Proof Assistant Projects
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Digesting proof assistant libraries for AI ingestion. • 103 items • Updated • 3
Datasets:
statement stringlengths 1 4.12k | proof stringclasses 366
values | type stringclasses 1
value | symbolic_name stringlengths 1 50 | library stringclasses 66
values | filename stringclasses 591
values | imports listlengths 0 0 | deps listlengths 0 37 | docstring stringclasses 1
value | source_url stringclasses 1
value | commit stringclasses 1
value |
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absurd : type. | constant | absurd | examples/alloc-sem | examples/alloc-sem/absurdum.elf | [] | [] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
dynsem!step_preserves_wf
: st_wf S1 -> step S1 E1 S2 E2 -> st_wf S2 -> type. | constant | dynsem!step_preserves_wf | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"st_wf",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-lam_alloc : dynsem!step_preserves_wf DSWf (lam_alloc_step DStAlloc) DSWf'
<- st!alloc_preserves_wf DSWf DStAlloc DSWf'. | constant | -lam_alloc | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step_preserves_wf",
"lam_alloc_step",
"st!alloc_preserves_wf"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-app_ctxt1 : dynsem!step_preserves_wf DSWf (app_ctxt1_step DStep) DSWf'
<- dynsem!step_preserves_wf DSWf DStep DSWf'. | constant | -app_ctxt1 | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"app_ctxt1_step",
"dynsem!step_preserves_wf"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-app_ctxt2 : dynsem!step_preserves_wf DSWf (app_ctxt2_step DStep) DSWf'
<- dynsem!step_preserves_wf DSWf DStep DSWf'. | constant | -app_ctxt2 | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"app_ctxt2_step",
"dynsem!step_preserves_wf"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-app_beta : dynsem!step_preserves_wf DSWf (app_beta_step _) DSWf. | constant | -app_beta | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"app_beta_step",
"dynsem!step_preserves_wf"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-unit_alloc : dynsem!step_preserves_wf DSWf (unit_alloc_step DStAlloc) DSWf'
<- st!alloc_preserves_wf DSWf DStAlloc DSWf'. | constant | -unit_alloc | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step_preserves_wf",
"st!alloc_preserves_wf",
"unit_alloc_step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-letunit_ctxt : dynsem!step_preserves_wf DSWf (letunit_ctxt_step DStep) DSWf'
<- dynsem!step_preserves_wf DSWf DStep DSWf'. | constant | -letunit_ctxt | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step_preserves_wf",
"letunit_ctxt_step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-letunit_beta : dynsem!step_preserves_wf DSWf (letunit_beta_step _) DSWf. | constant | -letunit_beta | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step_preserves_wf",
"letunit_beta_step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-pair_ctxt1 : dynsem!step_preserves_wf DSWf (pair_ctxt1_step DStep) DSWf'
<- dynsem!step_preserves_wf DSWf DStep DSWf'. | constant | -pair_ctxt1 | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step_preserves_wf",
"pair_ctxt1_step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-pair_ctxt2 : dynsem!step_preserves_wf DSWf (pair_ctxt2_step DStep) DSWf'
<- dynsem!step_preserves_wf DSWf DStep DSWf'. | constant | -pair_ctxt2 | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step_preserves_wf",
"pair_ctxt2_step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-pair_alloc : dynsem!step_preserves_wf DSWf (pair_alloc_step DStAlloc) DSWf'
