| Symbol | Specification | Kind | Type |
|---|
| # . | list-data | f | List('a) → Nat |
| # . | stream | f | Stream('a) → Natinf |
| . ! | remtau | f | ('a → Option('e)) → Stream('a) → Stream('e) |
| . ! | remtau | f | ('a → Option('e)) → List('a) → List('e) |
| . ' | list | f | 'a → List('a) |
| . + . | nat-basic | f | Nat × Nat → Nat |
| . + . | list-data | f | 'a × List('a) → List('a) |
| . + . | list | f | List('a) × List('a) → List('a) |
| . + . | list | f | List('a) × 'a → List('a) |
| . + . | nat-inf | f | Natinf × Natinf → Natinf |
| . + . | stream | f | 'a × Stream('a) → Stream('a) |
| . + . | stream | f | Stream('a) × Stream('a) → Stream('a) |
| . + . | stream | f | List('a) × (Nat → 'a) → Nat → 'a |
| . + . | remtau | f | Option('e) × Stream('e) → Stream('e) |
| . ++ . | list-dup | f | List('a) × 'a → List('a) |
| . +1 | nat-basic | f | Nat → Nat |
| . +2 . | list | f | 'a × 'a → List('a) |
| . - . | nat | pf | Nat × Nat → Nat with λ n, m. n ≥ m |
| . -1 | nat-basic | pf | Nat → Nat with λ n. n ≠ 0 |
| . -1l . | list-del | f | List('a) × 'a → List('a) |
| . -l . | list-del | f | List('a) × 'a → List('a) |
| . -p . | list-del | f | List('a) × Nat → List('a) |
| . .butlast | list-last | pf | List('a) → List('a) with λ x. x ≠ [] |
| . .distinct | list-dup | f | List('a) → List('a) |
| . .drop ( . ) | stream | f | (Nat → 'a) × Nat → Nat → 'a |
| . .drop ( . ) | list-del | pf | List('a) × Nat → List('a) with λ x, n. n ≤ # x |
| . .drop ( . ) | stream | pf | Stream('a) × Nat → Stream('a) with λ σ, n. finp(σ) → ⌜n⌝ < # σ ∨ ⌜n⌝ = # σ |
| . .dropRight ( . ) | list-last | pf | List('a) × Nat → List('a) with λ x, n. n ≤ # x |
| . .ext | IO-Aut-data | f | IOAutomaton('s, 'a, 'e) → 'a → Option('e) |
| . .f | stream-basic | pf | Stream('a) → Nat → 'a with λ σ. λ m. ∃ nf. σ = ⌜nf⌝ |
| . .foldLeft ( . ) | list | f | List('a) × 'b × ('b × 'a → 'b) → 'b |
| . .get | option | pf | Option('a) → 'a with λ opt. opt ≠ None |
| . .getOrElse ( . ) | option | f | Option('a) × 'a → 'a |
| . .head | list-data | pf | List('a) → 'a with λ x. x ≠ [] |
| . .indexOf ( . ) | list-del | f | List('a) × 'a → Nat |
| . .l | stream-basic | pf | Stream('a) → List('a) with λ σ. finp(σ) |
| . .last | list-last | pf | List('a) → 'a with λ x. x ≠ [] |
| . .map ( . ) | option | f | Option('a) × ('a → 'b) → Option('b) |
| . .map ( . ) | list | f | List('a) × ('a → 'b) → List('b) |
| . .n | nat-inf | pf | Natinf → Nat with λ n∞. n∞ ≠ ∞ |
| . .start | IO-Aut-data | f | IOAutomaton('s, 'a, 'e) → 's → Bool |
| . .step | IO-Aut-data | f | IOAutomaton('s, 'a, 'e) → 's × 'a × 's → Bool |
| . .sublist ( . ) | list-del | pf | List('a) × Nat × Nat → List('a) with λ x, n, m. n + m ≤ # x |
| . .tail | list-data | pf | List('a) → List('a) with λ x. x ≠ [] |
| . .take ( . ) | stream | f | (Nat → 'a) × Nat → List('a) |
| . .take ( . ) | list-del | pf | List('a) × Nat → List('a) with λ x, n. n ≤ # x |
