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comparison Paper/src/agda-hoare-write.agda.replaced @ 5:339fb67b4375

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INIT rbt.agda
author soto <soto@cr.ie.u-ryukyu.ac.jp>
date Sun, 07 Nov 2021 00:51:16 +0900
parents c59202657321
children
comparison
equal deleted inserted replaced
4:72667e8198e2 5:339fb67b4375
1 -- Nomal CodeGear 1 -- Nomal CodeGear
2 whileLoop' : {l : Level} {t : Set l} @$\rightarrow$@ (n : @$\mathbb{N}$@) @$\rightarrow$@ (env : Envc) 2 whileLoop!$\prime$! : {l : Level} {t : Set l} !$\rightarrow$! (n : !$\mathbb{N}$!) !$\rightarrow$! (env : Envc)
3 @$\rightarrow$@ (n @$\equiv$@ varn env) 3 !$\rightarrow$! (n !$\equiv$! varn env)
4 @$\rightarrow$@ (next : Envc @$\rightarrow$@ t) 4 !$\rightarrow$! (next : Envc !$\rightarrow$! t)
5 @$\rightarrow$@ (exit : Envc @$\rightarrow$@ t) @$\rightarrow$@ t 5 !$\rightarrow$! (exit : Envc !$\rightarrow$! t) !$\rightarrow$! t
6 whileLoop' zero env refl _ exit = exit env 6 whileLoop!$\prime$! zero env refl _ exit = exit env
7 whileLoop' (suc n) env refl next _ = next (record env {varn = pred (varn env) ; vari = suc (vari env) }) 7 whileLoop!$\prime$! (suc n) env refl next _ = next (record env {varn = pred (varn env) ; vari = suc (vari env) })
8 8
9 -- Hoare Logic base CodeGear 9 -- Hoare Logic base CodeGear
10 whileLoopPwP' : {l : Level} {t : Set l} @$\rightarrow$@ (n : @$\mathbb{N}$@) @$\rightarrow$@ (env : Envc ) 10 whileLoopPwP!$\prime$! : {l : Level} {t : Set l} !$\rightarrow$! (n : !$\mathbb{N}$!) !$\rightarrow$! (env : Envc )
11 @$\rightarrow$@ (n @$\equiv$@ varn env) @$\rightarrow$@ (pre : varn env + vari env @$\equiv$@ c10 env) 11 !$\rightarrow$! (n !$\equiv$! varn env) !$\rightarrow$! (pre : varn env + vari env !$\equiv$! c10 env)
12 @$\rightarrow$@ (next : (env : Envc ) @$\rightarrow$@ (pred n @$\equiv$@ varn env) @$\rightarrow$@ (post : varn env + vari env @$\equiv$@ c10 env) @$\rightarrow$@ t) 12 !$\rightarrow$! (next : (env : Envc ) !$\rightarrow$! (pred n !$\equiv$! varn env) !$\rightarrow$! (post : varn env + vari env !$\equiv$! c10 env) !$\rightarrow$! t)
13 @$\rightarrow$@ (exit : (env : Envc ) @$\rightarrow$@ (fin : vari env @$\equiv$@ c10 env) @$\rightarrow$@ t) @$\rightarrow$@ t 13 !$\rightarrow$! (exit : (env : Envc ) !$\rightarrow$! (fin : vari env !$\equiv$! c10 env) !$\rightarrow$! t) !$\rightarrow$! t
14 whileLoopPwP' zero env refl refl next exit = exit env refl 14 whileLoopPwP!$\prime$! zero env refl refl next exit = exit env refl
15 whileLoopPwP' (suc n) env refl refl next exit = next (record env {varn = pred (varn env) ; vari = suc (vari env) }) refl (+-suc n (vari env)) 15 whileLoopPwP!$\prime$! (suc n) env refl refl next exit = next (record env {varn = pred (varn env) ; vari = suc (vari env) }) refl (+-suc n (vari env))