<- st!alloc_preserves_wf DSWf DStAlloc DSWf'. | constant | -pair_alloc | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step_preserves_wf",
"pair_alloc_step",
"st!alloc_preserves_wf"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-letpair_ctxt : dynsem!step_preserves_wf DSWf (letpair_ctxt_step DStep) DSWf'
<- dynsem!step_preserves_wf DSWf DStep DSWf'. | constant | -letpair_ctxt | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step_preserves_wf",
"letpair_ctxt_step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-letpair_beta : dynsem!step_preserves_wf DSWf (letpair_beta_step _) DSWf. | constant | -letpair_beta | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step_preserves_wf",
"letpair_beta_step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
dynsem!step*_preserves_wf
: st_wf S1 -> step* S1 E1 S2 E2 -> st_wf S2 -> type. | constant | dynsem!step*_preserves_wf | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"st_wf",
"step*"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-refl : dynsem!step*_preserves_wf DSWf (refl_step*) DSWf. | constant | -refl | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step*_preserves_wf",
"refl_step*"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-trans : dynsem!step*_preserves_wf DSWf1 (trans_step* DSteps23 DSteps12) DSWf3
<- dynsem!step*_preserves_wf DSWf1 DSteps12 DSWf2
<- dynsem!step*_preserves_wf DSWf2 DSteps23 DSWf3. | constant | -trans | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step*_preserves_wf",
"trans_step*"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-step : dynsem!step*_preserves_wf DSWf (step_step* DStep) DSWf'
<- dynsem!step_preserves_wf DSWf DStep DSWf'. | constant | -step | examples/alloc-sem | examples/alloc-sem/dynsem-lemmas.elf | [] | [
"dynsem!step*_preserves_wf",
"dynsem!step_preserves_wf",
"step_step*"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
step : st -> exp -> st -> exp -> type. | constant | step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"exp",
"st"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
lam_alloc_step : step S (lam_e Tx F) S' (loc_e L')
<- st_alloc S (lam_v Tx F) S' L'. | constant | lam_alloc_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"lam_e",
"lam_v",
"loc_e",
"st_alloc",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
app_ctxt1_step : step S (app_e E1 E2) S' (app_e E1' E2)
<- step S E1 S' E1'. | constant | app_ctxt1_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"app_e",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
app_ctxt2_step : step S (app_e (loc_e L1) E2) S' (app_e (loc_e L1) E2')
<- step S E2 S' E2'. | constant | app_ctxt2_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"app_e",
"loc_e",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
app_beta_step : step S (app_e (loc_e L1) (loc_e L2)) S (F1' (loc_e L2))
<- st_lookup S L1 (lam_v Tx F1'). | constant | app_beta_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"app_e",
"lam_v",
"loc_e",
"st_lookup",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
unit_alloc_step
: step S (unit_e) S' (loc_e L')
<- st_alloc S (unit_v) S' L'. | constant | unit_alloc_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"loc_e",
"st_alloc",
"step",
"unit_e",
"unit_v"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
letunit_ctxt_step
: step S (letunit_e E1 E2) S' (letunit_e E1' E2)
<- step S E1 S' E1'. | constant | letunit_ctxt_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"letunit_e",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
letunit_beta_step
: step S (letunit_e (loc_e L1) E2) S E2
<- st_lookup S L1 (unit_v). | constant | letunit_beta_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"letunit_e",