| . .take ( . ) | stream | pf | Stream('a) × Nat → List('a) with λ σ, n. finp(σ) → ⌜n⌝ < # σ ∨ ⌜n⌝ = # σ |
| . .take ( . ) | stream | pf | Stream('a) × Natinf → Stream('a) with λ σ, n∞. finp(σ) → n∞ < # σ ∨ n∞ = # σ |
| . .takeRight ( . ) | list-del | pf | List('a) × Nat → List('a) with λ x, n. n ≤ # x |
| . < . | nat-basic | p | Nat × Nat |
| . < . | list-data | p | List('a) × List('a) |
| . < . | nat-inf | p | Natinf × Natinf |
| . > . | nat | p | Nat × Nat |
| . [ . := . ] | list-getput | pf | List('a) × Nat × 'a → List('a) with λ x, n, a. n < # x |
| . [ . := . ] | stream | pf | Stream('a) × Nat × 'a → Stream('a) with λ σ, n, a. finp(σ) → ⌜n⌝ < # σ |
| . [ . ] | list-getput | pf | List('a) × Nat → 'a with λ x, n. n < # x |
| . [ . ] | stream | pf | Stream('a) × Nat → 'a with λ σ, n. finp(σ) → ⌜n⌝ < # σ |
| . ∈ . | list | p | 'a × List('a) |
| . ≤ . | nat | p | Nat × Nat |
| . ≥ . | nat | p | Nat × Nat |
| . ⊑ . | list-last | p | List('a) × List('a) |
| . ⊑ . | stream | p | Stream('a) × Stream('a) |
| . ⊒ . | list-last | p | List('a) × List('a) |
| . o . | option | f | ('b → Option('c)) × ('a → Option('b)) → 'a → Option('c) |
| . o . | funops | f | ('a → 'b) × ('b → 'c) → 'a → 'c |
| [] | list-data | c | List('a) |
| [] | stream | c | Stream('a) |
| Π | product | f | ('ls → Bool) × ('rs → Bool) → ('ls, 'rs) → Bool |
| Π | product | f | ('ls × 'la × 'ls → Bool) × ('rs × 'ra × 'rs → Bool) × ('la → 'pa) × ('ra → 'pa) ×
('la → Option('e)) × ('ra → Option('e))
→ ('ls, 'rs) × 'pa × ('ls, 'rs) → Bool |
| Π | product | f | ('la → Option('e)) × ('ra → Option('e)) × ('la → 'pa) × ('ra → 'pa) → 'pa → Option('e) |
| Π | product | pf | IOAutomaton('ls, 'la, 'e) × IOAutomaton('rs, 'ra, 'e) × ('la → 'pa) × ('ra → 'pa)
→ IOAutomaton(('ls, 'rs), 'pa, 'e) with λ lioaut, rioaut, lren, rren. Πok(lioaut.ext, rioaut.ext, lren, rren) |
| Πh | product | f | ('la → Option('e)) × ('ra → Option('e)) × ('la → 'pa) × ('ra → 'pa) × ('e → Option('f))
→ 'pa → Option('f) |
| Πh | product | pf | IOAutomaton('ls, 'la, 'e) × IOAutomaton('rs, 'ra, 'e) × ('la → 'pa) × ('ra → 'pa) ×
('e → Option('f))
→ IOAutomaton(('ls, 'rs), 'pa, 'f) with λ lioaut, rioaut, lren, rren, hideext. Πhok(lioaut.ext, rioaut.ext, lren, rren, hideext) |
| Πhok | product | p | ('la → Option('e)) × ('ra → Option('e)) × ('la → 'pa) × ('ra → 'pa) × ('e → Option('f)) |
| Πok | product | p | ('la → Option('e)) × ('ra → Option('e)) × ('la → 'pa) × ('ra → 'pa) |
| β | product-refine | v | Stream('e) |
| πra | project-right | f | ('ls × 'la × 'ls → Bool) × ('rs × 'ra × 'rs → Bool) × ('la → 'pa) × ('ra → 'pa) ×
Stream(('ls, 'rs)) × Stream('pa)
→ Stream('ra) |
| πra | project-right | f | ('ls × 'la × 'ls → Bool) × ('rs × 'ra × 'rs → Bool) × ('la → 'pa) × ('ra → 'pa) ×
List(('ls, 'rs)) × List('pa)
→ List('ra) |
| πrs | project-right | f | ('ls × 'la × 'ls → Bool) × ('rs × 'ra × 'rs → Bool) × ('la → 'pa) × ('ra → 'pa) ×
Stream(('ls, 'rs)) × Stream('pa)
→ Stream('rs) |
