Mercurial > hg > Members > atton > agda-proofs
view cbc/stack-subtype-sample.agda @ 60:bd428bd6b394
Trying define n-push/n-pop
author | atton <atton@cr.ie.u-ryukyu.ac.jp> |
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date | Sat, 14 Jan 2017 00:00:40 +0000 |
parents | ddcd652969e0 |
children | 7af6c894f411 |
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module stack-subtype-sample where open import Data.Nat open import Data.Maybe open import Relation.Binary.PropositionalEquality open import stack-subtype ℕ as S open import subtype Context as N open import subtype (Meta Context) as M record Num : Set where field num : ℕ instance NumIsNormalDataSegment : N.DataSegment Num NumIsNormalDataSegment = record { get = (\c -> record { num = Context.n c}) ; set = (\c n -> record c {n = Num.num n})} NumIsMetaDataSegment : M.DataSegment Num NumIsMetaDataSegment = record { get = (\m -> record {num = Context.n (Meta.context m)}) ; set = (\m n -> record m {context = record (Meta.context m) {n = Num.num n}})} plus3 : Num -> Num plus3 record { num = n } = record {num = n + 3} plus3CS : N.CodeSegment Num Num plus3CS = N.cs plus3 setNext : {X Y : Set} {{x : N.DataSegment X}} {{y : N.DataSegment Y}} -> (N.CodeSegment X Y) -> M.CodeSegment (Meta Context) (Meta Context) setNext c = M.cs (\mc -> record mc {nextCS = liftContext c}) setElement : ℕ -> M.CodeSegment (Meta Context) (Meta Context) setElement x = M.cs (\mc -> record mc {context = record (Meta.context mc) {element = just x}}) plus5AndPushWithPlus3 : {mc : Meta Context} {{_ : N.DataSegment Num}} -> M.CodeSegment Num (Meta Context) plus5AndPushWithPlus3 {mc} {{nn}} = M.cs (\n -> record {context = con n ; nextCS = (liftContext {{nn}} {{nn}} plus3CS) ; stack = st} ) where co = Meta.context mc con : Num -> Context con record { num = num } = N.DataSegment.set nn co record {num = num + 5} st = Meta.stack mc push-sample : {{_ : N.DataSegment Num}} {{_ : M.DataSegment Num}} -> Meta Context push-sample {{nd}} {{md}} = M.exec {{md}} (plus5AndPushWithPlus3 {mc} {{nd}}) mc where con = record { n = 4 ; element = just 0} code = N.cs (\c -> c) mc = record {context = con ; stack = emptySingleLinkedStack ; nextCS = code} push-sample-equiv : push-sample ≡ record { nextCS = liftContext plus3CS ; stack = record { top = nothing} ; context = record { n = 9} } push-sample-equiv = refl pushed-sample : {m : Meta Context} {{_ : N.DataSegment Num}} {{_ : M.DataSegment Num}} -> Meta Context pushed-sample {m} {{nd}} {{md}} = M.exec {{md}} (M.csComp {m} {{md}} pushSingleLinkedStackCS (plus5AndPushWithPlus3 {mc} {{nd}})) mc where con = record { n = 4 ; element = just 0} code = N.cs (\c -> c) mc = record {context = con ; stack = emptySingleLinkedStack ; nextCS = code} pushed-sample-equiv : {m : Meta Context} -> pushed-sample {m} ≡ record { nextCS = liftContext plus3CS ; stack = record { top = just (cons 0 nothing) } ; context = record { n = 12} } pushed-sample-equiv = refl n-push : {{_ : M.DataSegment (Meta Context)}} -> Meta Context -> Meta Context n-push m = M.csComp (pushSingleLinkedStackCS) (setElement ?)