"loc_e",
"st_lookup",
"step",
"unit_v"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
pair_ctxt1_step
: step S (pair_e E1 E2) S' (pair_e E1' E2)
<- step S E1 S' E1'. | constant | pair_ctxt1_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"pair_e",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
pair_ctxt2_step
: step S (pair_e (loc_e L1) E2) S' (pair_e (loc_e L1) E2')
<- step S E2 S' E2'. | constant | pair_ctxt2_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"loc_e",
"pair_e",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
pair_alloc_step
: step S (pair_e (loc_e L1) (loc_e L2)) S' (loc_e L')
<- st_alloc S (pair_v L1 L2) S' L'. | constant | pair_alloc_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"loc_e",
"pair_e",
"pair_v",
"st_alloc",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
letpair_ctxt_step
: step S (letpair_e E1 F2) S' (letpair_e E1' F2)
<- step S E1 S' E1'. | constant | letpair_ctxt_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"letpair_e",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
letpair_beta_step
: step S (letpair_e (loc_e L1) F2) S (F2 (loc_e L11) (loc_e L12))
<- st_lookup S L1 (pair_v L11 L12). | constant | letpair_beta_step | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"letpair_e",
"loc_e",
"pair_v",
"st_lookup",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
step* : st -> exp -> st -> exp -> type. | constant | step* | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"exp",
"st"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
refl_step* : step* S E S E. | constant | refl_step* | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"step*"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
trans_step* : step* S1 E1 S3 E3
<- step* S1 E1 S2 E2
<- step* S2 E2 S3 E3. | constant | trans_step* | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"step*"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
step_step* : step* S1 E1 S2 E2
<- step S1 E1 S2 E2. | constant | step_step* | examples/alloc-sem | examples/alloc-sem/dynsem.elf | [] | [
"step",
"step*"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
loc_e : loc -> exp. | constant | loc_e | examples/alloc-sem | examples/alloc-sem/exp.elf | [] | [
"exp",
"loc"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
lam_e : tp -> (exp -> exp) -> exp. | constant | lam_e | examples/alloc-sem | examples/alloc-sem/exp.elf | [] | [
"exp",
"tp"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
app_e : exp -> exp -> exp. | constant | app_e | examples/alloc-sem | examples/alloc-sem/exp.elf | [] | [
"exp"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
unit_e : exp. | constant | unit_e | examples/alloc-sem | examples/alloc-sem/exp.elf | [] | [
"exp"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
letunit_e : exp -> exp -> exp. | constant | letunit_e | examples/alloc-sem | examples/alloc-sem/exp.elf | [] | [
"exp"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
pair_e : exp -> exp -> exp. | constant | pair_e | examples/alloc-sem | examples/alloc-sem/exp.elf | [] | [
"exp"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
letpair_e : exp -> (exp -> exp -> exp) -> exp. | constant | letpair_e | examples/alloc-sem | examples/alloc-sem/exp.elf | [] | [
"exp"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
exp_irred : exp -> type. | constant | exp_irred | examples/alloc-sem | examples/alloc-sem/exp.elf | [] | [
"exp"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
exp_irred_loc : exp_irred (loc_e _). | constant | exp_irred_loc | examples/alloc-sem | examples/alloc-sem/exp.elf | [] | [
"exp_irred",