| πrs | project-right | f | ('ls × 'la × 'ls → Bool) × ('rs × 'ra × 'rs → Bool) × ('la → 'pa) × ('ra → 'pa) ×
List(('ls, 'rs)) × List('pa)
→ List('rs) |
| ∞ | nat-inf | c | Natinf |
| ⌜ . ⌝ | stream-basic | f | List('a) → Stream('a) |
| ⌜ . ⌝ | stream-basic | f | (Nat → 'a) → Stream('a) |
| ⌜ . ⌝ | nat-inf | f | Nat → Natinf |
| C_≡*T_A | IOrefine-def | p | IOAutomaton('cs, 'ca, 'e) × IOAutomaton('as, 'aa, 'e) |
| C_≡ωT_A | IOrefine-def | p | IOAutomaton('cs, 'ca, 'e) × IOAutomaton('as, 'aa, 'e) |
| C_≡T_A | IOrefine-def | p | IOAutomaton('cs, 'ca, 'e) × IOAutomaton('as, 'aa, 'e) |
| C_≤*T_A | IOrefine-def | p | IOAutomaton('cs, 'ca, 'e) × IOAutomaton('as, 'aa, 'e) |
| C_≤ωT_A | IOrefine-def | p | IOAutomaton('cs, 'ca, 'e) × IOAutomaton('as, 'aa, 'e) |
| C_≤T_A | IOrefine-def | p | IOAutomaton('cs, 'ca, 'e) × IOAutomaton('as, 'aa, 'e) |
| IOAut | IO-Aut-data | f | ('s → Bool) × ('s × 'a × 's → Bool) × ('a → Option('e)) → IOAutomaton('s, 'a, 'e) |
| IOAut? | IO-Automaton | p | IOAutomaton('s, 'a, 'e) |
| IOAutomaton | IO-Aut-data | s | |
| List | list-data | s | |
| Nat | nat-basic | s | |
| Natinf | nat-inf | s | |
| None | option | c | Option('a) |
| Option | option | s | |
| Some | option | f | 'a → Option('a) |
| Stream | stream-basic | s | |
| a | product-refine | v | 'a |
| aα | product-refine | v | Stream('aa) |
| aσ | product-refine | v | Stream('as) |
| aa | product-refine | v | 'aa |
| aaf | product-refine | v | Nat → 'aa |
| aal | product-refine | v | List('aa) |
| aext | product-refine | v | 'aa → Option('e) |
| aren | product-refine | v | 'aa → 'pa |
| as | product-refine | v | 'as |
| asf | product-refine | v | Nat → 'as |
| asl | product-refine | v | List('as) |
| astart | product-refine | v | 'as → Bool |
| astep | product-refine | v | 'as × 'aa × 'as → Bool |
| cα | product-refine | v | Stream('ca) |
| cσ | product-refine | v | Stream('cs) |
| ca | product-refine | v | 'ca |
| caf | product-refine | v | Nat → 'ca |
| cal | product-refine | v | List('ca) |
| cext | product-refine | v | 'ca → Option('e) |
| cod | funops | f | ('a → 'b) → 'b → Bool |
| cont | contfun-lim | p | (Stream('a) → Stream('b)) |
| cont | contfun-lim | p | (Stream('s) × Stream('a) → Stream('b)) |
| cren | product-refine | v | 'ca → 'pa |
| cs | product-refine | v | 'cs |
| csf | product-refine | v | Nat → 'cs |
| csl | product-refine | v | List('cs) |
| cstart | product-refine | v | 'cs → Bool |
| cstep | product-refine | v | 'cs × 'ca × 'cs → Bool |
| disj | list-dup | p | List('a) × List('a) |
| dups | list-dup | p | List('a) |
| e | product-refine | v | 'e |
| el | product-refine | v | List('e) |
| exec | IOtrace | f | IOAutomaton('s, 'a, 'e) → Stream('s) × Stream('a) → Bool |
| exec* | IOtrace | f | IOAutomaton('s, 'a, 'e) → List('s) × List('a) → Bool |
| execω | IOtrace | f | IOAutomaton('s, 'a, 'e) → (Nat → 's) × (Nat → 'a) → Bool |
| ext | product-refine | v | 'a → Option('e) |
