Agda-2.4.2.4: A dependently typed functional programming language and proof assistant

Agda.TypeChecking.With

Synopsis

Documentation

Arguments

 :: 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.

Arguments

 :: 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). @

Arguments

 :: 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.