"loc_e"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
pres_|-st_inversion_aux
: sttp_wf ST -> st_wf S -> |-st S ST ->
sttp_lookup ST L T ->
st_lookup S L V
-> |-val ST V T -> type. | constant | pres_|-st_inversion_aux | examples/alloc-sem | examples/alloc-sem/inversion-pres.elf | [] | [
"st_lookup",
"st_wf",
"sttp_lookup",
"sttp_wf",
"|-st",
"|-val"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-hit_hit : pres_|-st_inversion_aux DSTWf DSWf (|-st_cons DValTc' _)
(sttp_lookup_hit)
(st_lookup_hit)
DValTc
<- sttp!wf_cons_implies_extend_cons DSTWf DSttpExtend
<- sttp_weak_|-val DValTc' DSttpEx... | constant | -hit_hit | examples/alloc-sem | examples/alloc-sem/inversion-pres.elf | [] | [
"pres_|-st_inversion_aux",
"st_lookup_hit",
"sttp!wf_cons_implies_extend_cons",
"sttp_lookup_hit",
"sttp_weak_|-val",
"|-st_cons"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-miss_hit_contra
: pres_|-st_inversion_aux DSTWf DSWf (|-st_cons DValTc' _)
(sttp_lookup_miss DSttpLookup' DLocLt)
(st_lookup_hit)
DValTc
<- loc!lt_contradict DLocLt Absurd
<- raa_|-val Ab... | constant | -miss_hit_contra | examples/alloc-sem | examples/alloc-sem/inversion-pres.elf | [] | [
"loc!lt_contradict",
"pres_|-st_inversion_aux",
"raa_|-val",
"st_lookup_hit",
"sttp_lookup_miss",
"|-st_cons"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-miss_miss : pres_|-st_inversion_aux DSTWf DSWf (|-st_cons _ DStTc')
(sttp_lookup_miss DSttpLookup' _)
(st_lookup_miss DStLookup' DLocLt)
DValTc
<- sttp!wf_tail DSTWf DSTWf'
<- st!wf_ta... | constant | -miss_miss | examples/alloc-sem | examples/alloc-sem/inversion-pres.elf | [] | [
"pres_|-st_inversion_aux",
"st!wf_tail",
"st_lookup_miss",
"sttp!wf_cons_implies_extend_cons",
"sttp!wf_tail",
"sttp_lookup_miss",
"sttp_weak_|-val",
"|-st_cons"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-miss_miss_contra
: pres_|-st_inversion_aux _ _ (|-st_cons _ _)
(sttp_lookup_miss _ DLocLtB)
(st_lookup_miss _ DLocLtA)
DValTc
<- loc!lt_trans DLocLtA DLocLtB DLocLtC
<- loc!... | constant | -miss_miss_contra | examples/alloc-sem | examples/alloc-sem/inversion-pres.elf | [] | [
"loc!lt_contradict",
"loc!lt_trans",
"pres_|-st_inversion_aux",
"raa_|-val",
"st_lookup_miss",
"sttp_lookup_miss",
"|-st_cons"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-hit_miss_contra
: pres_|-st_inversion_aux DSTWf DSWf (|-st_cons DValTc' _)
(sttp_lookup_hit)
(st_lookup_miss DStLookup' DLocLt)
DValTc
<- loc!lt_contradict DLocLt Absurd
<- ... | constant | -hit_miss_contra | examples/alloc-sem | examples/alloc-sem/inversion-pres.elf | [] | [
"loc!lt_contradict",
"pres_|-st_inversion_aux",
"raa_|-val",
"st_lookup_miss",
"sttp_lookup_hit",
"|-st_cons"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
pres_|-st_inversion
: |-stwf S ST ->
sttp_lookup ST L T ->
st_lookup S L V
-> |-val ST V T -> type. | constant | pres_|-st_inversion | examples/alloc-sem | examples/alloc-sem/inversion-pres.elf | [] | [
"st_lookup",
"sttp_lookup",
"|-stwf",
"|-val"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
- : pres_|-st_inversion (|-stwf_ DSTWf DSWf DStTc)
DSttpLookup
DStLookup
DValTc
<- pres_|-st_inversion_aux DSTWf DSWf DStTc
DSttpLookup
... | constant | pres_|-st_inversion | examples/alloc-sem | examples/alloc-sem/inversion-pres.elf | [] | [
"pres_|-st_inversion",
"pres_|-st_inversion_aux",
"|-stwf_"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
prog_|-st_inversion_aux
: sttp_wf ST -> st_wf S -> |-st S ST ->
sttp_lookup ST L T
-> st_lookup S L V ->
|-val ST V T -> type. | constant | prog_|-st_inversion_aux | examples/alloc-sem | examples/alloc-sem/inversion-prog.elf | [] | [
"st_lookup",
"st_wf",
"sttp_lookup",
