Safe Haskell | None |
---|---|
Language | Haskell98 |
- withFunctionType :: Telescope -> [Term] -> [Type] -> Telescope -> Type -> TCM Type
- buildWithFunction :: QName -> Type -> [NamedArg Pattern] -> Permutation -> Nat -> Nat -> [SpineClause] -> TCM [SpineClause]
- stripWithClausePatterns :: QName -> Type -> [NamedArg Pattern] -> Permutation -> [NamedArg Pattern] -> TCM [NamedArg Pattern]
- withDisplayForm :: QName -> QName -> Telescope -> Telescope -> Nat -> [NamedArg Pattern] -> Permutation -> Permutation -> TCM DisplayForm
- patsToElims :: Permutation -> [NamedArg Pattern] -> [Elim' DisplayTerm]
Documentation
:: QName | Name of the with-function. |
-> Type | Types of the parent function. |
-> [NamedArg Pattern] | Parent patterns. |
-> Permutation | Final permutation. |
-> Nat | Number of needed vars. |
-> Nat | Number of with expressions. |
-> [SpineClause] | With-clauses. |
-> TCM [SpineClause] | With-clauses flattened wrt. parent patterns. |
Compute the clauses for the with-function given the original patterns.
stripWithClausePatterns Source
:: QName | f |
-> Type | t |
-> [NamedArg Pattern] | qs |
-> Permutation | π |
-> [NamedArg Pattern] | ps |
-> TCM [NamedArg Pattern] | ps' |
stripWithClausePatterns f t qs π ps = ps'
Δ
- context bound by lhs of original function (not an argument)
f
- name of with-function
t
- type of the original function
qs
- internal patterns for original function
π
- permutation taking vars(qs)
to support(Δ)
ps
- patterns in with clause (eliminating type t
)
ps'
- patterns for with function (presumably of type Δ
)
Example: @ record Stream (A : Set) : Set where coinductive constructor delay field force : A × Stream A
record SEq (s t : Stream A) : Set where coinductive field ~force : let a , as = force s b , bs = force t in a ≡ b × SEq as bs
test : (s : Nat × Stream Nat) (t : Stream Nat) → SEq (delay s) t → SEq t (delay s) ~force (test (a , as) t p) with force t ~force (test (suc n , as) t p) | b , bs = {!!}
With function:
f : (t : Stream Nat) (w : Nat × Stream Nat) (a : Nat) (as : Stream Nat) (p : SEq (delay (a , as)) t) → (fst w ≡ a) × SEq (snd w) as
Δ = t a as p -- reorder to bring with-relevant (= needed) vars first π = a as t p → Δ qs = (a , as) t p ~force ps = (suc n , as) t p ~force ps' = (suc n) as t p
Resulting with-function clause is:
f t (b , bs) (suc n) as t p
Note: stripWithClausePatterns factors ps through qs, thus
ps = qs[ps']
where [..] is to be understood as substitution. The projection patterns have vanished from ps' (as they are already in qs). @
:: QName | The name of parent function. |
-> QName | The name of the with-function. |
-> Telescope | The arguments of the with function before the with exprs. |
-> Telescope | The arguments of the with function after the with exprs. |
-> Nat | The number of with expressions. |
-> [NamedArg Pattern] | The parent patterns. |
-> Permutation | Permutation to split into needed and unneeded vars. |
-> Permutation | Permutation reordering the variables in parent patterns. |
-> TCM DisplayForm |
Construct the display form for a with function. It will display
applications of the with function as applications to the original function.
For instance, aux a b c
as f (suc a) (suc b) | c
n
is the number of with arguments.
patsToElims :: Permutation -> [NamedArg Pattern] -> [Elim' DisplayTerm] Source