| fillfirst | list-last | f | Nat × 'a × List('a) → List('a) |
| finp | stream-basic | p | Stream('a) |
| frag | IOtrace | f | IOAutomaton('s, 'a, 'e) → Stream('s) × Stream('a) → Bool |
| frag* | IOtrace | f | IOAutomaton('s, 'a, 'e) → List('s) × List('a) → Bool |
| fragω | IOtrace | f | IOAutomaton('s, 'a, 'e) → (Nat → 's) × (Nat → 'a) → Bool |
| frome | list-del | f | List('a) × 'a → List('a) |
| fu | project-right | f | ('la → 'pa) × ('ra → 'pa) → 'pa → Option('pa) |
| hd | stream | pf | Stream('a) → 'a with λ σ. σ ≠ [] |
| hidingok | product | p | ('la → Option('e)) × ('ra → Option('e)) × ('la → 'pa) × ('ra → 'pa) × ('e → Option('f)) |
| inj | funops | p | ('a → 'b) |
| lift | contfun-lim | f | (List('a) → Bool) → Stream('a) → Bool |
| lift | contfun-lim | f | (List('s) × List('a) → Bool) → Stream('s) × Stream('a) → Bool |
| lift | product-refine | f | List('as) × 's → List(('s, 'as)) |
| lift | contfun-lim | pf | (List('a) → List('b)) → Stream('a) → Stream('b) with λ lf. λ α. mon(lf) |
| lift | contfun-lim | pf | (List('s) × List('a) → List('b)) → Stream('s) × Stream('a) → Stream('b) with λ trf. λ σ, α. mon(trf) |
| lifted | contfun-lim | f | (List('a) → Bool) → (List('a) → List('b)) × (Stream('a) → Stream('b)) → Bool |
| lifted | contfun-lim | f | (List('s) × List('a) → Bool)
→ (List('s) × List('a) → List('b)) × (Stream('s) × Stream('a) → Stream('b)) → Bool |
| lim | streamseq-mon-lim | pf | Stream(Stream('a)) → Stream('a) with λ σσ. mon(σσ) ∧ σσ ≠ [] |
| min | nat-inf | f | Natinf × Natinf → Natinf |
| mklist | list-last | f | 'a × Nat → List('a) |
| mon | streamseq-mon-lim | p | Stream(Stream('a)) |
| mon | contfun-lim | p | (Stream('a) → Stream('b)) |
| mon | contfun-lim | p | (Stream('s) × Stream('a) → Stream('b)) |
| mon | contfun-lim | p | (List('a) → List('b)) |
| mon | contfun-lim | p | (List('s) × List('a) → List('b)) |
| move | IOtrace | f | IOAutomaton('s, 'a, 'e) → 's × List('e) × 's → Bool |
| n | product-refine | v | Nat |
| nounsharedextR | product-refine | p | ('ca → 'pa) × ('ca → Option('e)) × ('a → 'pa) |
| oinj | option | p | ('a → Option('b)) |
| osurj | option | p | ('a → Option('b)) |
| pα | product-refine | v | Stream('pa) |
| pa | product-refine | v | 'pa |
| paσ | product-refine | v | Stream(('s, 'as)) |
| paf | product-refine | v | Nat → 'pa |
| pal | product-refine | v | List('pa) |
| pas | product-refine | v | ('s, 'as) |
| pasf | product-refine | v | Nat → ('s, 'as) |
| pasl | product-refine | v | List(('s, 'as)) |
| pastart | product-refine | v | ('s, 'as) → Bool |
| pastep | product-refine | v | ('s, 'as) × 'pa × ('s, 'as) → Bool |
| pbd | contfun-lim | p | (Stream('a) → Stream('b)) |
| pbd | contfun-lim | p | (Stream('s) × Stream('a) → Stream('b)) |
| pcσ | product-refine | v | Stream(('s, 'cs)) |
| pcont | contfun-lim | f | (Stream('a) → Bool) → (Stream('a) → Stream('b)) → Bool |