"sttp_wf",
"|-st",
"|-val"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-hit : prog_|-st_inversion_aux DSTWf DSWf (|-st_cons DValTc' _)
(sttp_lookup_hit)
(st_lookup_hit)
DValTc
<- sttp!wf_cons_implies_extend_cons DSTWf DSttpExtend
<- sttp_weak_|-val DValTc' DSttpEx... | constant | -hit | examples/alloc-sem | examples/alloc-sem/inversion-prog.elf | [] | [
"prog_|-st_inversion_aux",
"st_lookup_hit",
"sttp!wf_cons_implies_extend_cons",
"sttp_lookup_hit",
"sttp_weak_|-val",
"|-st_cons"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-miss : prog_|-st_inversion_aux DSTWf DSWf (|-st_cons _ DStTc')
(sttp_lookup_miss DSttpLookup' DLocLt)
(st_lookup_miss DStLookup' DLocLt)
DValTc
<- sttp!wf_tail DSTWf DSTWf'
<- st!... | constant | -miss | examples/alloc-sem | examples/alloc-sem/inversion-prog.elf | [] | [
"prog_|-st_inversion_aux",
"st!wf_tail",
"st_lookup_miss",
"sttp!wf_cons_implies_extend_cons",
"sttp!wf_tail",
"sttp_lookup_miss",
"sttp_weak_|-val",
"|-st_cons"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
prog_|-st_inversion
: |-stwf S ST ->
sttp_lookup ST L T
-> st_lookup S L V ->
|-val ST V T -> type. | constant | prog_|-st_inversion | examples/alloc-sem | examples/alloc-sem/inversion-prog.elf | [] | [
"st_lookup",
"sttp_lookup",
"|-stwf",
"|-val"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
- : prog_|-st_inversion (|-stwf_ DSTWf DSWf DStTc)
DSttpLookup
DStLookup
DValTc
<- prog_|-st_inversion_aux DSTWf DSWf DStTc
DSttpLookup
... | constant | prog_|-st_inversion | examples/alloc-sem | examples/alloc-sem/inversion-prog.elf | [] | [
"prog_|-st_inversion",
"prog_|-st_inversion_aux",
"|-stwf_"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
loc!lt_trans : loc_lt L1 L2 -> loc_lt L2 L3 -> loc_lt L1 L3 -> type. | constant | loc!lt_trans | examples/alloc-sem | examples/alloc-sem/loc-lemmas.elf | [] | [
"loc_lt"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
- : loc!lt_trans (loc_lt_ DNatLt12)
(loc_lt_ DNatLt23)
(loc_lt_ DNatLt13)
<- nat!lt_trans DNatLt12 DNatLt23 DNatLt13. | constant | loc!lt_trans | examples/alloc-sem | examples/alloc-sem/loc-lemmas.elf | [] | [
"loc!lt_trans",
"loc_lt_",
"nat!lt_trans"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
loc!lt_contradict
: loc_lt L L -> absurd -> type. | constant | loc!lt_contradict | examples/alloc-sem | examples/alloc-sem/loc-lemmas.elf | [] | [
"absurd",
"loc_lt"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
- : loc!lt_contradict (loc_lt_ DNatLt) Absurd
<- nat!lt_contradict DNatLt Absurd. | constant | loc!lt_contradict | examples/alloc-sem | examples/alloc-sem/loc-lemmas.elf | [] | [
"loc!lt_contradict",
"loc_lt_",
"nat!lt_contradict"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
mkLoc : nat -> loc. | constant | mkLoc | examples/alloc-sem | examples/alloc-sem/loc.elf | [] | [
"loc",
"nat"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
loc_lt : loc -> loc -> type. | constant | loc_lt | examples/alloc-sem | examples/alloc-sem/loc.elf | [] | [
"loc"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
loc_lt_ : loc_lt (mkLoc N1) (mkLoc N2)
<- nat_lt N1 N2. | constant | loc_lt_ | examples/alloc-sem | examples/alloc-sem/loc.elf | [] | [
"loc_lt",
"mkLoc",
"nat_lt"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
; : st -> exp -> mach. | constant | ; | examples/alloc-sem | examples/alloc-sem/machine.elf | [] | [
"exp",
"mach",
"st"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
mach_ok : st -> exp -> type. | constant | mach_ok | examples/alloc-sem | examples/alloc-sem/machine.elf | [] | [
"exp",
"st"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
mach_ok_irred : exp_irred E
