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# TAPL5-3. 型無しラムダ計算(λ)

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\begin{array}{l|l}

\begin{array}{l}

\begin{array}{llr}
t ::= &         & 項：\\
& x             & 変数\\
& \lambda x.t   & ラムダ抽象\\
& t\;t          & 関数適用\\
v::= &          & 値：\\
& \lambda x.t   & ラムダ抽象値\\
\end{array}
\end{array}&

\begin{array}{cr}

\dfrac{t_1 \longrightarrow t_1’}
{t_1 \;t_2 \longrightarrow t_1’ \;t_2} & \text{(E-App1)} \\

\dfrac{t_2 \longrightarrow t_2’}
{v_1 \; t_2 \longrightarrow v_1 \; t_2’} & \text{(E-App2)}\\

(\lambda x.t_{12}) v_2 \longrightarrow [x \mapsto v_2]t_{12} & \text{(E-AppAbs)}\\
\\
\end{array}
\end{array}

tapl05_3.pl
:- op(500, yfx, $). :- op(920, xfx, [ ==>, ==>> ]). :- op(1200, xfx, [ -- ]). :- style_check(-singleton). term_expansion(A -- B, B :- A). /* 構文 t ::= 項： x 変数 x -> t ラムダ抽象 t$ t   関数適用
v::=      値：
x->t    ラムダ抽象値
*/

t(X) :- var(X).
t(X->T) :- var(X), t(T).
t(T1$T2) :- t(T1),t(T2). v(X->T) :- var(X), t(T). % 評価 t ==> t’ \+ v(T1), T1 ==> T1_ --%---------------------------------------- (E-App1) T1$ T2 ==> T1_ $T2. T2 ==> T2_ --%---------------------------------------- (E-App2) V1$ T2 ==> V1 $T2_. copy_term(X->T12, V2->T12_) --%---------------------------------------- (E-AppAbs) (X->T12)$ V2 ==> T12_.

T ==>> T3 :- T ==> T2, T2 ==>> T3.
T ==>> T.

run(T) :- T ==>> T2, writeln(T==>>T2).

:- run(X->X).
:- run((X->X) \$ (Y->Y)).
:- halt.


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