| pcont | contfun-lim | f | (Stream('s) × Stream('a) → Bool) → (Stream('s) × Stream('a) → Stream('b)) → Bool |
| pcs | product-refine | v | ('s, 'cs) |
| pcsf | product-refine | v | Nat → ('s, 'cs) |
| pcsl | product-refine | v | List(('s, 'cs)) |
| pcstart | product-refine | v | ('s, 'cs) → Bool |
| pcstep | product-refine | v | ('s, 'cs) × 'pa × ('s, 'cs) → Bool |
| pext | product-refine | v | 'pa → Option('e) |
| pfxclosed | contfun-lim | p | (Stream('a) → Bool) |
| pfxclosed | contfun-lim | p | (List('a) → Bool) |
| pfxclosed | contfun-lim | p | (Stream('s) × Stream('a) → Bool) |
| pfxclosed | contfun-lim | p | (List('s) × List('a) → Bool) |
| pmon | contfun-lim | f | (Stream('a) → Bool) → (Stream('a) → Stream('b)) → Bool |
| pmon | contfun-lim | f | (List('a) → Bool) → (List('a) → List('b)) → Bool |
| pmon | contfun-lim | f | (Stream('s) × Stream('a) → Bool) → (Stream('s) × Stream('a) → Stream('b)) → Bool |
| pmon | contfun-lim | f | (List('s) × List('a) → Bool) → (List('s) × List('a) → List('b)) → Bool |
| ppbd | contfun-lim | f | (Stream('a) → Bool) → (Stream('a) → Stream('b)) → Bool |
| ppbd | contfun-lim | f | (Stream('s) × Stream('a) → Bool) → (Stream('s) × Stream('a) → Stream('b)) → Bool |
| redext | product-refine | v | 'e → Option('f) |
| ren | product-refine | v | 'a → 'pa |
| repla | product-refine | f | ('s × 'a × 's → Bool) × ('cs × 'ca × 'cs → Bool) × ('ca → 'pa) × ('a → 'pa) × ('aa → 'pa) ×
('ca → Option('e)) × ('aa → Option('e)) × Stream(('s, 'cs)) × Stream('pa) × Stream('as) ×
Stream('aa)
→ Stream('pa) |
| repla | product-refine | f | ('s × 'a × 's → Bool) × ('cs × 'ca × 'cs → Bool) × ('ca → 'pa) × ('a → 'pa) × ('aa → 'pa) ×
('ca → Option('e)) × ('aa → Option('e)) × List(('s, 'cs)) × List('pa) × Stream('as) ×
Stream('aa)
→ List('pa) |
| repls | product-refine | f | ('s × 'a × 's → Bool) × ('cs × 'ca × 'cs → Bool) × ('ca → 'pa) × ('a → 'pa) × ('aa → 'pa) ×
('ca → Option('e)) × ('aa → Option('e)) × Stream(('s, 'cs)) × Stream('pa) × Stream('as) ×
Stream('aa)
→ Stream(('s, 'as)) |
| repls | product-refine | f | ('s × 'a × 's → Bool) × ('cs × 'ca × 'cs → Bool) × ('ca → 'pa) × ('a → 'pa) × ('aa → 'pa) ×
('ca → Option('e)) × ('aa → Option('e)) × List(('s, 'cs)) × List('pa) × Stream('as) ×
Stream('aa)
→ List(('s, 'as)) |
| rev | list-last | f | List('a) → List('a) |
| s | product-refine | v | 's |
| sameshared | product-refine | p | ('ca → 'pa) × ('aa → 'pa) × ('a → 'pa) |
| sharingok | product | p | ('la → Option('e)) × ('ra → Option('e)) × ('la → 'pa) × ('ra → 'pa) |
| start | product-refine | v | 's → Bool |
| step | product-refine | v | 's × 'a × 's → Bool |
| surj | funops | p | ('a → 'b) |
| surj | product | p | ('la → 'pa) × ('ra → 'pa) |
| tl | stream | pf | Stream('a) → Stream('a) with λ σ. σ ≠ [] |
| trace | IOtrace | f | IOAutomaton('s, 'a, 'e) → Stream('e) → Bool |
| trace* | IOtrace | f | IOAutomaton('s, 'a, 'e) → List('e) → Bool |
| traceω | IOtrace | f | IOAutomaton('s, 'a, 'e) → (Nat → 'e) → Bool |