-> mach_ok S E. | constant | mach_ok_irred | examples/alloc-sem | examples/alloc-sem/machine.elf | [] | [
"exp_irred",
"mach_ok"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
mach_ok_step : step S E S' E'
-> mach_ok S E. | constant | mach_ok_step | examples/alloc-sem | examples/alloc-sem/machine.elf | [] | [
"mach_ok",
"step"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
nat!N_lt_sN : {N:nat} nat_lt N (s_nat N) -> type. | constant | nat!N_lt_sN | examples/alloc-sem | examples/alloc-sem/nat-lemmas.elf | [] | [
"nat",
"nat_lt",
"s_nat"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-z : nat!N_lt_sN z_nat (nat_lt_z). | constant | -z | examples/alloc-sem | examples/alloc-sem/nat-lemmas.elf | [] | [
"nat!N_lt_sN",
"nat_lt_z",
"z_nat"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-s : nat!N_lt_sN (s_nat N) (nat_lt_s DNatLt)
<- nat!N_lt_sN N DNatLt. | constant | -s | examples/alloc-sem | examples/alloc-sem/nat-lemmas.elf | [] | [
"nat!N_lt_sN",
"nat_lt_s",
"s_nat"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
nat!lt_trans : nat_lt N1 N2 -> nat_lt N2 N3 -> nat_lt N1 N3 -> type. | constant | nat!lt_trans | examples/alloc-sem | examples/alloc-sem/nat-lemmas.elf | [] | [
"nat_lt"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-z : nat!lt_trans nat_lt_z _ nat_lt_z. | constant | -z | examples/alloc-sem | examples/alloc-sem/nat-lemmas.elf | [] | [
"nat!lt_trans",
"nat_lt_z"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-s : nat!lt_trans (nat_lt_s DNatLt12)
(nat_lt_s DNatLt23)
(nat_lt_s DNatLt13)
<- nat!lt_trans DNatLt12 DNatLt23 DNatLt13. | constant | -s | examples/alloc-sem | examples/alloc-sem/nat-lemmas.elf | [] | [
"nat!lt_trans",
"nat_lt_s"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
nat!lt_contradict
: nat_lt N N -> absurd -> type. | constant | nat!lt_contradict | examples/alloc-sem | examples/alloc-sem/nat-lemmas.elf | [] | [
"absurd",
"nat_lt"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-s : nat!lt_contradict (nat_lt_s DNatLt) Absurd
<- nat!lt_contradict DNatLt Absurd. | constant | -s | examples/alloc-sem | examples/alloc-sem/nat-lemmas.elf | [] | [
"nat!lt_contradict",
"nat_lt_s"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
nat : type. | constant | nat | examples/alloc-sem | examples/alloc-sem/nat.elf | [] | [] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
z_nat : nat. | constant | z_nat | examples/alloc-sem | examples/alloc-sem/nat.elf | [] | [
"nat"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
s_nat : nat -> nat. | constant | s_nat | examples/alloc-sem | examples/alloc-sem/nat.elf | [] | [
"nat"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
nat_lt : nat -> nat -> type. | constant | nat_lt | examples/alloc-sem | examples/alloc-sem/nat.elf | [] | [
"nat"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
nat_lt_z : nat_lt z_nat (s_nat _). | constant | nat_lt_z | examples/alloc-sem | examples/alloc-sem/nat.elf | [] | [
"nat_lt",
"s_nat",
"z_nat"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
nat_lt_s : nat_lt (s_nat N1) (s_nat N2)
<- nat_lt N1 N2. | constant | nat_lt_s | examples/alloc-sem | examples/alloc-sem/nat.elf | [] | [
"nat_lt",
"s_nat"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
pres_alloc : |-stwf S ST ->
|-val ST V T ->
st_alloc S V S' L'
-> sttp_extend ST ST' ->
|-stwf S' ST' ->
|-exp ST' (loc_e L') T -> type. | constant | pres_alloc | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"loc_e",
"st_alloc",
"sttp_extend",
"|-exp",
"|-stwf",
"|-val"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-nil : pres_alloc (|-stwf_ DSTWf DSWf
|-st_nil)
(DValTc : |-val _ _ T)
(st_alloc_nil)
