ nat%)",
" (rec : ∀ Γ A , Tm% Γ nat% → Tm% Γ (arr% nat% (arr% A A)) → Tm% Γ A → Tm% Γ A)",
" , Tm% Γ A",
"",
"def var% : ∀ {Γ A}, Var% Γ A → Tm% Γ A",
" := λ x Tm% var% lam app tt pair fst snd left right case zero suc rec =>",
" var% _ _ x",
"",
"def lam% : ∀ {Γ A B} , Tm% (snoc% Γ A) B → Tm% Γ (arr% A B)",
" := λ t Tm% var% lam% app tt pair fst snd left right case zero suc rec =>",
" lam% _ _ _ (t Tm% var% lam% app tt pair fst snd left right case zero suc rec)",
"",
"def app% : ∀ {Γ A B} , Tm% Γ (arr% A B) → Tm% Γ A → Tm% Γ B",
" := λ t u Tm% var% lam% app% tt pair fst snd left right case zero suc rec =>",
" app% _ _ _",
" (t Tm% var% lam% app% tt pair fst snd left right case zero suc rec)",
" (u Tm% var% lam% app% tt pair fst snd left right case zero suc rec)",
"",
"def tt% : ∀ {Γ} , Tm% Γ top%",
" := λ Tm% var% lam% app% tt% pair fst snd left right case zero suc rec => tt% _",
"",
"def pair% : ∀ {Γ A B} , Tm% Γ A → Tm% Γ B → Tm% Γ (prod% A B)",
" := λ t u Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec =>",
" pair% _ _ _",
" (t Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec)",
" (u Tm% var% lam% app% tt% pair% fst snd left right case zero suc rec)",
"",
"def fst% : ∀ {Γ A B} , Tm% Γ (prod% A B) → Tm% Γ A",
" := λ t Tm% var% lam% app% tt% pair% fst% snd left right case zero suc rec =>",
" fst% _ _ _",
" (t Tm% var% lam% app% tt% pair% fst% snd left right case zero suc rec)",
"",
"def snd% : ∀ {Γ A B} , Tm% Γ (prod% A B) → Tm% Γ B",