DSttpExtend
(|-stwf_ DSTWf' DSWf'
(|-st_cons DValTc (|-st_nil))... | constant | -nil | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_alloc",
"st!alloc_preserves_wf",
"st_alloc_nil",
"sttp!alloc_implies_extend",
"sttp!alloc_preserves_wf",
"sttp_alloc_nil",
"sttp_lookup_hit",
"|-exp_loc",
"|-loc_",
"|-st_cons",
"|-st_nil",
"|-stwf_",
"|-val"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-cons : pres_alloc (|-stwf_ DSTWf DSWf
(|-st_cons DValTcX DStTc))
(DValTc : |-val _ _ T)
(st_alloc_cons)
DSttpExtend
(|-stwf_ DSTWf' DSWf'
(|-st_cons DValTc (|-st_co... | constant | -cons | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_alloc",
"st!alloc_preserves_wf",
"st_alloc_cons",
"sttp!alloc_implies_extend",
"sttp!alloc_preserves_wf",
"sttp_alloc_cons",
"sttp_lookup_hit",
"|-exp_loc",
"|-loc_",
"|-st_cons",
"|-stwf_",
"|-val"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
pres_var : ({z} |-var z Tz -> |-exp ST (F z) T) ->
|-exp ST E Tz
-> |-exp ST (F E) T -> type. | constant | pres_var | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"|-exp",
"|-var"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-refl : pres_var ([z][DVarTcZ] T) _ T. | constant | -refl | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_var"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-var : pres_var ([z][DVarTcZ] (|-exp_var DVarTcZ)) DExpTcZ DExpTcZ. | constant | -var | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_var",
"|-exp_var"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-loc : pres_var ([z][DVarTcZ] (|-exp_loc DLocTc)) _ (|-exp_loc DLocTc). | constant | -loc | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_var",
"|-exp_loc"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-lam : pres_var ([z][DVarTcZ] (|-exp_lam (DExpTcF z DVarTcZ)))
DExpTcZ
(|-exp_lam (DExpTcF'))
<- ({x}{DVarTcX: |-var x Tx}
pres_var ([z][DVarTcZ] (DExpTcF z DVarTcZ x DVarTcX))
DExpTcZ
... | constant | -lam | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_var",
"|-exp_lam",
"|-var"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-app : pres_var ([z][DVarTcZ] (|-exp_app (DExpTcE2 z DVarTcZ)
(DExpTcE1 z DVarTcZ)))
DExpTcZ
(|-exp_app DExpTcE2' DExpTcE1')
<- pres_var DExpTcE1 DExpTcZ DExpTcE1'
<- pres_var DExpTcE2 DExpTcZ DExpT... | constant | -app | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_var",
"|-exp_app"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-unit : pres_var ([z][DVarTcZ] (|-exp_unit)) _ (|-exp_unit). | constant | -unit | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_var",
"|-exp_unit"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-letunit : pres_var ([z][DVarTcZ] (|-exp_letunit (DExpTcE2 z DVarTcZ)
(DExpTcE1 z DVarTcZ)))
DExpTcZ
(|-exp_letunit DExpTcE2' DExpTcE1')
<- pres_var DExpTcE1 DExpTcZ DExpTcE1'
<- pres_var DExpTcE2 D... | constant | -letunit | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_var",
"|-exp_letunit"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-pair : pres_var ([z][DVarTcZ] (|-exp_pair (DExpTcE2 z DVarTcZ)
(DExpTcE1 z DVarTcZ)))
DExpTcZ
(|-exp_pair DExpTcE2' DExpTcE1')
<- pres_var DExpTcE1 DExpTcZ DExpTcE1'
<- pres_var DExpTcE2 DExpTcZ DE... | constant | -pair | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_var",
"|-exp_pair"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-letpair : pres_var ([z][DVarTcZ] (|-exp_letpair (DExpTcF2 z DVarTcZ)
(DExpTcE1 z DVarTcZ)))
DExpTcZ
(|-exp_letpair DExpTcF2' DExpTcE1')
<- pres_var DExpTcE1 DExpTcZ DExpTcE1'
<- ({x}{DVarTcX: |-var ... | constant | -letpair | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_var",
"|-exp_letpair",
"|-var"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
pres_|-val_lam_inversion
: |-val ST (lam_v Tx' F) (fn_t Tx T)
-> ({x:exp} |-var x Tx -> |-exp ST (F x) T) -> type. | constant | pres_|-val_lam_inversion | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"exp",
"fn_t",
"lam_v",
"|-exp",
"|-val",
"|-var"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
- : pres_|-val_lam_inversion (|-val_lam DExpTcF) DExpTcF. | constant | pres_|-val_lam_inversion | examples/alloc-sem | examples/alloc-sem/preservation-lemmas.elf | [] | [
"pres_|-val_lam_inversion",
"|-val_lam"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
pres : step S1 E1 S2 E2 ->
|-stwf S1 ST1 ->
|-exp ST1 E1 T
-> sttp_extend ST1 ST2 ->
|-stwf S2 ST2 ->
|-exp ST2 E2 T -> type. | constant | pres | examples/alloc-sem | examples/alloc-sem/preservation.elf | [] | [
"step",
"sttp_extend",
"|-exp",
"|-stwf"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-lam_alloc : pres (lam_alloc_step DStAlloc)
DStTcWf
(|-exp_lam DExpTcF)
DSttpExtend
DStTcWf'
DExpTcL
<- pres_alloc DStTcWf
(|-val_lam DExpTcF)
DStAlloc
... | constant | -lam_alloc | examples/alloc-sem | examples/alloc-sem/preservation.elf | [] | [
"lam_alloc_step",
"pres",
"pres_alloc",
"|-exp_lam",
"|-val_lam"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a | ||
-app_ctxt1 : pres (app_ctxt1_step DStep)
DStTcWf
(|-exp_app DExpTcE2 DExpTcE1)
DSttpExtend
DStTcWf'
(|-exp_app DExpTcE2' DExpTcE1')
<- pres DStep
DStTcWf
... | constant | -app_ctxt1 | examples/alloc-sem | examples/alloc-sem/preservation.elf | [] | [
"app_ctxt1_step",
"pres",
"sttp_weak_|-exp",
"|-exp_app"
] | https://github.com/standardml/twelf | b72cc28cd61c1114a79dcbb32f04ac6202fb379a |
End of preview. Expand in Data Studio
Twelf
Twelf declarations, each row carrying the statement and, where present, the proof.
Source
- Repository: https://github.com/standardml/twelf
- Commit:
b72cc28cd61c1114a79dcbb32f04ac6202fb379a - Files: 1004
- License: other
Schema
| Column | Type | Description |
|---|---|---|
| statement | string | Declaration signature/claim with the leading keyword removed (verbatim slice); the full declaration minus its proof |
| proof | string | Verbatim proof/body, empty if the declaration has none |
| type | string | Declaration keyword |
| symbolic_name | string | Declaration identifier |
| library | string | Sub-library |
| filename | string | Repository-relative source path |
| imports | list[string] | File-level Require/Import modules |
| deps | list[string] | Intra-corpus identifiers referenced |
| docstring | string | Preceding documentation comment, empty if absent |
| source_url | string | Upstream repository |
| commit | string | Upstream commit extracted |
Statistics
- Entries: 21,193
- With proof: 380 (1.8%)
- With docstring: 0 (0.0%)
- Libraries: 66
By type
| Type | Count |
|---|---|
| constant | 21,193 |
Example
_ : nd (A imp A)
= (impe
(impe
(impi
([u:nd (A imp (B imp A) imp A)]
impi
([v:nd (A imp B imp A)]
impi ([w:nd A] impe (impe u w) (impe v w)))))
(impi ([u:nd A] impi ([v:nd (B imp A)] u))))
(impi ([u:nd A] impi ([v:nd B] u)))).
- type: constant | symbolic_name:
_| examples/handbook/fol.elf
Use
Each declaration is split into a statement (signature/claim) and a proof (body) that are disjoint
and together form the complete declaration, for proof modeling, autoformalization, retrieval, and
dependency analysis via deps.
Citation
@misc{twelf_dataset,
title = {Twelf},
author = {Norton, Charles},
year = {2026},
note = {Extracted from https://github.com/standardml/twelf, commit b72cc28cd61c},
url = {https://huggingface.co/datasets/phanerozoic/Twelf}
}
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